* algebra/catdef.spad.pamphlet (DifferentialModule): Tidy.

	(DifferentialModuleExtension): Likewise.
	(PartialDifferentialModule): New.

10 files changed, 27215 insertions, 27146 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index 939bb682..06375070 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,9 @@
+2010-06-18  Gabriel Dos Reis  <gdr@cse.tamu.edu>
+
+	* algebra/catdef.spad.pamphlet (DifferentialModule): Tidy.
+	(DifferentialModuleExtension): Likewise.
+	(PartialDifferentialModule): New.
+
 2010-06-18  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
 	* algebra/fparfrac.spad.pamphlet (FullPartialFractionExpansion):
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index ebfc81c3..eeac7514 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -427,6 +427,10 @@ $(OUT)/BINDING.$(FASLEXT): $(OUT)/PROPERTY.$(FASLEXT)
 $(OUT)/OPERCAT.$(FASLEXT): $(OUT)/ARITY.$(FASLEXT)
 $(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/DIFRING.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
+$(OUT)/PDMOD.$(FASLEXT): $(OUT)/RING.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT) \
+	$(OUT)/COMRING.$(FASLEXT) $(OUT)/MODULE.$(FASLEXT)
+$(OUT)/DMEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT) $(OUT)/DIFFMOD.$(FASLEXT) \
+	$(OUT)/PDMOD.$(FASLEXT)
 
 axiom_algebra_layer_1 = \
   ABELGRP  ABELGRP- ABELMON  ABELMON- FORTCAT   ITUPLE   \
@@ -439,7 +443,7 @@ axiom_algebra_layer_1 = \
   OSGROUP  MAYBE    DATAARY  PROPLOG  HOMOTOP   BYTEORD  \
   FIELD    FIELD-   VECTCAT  VECTCAT- IARRAY1   BOOLE    \
   PROPERTY ARITY    OPERCAT  OPERCAT- PAIR               \
-  RADCAT   RADCAT-
+  RADCAT   RADCAT-  PDMOD    DMEXT
 
 axiom_algebra_layer_1_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_1))
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 29e74be9..811f7fbb 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -386,6 +386,10 @@ $(OUT)/BINDING.$(FASLEXT): $(OUT)/PROPERTY.$(FASLEXT)
 $(OUT)/OPERCAT.$(FASLEXT): $(OUT)/ARITY.$(FASLEXT)
 $(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/DIFRING.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
+$(OUT)/PDMOD.$(FASLEXT): $(OUT)/RING.$(FASLEXT) $(OUT)/PDSPC.$(FASLEXT) \
+	$(OUT)/COMRING.$(FASLEXT) $(OUT)/MODULE.$(FASLEXT)
+$(OUT)/DMEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT) $(OUT)/DIFFMOD.$(FASLEXT) \
+	$(OUT)/PDMOD.$(FASLEXT)
 
 axiom_algebra_layer_1 = \
   ABELGRP  ABELGRP- ABELMON  ABELMON- FORTCAT   ITUPLE   \
@@ -398,7 +402,7 @@ axiom_algebra_layer_1 = \
   OSGROUP  MAYBE    DATAARY  PROPLOG  HOMOTOP   BYTEORD  \
   FIELD    FIELD-   VECTCAT  VECTCAT- IARRAY1   BOOLE    \
   PROPERTY ARITY    OPERCAT  OPERCAT- PAIR               \
-  RADCAT   RADCAT-
+  RADCAT   RADCAT-  PDMOD    DMEXT
 
 axiom_algebra_layer_1_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_1))
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet
index 49ada95e..f5ecae65 100644
--- a/src/algebra/catdef.spad.pamphlet
+++ b/src/algebra/catdef.spad.pamphlet
@@ -495,8 +495,9 @@ DifferentialRing(): Category == Join(Ring,DifferentialSpace)
 ++   \spad{differentiate(x + y) = differentiate(x) + differentiate(x)}
 ++   \spad{differentiate(r*y) = r*differentiate(y) + differentiate(r)*y}
 
-DifferentialModule(R: CommutativeRing): Category ==
-  Join(Module R, DifferentialSpace)
+DifferentialModule(R: Ring): Category ==
+  Join(BiModule(R,R), DifferentialSpace) with
+    if R has CommutativeRing then Module R
 @
 
 
@@ -537,8 +538,11 @@ DifferentialExtension(R:Ring): Category ==
 ++ Description:
 ++   Category of modules that extend differential rings.
 ++
-DifferentialModuleExtension(R: CommutativeRing): Category ==
-  Join(Module(R),DifferentialSpaceExtension R)
+DifferentialModuleExtension(R: Ring): Category ==
+  Join(BiModule(R,R),DifferentialSpaceExtension R) with
+    if R has DifferentialSpace then DifferentialModule R
+    if R has PartialDifferentialSpace Symbol then
+      PartialDifferentialModule(R,Symbol)
 @
 
 
@@ -1544,8 +1548,6 @@ PartialDifferentialSpace(S: SetCategory): Category ==
 
 @
 
-
-
 \section{category PDRING PartialDifferentialRing}
 <<category PDRING PartialDifferentialRing>>=
 )abbrev category PDRING PartialDifferentialRing
@@ -1569,6 +1571,35 @@ PartialDifferentialRing(S:SetCategory): Category ==
   Join(Ring,PartialDifferentialSpace S)
 
 @
+
+\section{Partial Differential Module}
+
+<<category PDMOD PartialDifferentialModule>>=
+)abbrev category PDMOD PartialDifferentialModule
+++ Author: Gabriel Dos Reis
+++ Date Created: June 16, 2010
+++ Date Last Updated: June 18, 2010
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords:
+++ References:
+++ Description:
+++   A partial differential R-module with differentiations
+++   indexed by a parameter type S.
+++
+++ Axioms:
+++   \spad{differentiate(x+y,e) = differentiate(x,e)+differentiate(y,e)}
+++   \spad{differentiate(r*x,e) = r*differentiate(x,e) + differentiate(r,e)*x}
+++   \spad{differentiate(x*r,e) = x*differentiate(r,e) + differentiate(x,e)*r}
+
+PartialDifferentialModule(R: Ring,S: SetCategory): Category ==
+  Join(BiModule(R,R),PartialDifferentialSpace S) with
+     if R has CommutativeRing then Module R
+
+@
+
+
 \section{category PFECAT PolynomialFactorizationExplicit}
 <<category PFECAT PolynomialFactorizationExplicit>>=
 )abbrev category PFECAT PolynomialFactorizationExplicit
@@ -2031,6 +2062,7 @@ VectorSpace(S:Field): Category ==  Module(S) with
 <<category PDDOM PartialDifferentialDomain>>
 <<category PDSPC PartialDifferentialSpace>>
 <<category PDRING PartialDifferentialRing>>
+<<category PDMOD PartialDifferentialModule>>
 <<category DIFEXT DifferentialExtension>>
 <<category DSEXT DifferentialSpaceExtension>>
 @
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index 80bb4c66..ad128a63 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -736,6 +736,7 @@
   (|OutputByteConduit| . OUTBCON)
   (|PAdicIntegerCategory| . PADICCT)
   (|PartialDifferentialDomain| . PDDOM)
+  (|PartialDifferentialModule| . PDMOD)
   (|PartialDifferentialRing| . PDRING)
   (|PartialDifferentialSpace| . PDSPC)
   (|PartialTranscendentalFunctions| . PTRANFN)
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 826b5d14..244761b0 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2279591 . 3485856132)       
+(2279911 . 3485863922)       
 (-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."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
@@ -38,7 +38,7 @@ NIL
 NIL 
 (-27) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\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(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| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(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(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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(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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4457 . T) (-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4453 . T) (-4458 . T) (-4452 . T)) 
+((-4459 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,14 +56,14 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3027) 
+(-32 R -3003) 
 ((|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 -1055) (QUOTE (-575))))) 
+((|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) 
 (-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 -4460))) 
+((|HasAttribute| |#1| (QUOTE -4462))) 
 (-34) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
@@ -74,7 +74,7 @@ NIL
 NIL 
 (-36 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
 (-37 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
@@ -82,20 +82,20 @@ NIL
 NIL 
 (-38 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . 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 -3027 UP UPUP -1444) 
+(-40 -3003 UP UPUP -2703) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4453 |has| (-418 |#2|) (-373)) (-4458 |has| (-418 |#2|) (-373)) (-4452 |has| (-418 |#2|) (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
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-(-41 R -3027) 
+((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3739 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3739 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3739 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3739 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3739 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3739 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) 
+(-41 R -3003) 
 ((|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 (-463))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -441) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|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 (-316)))) 
+((|HasCategory| |#1| (QUOTE (-317)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-4457 |has| |#1| (-567)) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) 
+((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) 
+((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) 
 (-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."))) 
-((-4460 . T) (-4461 . T)) 
-((-3763 (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) 
+((-4462 . T) (-4463 . T)) 
+((-3739 (-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|))))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|))))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-373)))) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| $ (QUOTE (-1066))) (|HasCategory| $ (LIST (QUOTE -1055) (QUOTE (-575))))) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
 (-51 S) 
 ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3027) 
+(-54 |Base| R -3003) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,7 +158,7 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
 (-58 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
@@ -166,65 +166,65 @@ NIL
 NIL 
 (-59 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-61 -1777) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-61 -1811) 
 ((|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 -1777) 
+(-62 -1811) 
 ((|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 -1777) 
+(-63 -1811) 
 ((|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 -1777) 
+(-64 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-65 -1777) 
+(-65 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -1777) 
+(-66 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-67 -1777) 
+(-67 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-68 -1777) 
+(-68 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -1777) 
+(-69 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-70 -1777) 
+(-70 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-71 -1777) 
+(-71 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-72 -1777) 
+(-72 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-73 -1777) 
+(-73 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-74 -1777) 
+(-74 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
@@ -236,66 +236,66 @@ 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 -1777) 
+(-77 -1811) 
 ((|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 -1777) 
+(-78 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -1777) 
+(-79 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -1777) 
+(-80 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -1777) 
+(-81 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-82 -1777) 
+(-82 -1811) 
 ((|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 -1777) 
+(-83 -1811) 
 ((|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 -1777) 
+(-84 -1811) 
 ((|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 -1777) 
+(-85 -1811) 
 ((|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 -1777) 
+(-86 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -1777) 
+(-87 -1811) 
 ((|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 -1777) 
+(-88 -1811) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-89 -1777) 
+(-89 -1811) 
 ((|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 
 (-90 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 (-373)))) 
+((|HasCategory| |#1| (QUOTE (-374)))) 
 (-91 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -318,15 +318,15 @@ NIL
 NIL 
 (-97) 
 ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) 
-((-4460 . T)) 
+((-4462 . T)) 
 NIL 
 (-98) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) 
-((-4460 . T) ((-4462 "*") . T) (-4461 . T) (-4457 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4458 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4449 . T) (-4448 . T) (-4456 . T) (-4459 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4447 . T)) 
+((-4462 . T) ((-4464 "*") . T) (-4463 . T) (-4459 . T) (-4457 . T) (-4456 . T) (-4455 . T) (-4460 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4458 . T) (-4461 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4449 . T)) 
 NIL 
 (-99 R) 
 ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
 (-100 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -342,15 +342,15 @@ NIL
 NIL 
 (-103 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\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}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-104 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4462 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4464 "*")))) 
 (-105) 
 ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) 
-((-4460 . T)) 
+((-4462 . T)) 
 NIL 
 (-106 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
@@ -358,23 +358,23 @@ NIL
 NIL 
 (-107 S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
 (-108) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3739 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) 
 (-109) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
 NIL 
 (-110) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1117))) (|HasCategory| (-112) (LIST (QUOTE -318) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1117))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-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}"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
 (-112) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) 
@@ -392,22 +392,22 @@ NIL
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
 NIL 
 NIL 
-(-116 -3027 UP) 
+(-116 -3003 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 
 (-117 |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}."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-118 |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}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-117 |#1|) (QUOTE (-924))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-117 |#1|) (QUOTE (-1039))) (|HasCategory| (-117 |#1|) (QUOTE (-831))) (-3763 (|HasCategory| (-117 |#1|) (QUOTE (-831))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-1169))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-316))) (|HasCategory| (-117 |#1|) (QUOTE (-556))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-3739 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
 (-119 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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4461))) 
+((|HasAttribute| |#1| (QUOTE -4463))) 
 (-120 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 
@@ -418,15 +418,15 @@ NIL
 NIL 
 (-122 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"))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-123 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-124) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
 (-125 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -434,20 +434,20 @@ NIL
 NIL 
 (-126 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-128 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."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-129) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130)))))) (-3763 (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117)))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130)))))) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-3739 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) 
 (-130) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) 
 NIL 
@@ -470,13 +470,13 @@ NIL
 NIL 
 (-135) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4462 "*") . T)) 
+(((-4464 "*") . T)) 
 NIL 
-(-136 |minix| -2831 S T$) 
+(-136 |minix| -2809 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -2831 R) 
+(-137 |minix| -2809 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
@@ -498,8 +498,8 @@ NIL
 NIL 
 (-142) 
 ((|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}."))) 
-((-4460 . T) (-4450 . T) (-4461 . T)) 
-((-3763 (-12 (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) 
+((-4462 . T) (-4452 . T) (-4463 . T)) 
+((-3739 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) 
 (-143 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -514,7 +514,7 @@ NIL
 NIL 
 (-146) 
 ((|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."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
 (-147 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}."))) 
@@ -522,9 +522,9 @@ NIL
 NIL 
 (-148) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-149 -3027 UP UPUP) 
+(-149 -3003 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 
@@ -535,14 +535,14 @@ NIL
 (-151 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 -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasAttribute| |#1| (QUOTE -4460))) 
+((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasAttribute| |#1| (QUOTE -4462))) 
 (-152 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
 (-153 |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."))) 
-((-4455 . T) (-4454 . T) (-4457 . T)) 
+((-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
 (-154) 
 ((|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."))) 
@@ -564,7 +564,7 @@ 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 
-(-159 R -3027) 
+(-159 R -3003) 
 ((|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 
@@ -595,10 +595,10 @@ NIL
 (-166 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 (-924))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1220))) (|HasCategory| |#2| (QUOTE (-1077))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasAttribute| |#2| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-567)))) 
+((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1222))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) 
 (-167 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})"))) 
-((-4453 -3763 (|has| |#1| (-567)) (-12 (|has| |#1| (-316)) (|has| |#1| (-924)))) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4456 |has| |#1| (-6 -4456)) (-4459 |has| |#1| (-6 -4459)) (-3501 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 -3739 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-3477 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-168 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -614,8 +614,8 @@ NIL
 NIL 
 (-171 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-4453 -3763 (|has| |#1| (-567)) (-12 (|has| |#1| (-316)) (|has| |#1| (-924)))) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4456 |has| |#1| (-6 -4456)) (-4459 |has| |#1| (-6 -4459)) (-3501 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-359))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-3763 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-359)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-924))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-924)))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-924))))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1220)))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (QUOTE (-1077))) (-12 (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-1220)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasAttribute| |#1| (QUOTE -4459)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-359))))) 
+((-4455 -3739 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-3477 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3739 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1222)))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1222)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4461)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-360))))) 
 (-172 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -626,7 +626,7 @@ NIL
 NIL 
 (-174) 
 ((|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."))) 
-(((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-175) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -634,7 +634,7 @@ NIL
 NIL 
 (-176 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) 
-(((-4462 "*") . T) (-4453 . T) (-4458 . T) (-4452 . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-177) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -651,7 +651,7 @@ NIL
 (-180 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| (-967 |#2|) (LIST (QUOTE -898) (|devaluate| |#1|)))) 
+((|HasCategory| (-969 |#2|) (LIST (QUOTE -899) (|devaluate| |#1|)))) 
 (-181 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 
@@ -688,7 +688,7 @@ NIL
 ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-190 R -3027) 
+(-190 R -3003) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -796,23 +796,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-217 -3027 UP UPUP R) 
+(-217 -3003 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 
-(-218 -3027 FP) 
+(-218 -3003 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 
 (-219) 
 ((|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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3739 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) 
 (-220) 
 ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-221 R -3027) 
+(-221 R -3003) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -826,19 +826,19 @@ NIL
 NIL 
 (-224 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-225 |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}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-226 R -3027) 
+(-226 R -3003) 
 ((|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 
 (-227) 
 ((|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}."))) 
-((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-3468 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-228) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -846,19 +846,19 @@ NIL
 NIL 
 (-229 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}"))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
 (-230 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 
 (-231 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."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
 (-232 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
 (-233 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -870,7 +870,7 @@ NIL
 NIL 
 (-235 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
 (-236 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
@@ -882,36 +882,36 @@ NIL
 NIL 
 (-238) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
 (-239 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4460))) 
+((|HasAttribute| |#1| (QUOTE -4462))) 
 (-240 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}."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
 (-241) 
 ((|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 
-(-242 S -2831 R) 
+(-242 S -2809 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-804))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4457)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#3| (QUOTE (-737))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (QUOTE (-1117)))) 
-(-243 -2831 R) 
+((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4459)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (QUOTE (-1119)))) 
+(-243 -2809 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
-((-4454 |has| |#2| (-1066)) (-4455 |has| |#2| (-1066)) (-4457 |has| |#2| (-6 -4457)) (-4460 . T)) 
+((-4456 |has| |#2| (-1068)) (-4457 |has| |#2| (-1068)) (-4459 |has| |#2| (-6 -4459)) (-4462 . T)) 
 NIL 
-(-244 -2831 A B) 
+(-244 -2809 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-245 -2831 R) 
+(-245 -2809 R) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) 
-((-4454 |has| |#2| (-1066)) (-4455 |has| |#2| (-1066)) (-4457 |has| |#2| (-6 -4457)) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-378))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-737))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-804))) (|HasCategory| |#2| (LIST (QUOTE 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(LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE 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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 
@@ -922,7 +922,7 @@ NIL
 NIL 
 (-248) 
 ((|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}."))) 
-((-4453 . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 (-249 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."))) 
@@ -930,4263 +930,4271 @@ NIL
 NIL 
 (-250 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
 (-251 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
-(-252 |vl| R) 
+(-252 R) 
+((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
+((-4457 . T) (-4456 . T)) 
+NIL 
+(-253 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-253) 
+(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
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+(-254) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 
 NIL 
 NIL 
-(-254) 
+(-255) 
 ((|constructor| (NIL "This domain provides representations for domains constructors.")) (|functorData| (((|FunctorData|) $) "\\spad{functorData x} returns the functor data associated with the domain constructor \\spad{x}."))) 
 NIL 
 NIL 
-(-255) 
+(-256) 
 ((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
 NIL 
 NIL 
-(-256 |n| R M S) 
+(-257 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4457 -3763 (-3224 (|has| |#4| (-1066)) (|has| |#4| (-238))) (|has| |#4| (-6 -4457)) (-3224 (|has| |#4| (-1066)) (|has| |#4| (-913 (-1194))))) (-4454 |has| |#4| (-1066)) (-4455 |has| |#4| (-1066)) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-238))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-378))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-737))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-804))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-861))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST 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-(-258 A R S V E) 
+((-4459 -3739 (-3200 (|has| |#3| (-1068)) (|has| |#3| (-238))) (|has| |#3| (-6 -4459)) (-3200 (|has| |#3| (-1068)) (|has| |#3| (-915 (-1196))))) (-4456 |has| |#3| (-1068)) (-4457 |has| |#3| (-1068)) (-4462 . T)) 
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(QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))))) (|HasCategory| |#3| (QUOTE (-374))) (-3739 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1068)))) (-3739 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-805))) (-3739 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862)))) (|HasCategory| |#3| (QUOTE (-379))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576)))))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (-3739 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (|HasCategory| |#3| (QUOTE (-238))) (-3739 (|HasCategory| |#3| (QUOTE (-238))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068))))) (-3739 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1196)))))) (|HasCategory| |#3| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-21)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-238)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-374)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-379)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-738)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-805)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-862)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119))))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1068))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-862))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-3739 (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1196)))))) (-3739 (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068))))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-3739 (|HasCategory| |#3| (QUOTE (-1068))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119)))) (-3739 (|HasAttribute| |#3| (QUOTE -4459)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1196))))) (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) 
+(-259 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 (-238)))) 
-(-259 R S V E) 
+(-260 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."))) 
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+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-260 S) 
+(-261 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}."))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
-(-261) 
+(-262) 
 ((|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 
-(-262 R |Ex|) 
+(-263 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 
-(-263) 
+(-264) 
 ((|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*\\%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 
-(-264 R) 
+(-265 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 
-(-265 |Ex|) 
+(-266 |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 
-(-266) 
+(-267) 
 ((|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 
-(-267) 
+(-268) 
 ((|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 
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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 
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 ((|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}."))) 
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 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-237)))) 
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 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
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-(-272 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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+(-274 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
 NIL 
-(-274 S) 
+(-275 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| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#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 
-(-275) 
+(-276) 
 ((|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 
-(-276) 
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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 
-(-277) 
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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 
-(-280) 
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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 
-(-281) 
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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 
-(-282) 
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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 
-(-283) 
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 ((|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 
-(-284 R -3027) 
+(-285 R -3003) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-285 R -3027) 
+(-286 R -3003) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
-(-286 |Coef| UTS ULS) 
+(-287 |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 (-373)))) 
-(-287 |Coef| ULS UPXS EFULS) 
+((|HasCategory| |#1| (QUOTE (-374)))) 
+(-288 |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 (-373)))) 
-(-288) 
+((|HasCategory| |#1| (QUOTE (-374)))) 
+(-289) 
 ((|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| (|Identifier|) "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| (|Identifier|) "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| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) 
 NIL 
 NIL 
-(-289) 
+(-290) 
 ((|environment| (((|Environment|) $) "\\spad{environment(x)} returns the environment of the elaboration \\spad{x}.")) (|typeForm| (((|InternalTypeForm|) $) "\\spad{typeForm(x)} returns the type form of the elaboration \\spad{x}.")) (|irForm| (((|InternalRepresentationForm|) $) "\\spad{irForm(x)} returns the internal representation form of the elaboration \\spad{x}.")) (|elaboration| (($ (|InternalRepresentationForm|) (|InternalTypeForm|) (|Environment|)) "\\spad{elaboration(ir,ty,env)} construct an elaboration object for for the internal representation form \\spad{ir},{} with type \\spad{ty},{} and environment \\spad{env}."))) 
 NIL 
 NIL 
-(-290 A S) 
+(-291 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 (-861))) (|HasCategory| |#2| (QUOTE (-1117)))) 
-(-291 S) 
+((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) 
+(-292 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}."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
-(-292 S) 
+(-293 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-293) 
+(-294) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-294 |Coef| UTS) 
+(-295 |Coef| UTS) 
 ((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) 
 NIL 
 NIL 
-(-295 S T$) 
+(-296 S T$) 
 ((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. 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,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) 
 NIL 
 NIL 
-(-296 S |Dom| |Im|) 
+(-297 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 -4461))) 
-(-297 |Dom| |Im|) 
+((|HasAttribute| |#1| (QUOTE -4463))) 
+(-298 |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 
-(-298 S R |Mod| -1745 -4167 |exactQuo|) 
+(-299 S R |Mod| -1880 -3343 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-299) 
+(-300) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4453 . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-300) 
+(-301) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
 NIL 
 NIL 
-(-301 R) 
+(-302 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 
-(-302 S R) 
+(-303 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 
-(-303 S) 
+(-304 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."))) 
-((-4457 -3763 (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4454 |has| |#1| (-1066)) (-4455 |has| |#1| (-1066))) 
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-(-304 |Key| |Entry|) 
+((-4459 -3739 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4456 |has| |#1| (-1068)) (-4457 |has| |#1| (-1068))) 
+((|HasCategory| |#1| (QUOTE (-374))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-1068)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1068)))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1068)))) (-3739 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738)))) (|HasCategory| |#1| (QUOTE (-485))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1119)))) (-3739 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-312))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485)))) (-3739 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738)))) (-3739 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-738)))) 
+(-305 |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."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-305) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-306) 
 ((|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 
-(-306 -3027 S) 
+(-307 -3003 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 
-(-307 E -3027) 
+(-308 E -3003) 
 ((|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 
-(-308 A B) 
+(-309 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 
-(-309) 
+(-310) 
 ((|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 
-(-310 S) 
+(-311 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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 -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-1066)))) 
-(-311) 
+((|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1068)))) 
+(-312) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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 
-(-312 R1) 
+(-313 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 
-(-313 R1 R2) 
+(-314 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 
-(-314) 
+(-315) 
 ((|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 
-(-315 S) 
+(-316 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 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 
-(-316) 
+(-317) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-317 S R) 
+(-318 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 
-(-318 R) 
+(-319 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 
-(-319 -3027) 
+(-320 -3003) 
 ((|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 
-(-320) 
+(-321) 
 ((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) 
 NIL 
 NIL 
-(-321) 
+(-322) 
 ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) 
 NIL 
 NIL 
-(-322 R FE |var| |cen|) 
+(-323 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-924))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-1039))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (-3763 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-861)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-1169))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -318) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -295) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-316))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-556))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-924))) (|HasCategory| $ (QUOTE (-146)))) (-3763 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-924))) (|HasCategory| $ (QUOTE (-146)))))) 
-(-323 R S) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-1041))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-3739 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-862)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-1171))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-862))) (-12 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))) (-3739 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))))) 
+(-324 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 
-(-324 R FE) 
+(-325 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 
-(-325 R) 
+(-326 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-4457 -3763 (-12 (|has| |#1| (-567)) (-3763 (|has| |#1| (-1066)) (|has| |#1| (-484)))) (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) ((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) 
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-(-326 R -3027) 
+((-4459 -3739 (-12 (|has| |#1| (-568)) (-3739 (|has| |#1| (-1068)) (|has| |#1| (-485)))) (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) 
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+(-327 R -3003) 
 ((|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{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
 NIL 
-(-327) 
+(-328) 
 ((|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 
-(-328 FE |var| |cen|) 
+(-329 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."))) 
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-(-329 M) 
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+(-330 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 
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 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) 
-((-4455 . T) (-4454 . T)) 
-((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-803)))) 
-(-332 S E) 
+((-4457 . T) (-4456 . T)) 
+((|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-804)))) 
+(-333 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-782) (QUOTE (-803)))) 
-(-334 S R E) 
+((|HasCategory| (-783) (QUOTE (-804)))) 
+(-335 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-335 R E) 
+((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-336 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
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 ((|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."))) 
-((-4461 . T) (-4460 . T)) 
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-(-337 S -3027) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-338 S -3003) 
 ((|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 (-378)))) 
-(-338 -3027) 
+((|HasCategory| |#2| (QUOTE (-379)))) 
+(-339 -3003) 
 ((|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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-339) 
+(-340) 
 ((|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."))) 
 NIL 
 NIL 
-(-340 E) 
+(-341 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 
-(-341) 
+(-342) 
 ((|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 
-(-342) 
+(-343) 
 ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) 
 NIL 
 NIL 
-(-343 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+(-344 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 
-(-344 S -3027 UP UPUP R) 
+(-345 S -3003 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 
-(-345 -3027 UP UPUP R) 
+(-346 -3003 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 
-(-346 -3027 UP UPUP R) 
+(-347 -3003 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
-(-347 S R) 
+(-348 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -295) (|devaluate| |#2|) (|devaluate| |#2|)))) 
-(-348 R) 
+((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+(-349 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
-(-349 |basicSymbols| |subscriptedSymbols| R) 
+(-350 |basicSymbols| |subscriptedSymbols| R) 
 ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\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.}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#3| (LIST (QUOTE -1055) (QUOTE (-389)))) (|HasCategory| $ (QUOTE (-1066))) (|HasCategory| $ (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-350 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-351 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 
-(-351 S -3027 UP UPUP) 
+(-352 S -3003 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(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 (-378))) (|HasCategory| |#2| (QUOTE (-373)))) 
-(-352 -3027 UP UPUP) 
+((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-374)))) 
+(-353 -3003 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(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."))) 
-((-4453 |has| (-418 |#2|) (-373)) (-4458 |has| (-418 |#2|) (-373)) (-4452 |has| (-418 |#2|) (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-353 |p| |extdeg|) 
+(-354 |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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) 
-(-354 GF |defpol|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) 
+(-355 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-355 GF |extdeg|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-356 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-356 GF) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-357 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 
-(-357 F1 GF F2) 
+(-358 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 
-(-358 S) 
+(-359 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 
-(-359) 
+(-360) 
 ((|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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-360 R UP -3027) 
+(-361 R UP -3003) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-361 |p| |extdeg|) 
+(-362 |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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) 
-(-362 GF |uni|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) 
+(-363 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-363 GF |extdeg|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-364 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-364 |p| |n|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-365 |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}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) 
-(-365 GF |defpol|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) 
+(-366 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-366 -3027 GF) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-367 -3003 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 
-(-367 GF) 
+(-368 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 
-(-368 -3027 FP FPP) 
+(-369 -3003 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-369 GF |n|) 
+(-370 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}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-370 R |ls|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-371 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 
-(-371 S) 
+(-372 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-372 S) 
+(-373 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
 NIL 
 NIL 
-(-373) 
+(-374) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-374 |Name| S) 
+(-375 |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 
-(-375 S) 
+(-376 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 
-(-376 S R) 
+(-377 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{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{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 (-567)))) 
-(-377 R) 
+((|HasCategory| |#2| (QUOTE (-568)))) 
+(-378 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{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4457 |has| |#1| (-567)) (-4455 . T) (-4454 . T)) 
+((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) 
 NIL 
-(-378) 
+(-379) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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 
-(-379 S R UP) 
+(-380 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 (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-373)))) 
-(-380 R UP) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-374)))) 
+(-381 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-381 S A R B) 
+(-382 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-382 A S) 
+(-383 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117)))) 
-(-383 S) 
+((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) 
+(-384 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4460 . T)) 
+((-4462 . T)) 
 NIL 
-(-384 |VarSet| R) 
+(-385 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4455 . T) (-4454 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) 
 NIL 
-(-385 S V) 
+(-386 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 
-(-386 S R) 
+(-387 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 -650) (QUOTE (-575))))) 
-(-387 R) 
+((|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) 
+(-388 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 
 NIL 
-(-388 |Par|) 
+(-389 |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 
-(-389) 
+(-390) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4443 . T) (-4451 . T) (-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4445 . T) (-4453 . T) (-3468 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-390 |Par|) 
+(-391 |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 
-(-391 R S) 
+(-392 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}"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174)))) 
-(-392 R |Basis|) 
+(-393 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}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-393) 
+(-394) 
 ((|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}."))) 
 NIL 
 NIL 
-(-394) 
+(-395) 
 ((|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.}"))) 
 NIL 
 NIL 
-(-395 R S) 
+(-396 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."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174)))) 
-(-396 S) 
+(-397 S) 
 ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
 NIL 
-(-397 S) 
+(-398 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-861)))) 
-(-398) 
+((|HasCategory| |#1| (QUOTE (-862)))) 
+(-399) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-399) 
+(-400) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
 NIL 
-(-400) 
+(-401) 
 ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|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."))) 
 NIL 
 NIL 
-(-401 |n| |class| R) 
+(-402 |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"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-402) 
+(-403) 
 ((|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 
-(-403 -3027 UP UPUP R) 
+(-404 -3003 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 
-(-404 S) 
+(-405 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 
-(-405) 
+(-406) 
 ((|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."))) 
 NIL 
 NIL 
-(-406) 
+(-407) 
 ((|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."))) 
 NIL 
 NIL 
-(-407) 
+(-408) 
 ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-408) 
+(-409) 
 ((|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 
-(-409 -1777 |returnType| -4223 |symbols|) 
+(-410 -1811 |returnType| -4200 |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 
-(-410 -3027 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.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
+(-411 -3003 UP) 
+((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
-(-411 R) 
+(-412 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
 NIL 
 NIL 
-(-412 S) 
+(-413 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
 NIL 
 NIL 
-(-413) 
+(-414) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-414 S) 
+(-415 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4443)) (|HasAttribute| |#1| (QUOTE -4451))) 
-(-415) 
+((|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4453))) 
+(-416) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\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\"."))) 
-((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-3468 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-416 R S) 
+(-417 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
 NIL 
 NIL 
-(-417 A B) 
+(-418 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 
-(-418 S) 
+(-419 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\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."))) 
-((-4447 -12 (|has| |#1| (-6 -4458)) (|has| |#1| (-463)) (|has| |#1| (-6 -4447))) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-831))) (-3763 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-861)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-556))) (-12 (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-463)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-419 S R UP) 
+((-4449 -12 (|has| |#1| (-6 -4460)) (|has| |#1| (-464)) (|has| |#1| (-6 -4449))) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-3739 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-420 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 
-(-420 R UP) 
+(-421 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-421 A S) 
+(-422 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 -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-422 S) 
+((|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-423 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 
-(-423 R1 F1 U1 A1 R2 F2 U2 A2) 
+(-424 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 
-(-424 R -3027 UP A) 
+(-425 R -3003 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)}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-425 R -3027 UP A |ibasis|) 
+(-426 R -3003 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (LIST (QUOTE -1055) (|devaluate| |#2|)))) 
-(-426 AR R AS S) 
+((|HasCategory| |#4| (LIST (QUOTE -1057) (|devaluate| |#2|)))) 
+(-427 AR R AS S) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
 NIL 
-(-427 S R) 
+(-428 S R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is 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{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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-373)))) 
-(-428 R) 
+((|HasCategory| |#2| (QUOTE (-374)))) 
+(-429 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4457 |has| |#1| (-567)) (-4455 . T) (-4454 . T)) 
+((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) 
 NIL 
-(-429 R) 
-((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -318) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -295) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1239))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-1239)))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-463)))) 
 (-430 R) 
+((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1241))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1241)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) 
+(-431 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
 NIL 
 NIL 
-(-431 R FE |x| |cen|) 
+(-432 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 
-(-432 R A S B) 
+(-433 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 
-(-433 R FE |Expon| UPS TRAN |x|) 
+(-434 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| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) 
 NIL 
 NIL 
-(-434 S A R B) 
+(-435 S A R B) 
 ((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-435 A S) 
+(-436 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 (-861))) (|HasCategory| |#2| (QUOTE (-378)))) 
-(-436 S) 
+((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) 
+(-437 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4460 . T) (-4450 . T) (-4461 . T)) 
+((-4462 . T) (-4452 . T) (-4463 . T)) 
 NIL 
-(-437 R -3027) 
+(-438 R -3003) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
-(-438 R E) 
+(-439 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) 
-((-4447 -12 (|has| |#1| (-6 -4447)) (|has| |#2| (-6 -4447))) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#2| (QUOTE -4447)))) 
-(-439 R -3027) 
+((-4449 -12 (|has| |#1| (-6 -4449)) (|has| |#2| (-6 -4449))) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#2| (QUOTE -4449)))) 
+(-440 R -3003) 
 ((|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 
-(-440 S R) 
+(-441 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\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 -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-1129))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) 
-(-441 R) 
+((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) 
+(-442 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\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}."))) 
-((-4457 -3763 (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) ((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) 
+((-4459 -3739 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) 
 NIL 
-(-442 R -3027) 
+(-443 R -3003) 
 ((|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 
-(-443 R -3027) 
+(-444 R -3003) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for 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{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-444 R -3027) 
+(-445 R -3003) 
 ((|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 
-(-445) 
+(-446) 
 ((|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 
-(-446 R -3027 UP) 
+(-447 R -3003 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 -1055) (QUOTE (-48))))) 
-(-447) 
+((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-48))))) 
+(-448) 
 ((|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 
-(-448) 
+(-449) 
 ((|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| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|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| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
 NIL 
-(-449 |f|) 
+(-450 |f|) 
 ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-450) 
+(-451) 
 ((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) 
 NIL 
 NIL 
-(-451) 
+(-452) 
 ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|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}."))) 
 NIL 
 NIL 
-(-452) 
+(-453) 
 ((|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.}"))) 
 NIL 
 NIL 
-(-453 UP) 
+(-454 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 
-(-454 R UP -3027) 
+(-455 R UP -3003) 
 ((|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 
-(-455 R UP) 
+(-456 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 
-(-456 R) 
+(-457 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 (-415)))) 
-(-457) 
+((|HasCategory| |#1| (QUOTE (-416)))) 
+(-458) 
 ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(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(zi)} produces the complete factorization of the complex integer \\spad{zi}."))) 
 NIL 
 NIL 
-(-458 |Dom| |Expon| |VarSet| |Dpol|) 
+(-459 |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 
-(-459 |Dom| |Expon| |VarSet| |Dpol|) 
+(-460 |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 
-(-460 |Dom| |Expon| |VarSet| |Dpol|) 
+(-461 |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 
-(-461 |Dom| |Expon| |VarSet| |Dpol|) 
+(-462 |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 (-373)))) 
-(-462 S) 
+((|HasCategory| |#1| (QUOTE (-374)))) 
+(-463 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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-463) 
+(-464) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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}."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-464 R |n| |ls| |gamma|) 
+(-465 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) 
-((-4457 |has| (-418 (-967 |#1|)) (-567)) (-4455 . T) (-4454 . T)) 
-((|HasCategory| (-418 (-967 |#1|)) (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| (-418 (-967 |#1|)) (QUOTE (-567)))) 
-(-465 |vl| R E) 
+((-4459 |has| (-419 (-969 |#1|)) (-568)) (-4457 . T) (-4456 . T)) 
+((|HasCategory| (-419 (-969 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-969 |#1|)) (QUOTE (-568)))) 
+(-466 |vl| R E) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-466 R BP) 
+(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-926))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-467 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) 
 NIL 
 NIL 
-(-467 OV E S R P) 
+(-468 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 
-(-468 E OV R P) 
+(-469 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 
-(-469 R) 
+(-470 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 
-(-470 R FE) 
+(-471 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 
-(-471 RP TP) 
+(-472 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 
-(-472 |vl| R IS E |ff| P) 
+(-473 |vl| R IS E |ff| P) 
 ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-473 E V R P Q) 
+(-474 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
 NIL 
 NIL 
-(-474 R E |VarSet| P) 
+(-475 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-475 S R E) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-476 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 
-(-476 R E) 
+(-477 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 
-(-477) 
+(-478) 
 ((|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 
-(-478) 
+(-479) 
 ((|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 
-(-479) 
+(-480) 
 ((|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|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|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(gi,pt,pal)} modifies the graph \\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(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\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(gi,pt)} modifies the graph \\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(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\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(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\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{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\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{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|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.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\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 
-(-480 S R E) 
+(-481 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-481 R E) 
+(-482 R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-482 |lv| -3027 R) 
+(-483 |lv| -3003 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
-(-483 S) 
+(-484 S) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
 NIL 
 NIL 
-(-484) 
+(-485) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-485 |Coef| |var| |cen|) 
+(-486 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) 
-(-486 |Key| |Entry| |Tbl| |dent|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) 
+(-487 |Key| |Entry| |Tbl| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) 
-(-487 R E V P) 
+((-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119)))) 
+(-488 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-488) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-489) 
 ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-489) 
+(-490) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) 
 NIL 
 NIL 
-(-490 |Key| |Entry| |hashfn|) 
+(-491 |Key| |Entry| |hashfn|) 
 ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) 
-((-4460 . T) (-4461 . T)) 
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-(-491) 
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+(-492) 
 ((|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 
-(-492 |vl| R) 
+(-493 |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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 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\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| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
 NIL 
-(-495 S) 
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 ((|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}."))) 
-((-4460 . T) (-4461 . T)) 
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-(-496 -3027 UP UPUP R) 
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+(-497 -3003 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 
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 ((|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 
-(-498) 
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 ((|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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) 
-(-499 A S) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3739 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) 
+(-500 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-500 S) 
+((|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-501 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
 NIL 
-(-501 S) 
+(-502 S) 
 ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) 
 NIL 
 NIL 
-(-502) 
+(-503) 
 ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) 
 NIL 
 NIL 
-(-503 S) 
+(-504 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-504) 
+(-505) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-505 -3027 UP |AlExt| |AlPol|) 
+(-506 -3003 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
-(-506) 
+(-507) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| $ (QUOTE (-1066))) (|HasCategory| $ (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-507 S |mn|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-508 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-508 R |mnRow| |mnCol|) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-509 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\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."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-509 K R UP) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-510 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) 
 NIL 
 NIL 
-(-510 R UP -3027) 
+(-511 R UP -3003) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-511 |mn|) 
+(-512 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1117))) (|HasCategory| (-112) (LIST (QUOTE -318) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1117))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-512 K R UP L) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-513 K R UP L) 
 ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) 
 NIL 
 NIL 
-(-513) 
+(-514) 
 ((|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 
-(-514 R Q A B) 
+(-515 R Q A B) 
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
 NIL 
-(-515 -3027 |Expon| |VarSet| |DPoly|) 
+(-516 -3003 |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 -625) (QUOTE (-1194))))) 
-(-516 |vl| |nv|) 
+((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1196))))) 
+(-517 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
 NIL 
-(-517) 
+(-518) 
 ((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-518 A S) 
+(-519 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-519 A S) 
+(-520 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-520 A S) 
+(-521 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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-521 A S) 
+(-522 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-522 A S) 
+(-523 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-523 A S) 
+(-524 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) 
 NIL 
 NIL 
-(-524 S A B) 
+(-525 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|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 
-(-525 A B) 
+(-526 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 
-(-526 S E |un|) 
+(-527 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-803)))) 
-(-527 S |mn|) 
+((|HasCategory| |#2| (QUOTE (-804)))) 
+(-528 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}"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-528) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-529) 
 ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) 
 NIL 
 NIL 
-(-529 |p| |n|) 
+(-530 |p| |n|) 
 ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| (-592 |#1|) (QUOTE (-146))) (|HasCategory| (-592 |#1|) (QUOTE (-378)))) (|HasCategory| (-592 |#1|) (QUOTE (-148))) (|HasCategory| (-592 |#1|) (QUOTE (-378))) (|HasCategory| (-592 |#1|) (QUOTE (-146)))) 
-(-530 R |mnRow| |mnCol| |Row| |Col|) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((-3739 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) 
+(-531 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-531 S |mn|) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-532 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-532 R |Row| |Col| M) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-533 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\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 -4461))) 
-(-533 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasAttribute| |#3| (QUOTE -4463))) 
+(-534 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasAttribute| |#7| (QUOTE -4461))) 
-(-534 R |mnRow| |mnCol|) 
+((|HasAttribute| |#7| (QUOTE -4463))) 
+(-535 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-535) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-536) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
 NIL 
-(-536) 
+(-537) 
 ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) 
 NIL 
 NIL 
-(-537 S) 
+(-538 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\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,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-538) 
+(-539) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\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,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-539 GF) 
+(-540 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 
-(-540) 
+(-541) 
 ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{`f'}.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(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 
-(-541 R) 
+(-542 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 
-(-542 |Varset|) 
+(-543 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
 NIL 
-(-543 K -3027 |Par|) 
+(-544 K -3003 |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 
-(-544) 
+(-545) 
 NIL 
 NIL 
 NIL 
-(-545) 
+(-546) 
 ((|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 
-(-546 R) 
+(-547 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 
-(-547) 
+(-548) 
 ((|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 
-(-548 |Coef| UTS) 
+(-549 |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 
-(-549 K -3027 |Par|) 
+(-550 K -3003 |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 
-(-550 R BP |pMod| |nextMod|) 
+(-551 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 
-(-551 OV E R P) 
+(-552 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 
-(-552 K UP |Coef| UTS) 
+(-553 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 
-(-553 |Coef| UTS) 
+(-554 |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 
-(-554 R UP) 
+(-555 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-555 S) 
+(-556 S) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-556) 
+(-557) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
-((-4458 . T) (-4459 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-557) 
+(-558) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-558) 
+(-559) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-559) 
+(-560) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-560) 
+(-561) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-561 |Key| |Entry| |addDom|) 
+(-562 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-562 R -3027) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-563 R -3003) 
 ((|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 
-(-563 R0 -3027 UP UPUP R) 
+(-564 R0 -3003 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 
-(-564) 
+(-565) 
 ((|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 
-(-565 R) 
+(-566 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."))) 
-((-3493 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-3468 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-566 S) 
+(-567 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 
-(-567) 
+(-568) 
 ((|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."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-568 R -3027) 
+(-569 R -3003) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-569 I) 
+(-570 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 
-(-570) 
+(-571) 
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-571 R -3027 L) 
+(-572 R -3003 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
-((|HasCategory| |#3| (LIST (QUOTE -667) (|devaluate| |#2|)))) 
-(-572) 
+((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) 
+(-573) 
 ((|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 
-(-573 -3027 UP UPUP R) 
+(-574 -3003 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 
-(-574 -3027 UP) 
+(-575 -3003 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 
-(-575) 
+(-576) 
 ((|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."))) 
-((-4442 . T) (-4448 . T) (-4452 . T) (-4447 . T) (-4458 . T) (-4459 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4444 . T) (-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-576) 
+(-577) 
 ((|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 
-(-577 R -3027 L) 
+(-578 R -3003 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#3| (LIST (QUOTE -667) (|devaluate| |#2|)))) 
-(-578 R -3027) 
+((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) 
+(-579 R -3003) 
 ((|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 -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1156)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-640))))) 
-(-579 -3027 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) 
+(-580 -3003 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
-(-580 S) 
+(-581 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 
-(-581 -3027) 
+(-582 -3003) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
-(-582 R) 
+(-583 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) 
-((-3493 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-3468 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-583) 
+(-584) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-584 R -3027) 
+(-585 R -3003) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-293))) (|HasCategory| |#2| (QUOTE (-640))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-293)))) (|HasCategory| |#1| (QUOTE (-567)))) 
-(-585 -3027 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) 
+(-586 -3003 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-586 R -3027) 
+(-587 R -3003) 
 ((|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 
-(-587) 
+(-588) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-588) 
+(-589) 
 ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if \\spad{`f'} is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by \\spad{`f'} as a binary file."))) 
 NIL 
 NIL 
-(-589) 
+(-590) 
 ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) 
 NIL 
 NIL 
-(-590) 
+(-591) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet IP4 addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the IP4 address of host \\spad{`h'}.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address \\spad{`x'}.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-591 |p| |unBalanced?|) 
+(-592 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-592 |p|) 
+(-593 |p|) 
 ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-378)))) 
-(-593) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) 
+(-594) 
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-594 R -3027) 
+(-595 R -3003) 
 ((|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 
-(-595 E -3027) 
+(-596 E -3003) 
 ((|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 
-(-596) 
+(-597) 
 ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) 
 NIL 
 NIL 
-(-597 -3027) 
+(-598 -3003) 
 ((|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}."))) 
-((-4455 . T) (-4454 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-1194))))) 
-(-598 I) 
+((-4457 . T) (-4456 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1196))))) 
+(-599 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 
-(-599 GF) 
+(-600 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 
-(-600 R) 
+(-601 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 (-148)))) 
-(-601) 
+(-602) 
 ((|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| (|PositiveInteger|)) (|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| (|PositiveInteger|))) "\\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| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\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 
-(-602 R E V P TS) 
+(-603 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 
-(-603) 
+(-604) 
 ((|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|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-604 |mn|) 
+(-605 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (-3763 (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) 
-(-605 E V R P) 
+((-4463 . T) (-4462 . T)) 
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+(-606 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-606 |Coef|) 
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|)))) (|HasCategory| (-575) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575)))))) 
 (-607 |Coef|) 
+((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
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+(-608 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
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-((|HasCategory| |#1| (QUOTE (-567)))) 
-(-608) 
+(((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-568)))) 
+(-609) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) 
 NIL 
 NIL 
-(-609 A B) 
+(-610 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 
-(-610 A B C) 
+(-611 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 
-(-611 R -3027 FG) 
+(-612 R -3003 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
-(-612 S) 
+(-613 S) 
 ((|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 
-(-613 R |mn|) 
+(-614 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-614 S |Index| |Entry|) 
+((-4463 . T) (-4462 . T)) 
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+(-615 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#3| (QUOTE (-1117)))) 
-(-615 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#3| (QUOTE (-1119)))) 
+(-616 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
 NIL 
-(-616) 
+(-617) 
 ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) 
 NIL 
 NIL 
-(-617) 
+(-618) 
 ((|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 
-(-618 R A) 
+(-619 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4457 -3763 (-3224 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) 
-((-3763 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) 
-(-619 |Entry|) 
+((-4459 -3739 (-3200 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) 
+((-3739 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) 
+(-620 |Entry|) 
 ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| (-1176) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-620 S |Key| |Entry|) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1178) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-621 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
-(-621 |Key| |Entry|) 
+(-622 |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}."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
-(-622 R S) 
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 ((|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 
-(-623 S) 
+(-624 S) 
 ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) 
-(-624 S) 
+((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) 
+(-625 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 
-(-625 S) 
+(-626 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-626 -3027 UP) 
+(-627 -3003 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-627 S) 
+(-628 S) 
 ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'."))) 
 NIL 
 NIL 
-(-628) 
+(-629) 
 ((|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'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-629 S) 
+(-630 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) 
 NIL 
 NIL 
-(-630 S R) 
+(-631 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 
-(-631 R) 
+(-632 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."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-632 A R S) 
+(-633 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}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-859)))) 
-(-633 R -3027) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-634 R -3003) 
 ((|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 
-(-634 R UP) 
+(-635 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"))) 
-((-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4453 . T) (-4457 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-635 R E V P TS ST) 
+((-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4459 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-636 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 
-(-636 OV E Z P) 
+(-637 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 
-(-637) 
+(-638) 
 ((|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 
-(-638 |VarSet| R |Order|) 
+(-639 |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}}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-639 R |ls|) 
+(-640 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 
-(-640) 
+(-641) 
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-641 R -3027) 
+(-642 R -3003) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
-(-642 |lv| -3027) 
+(-643 |lv| -3003) 
 ((|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 
-(-643) 
+(-644) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
-((-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-1176) (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117)))) 
-(-644 S R) 
+((-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -3153) (QUOTE (-52))))))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1178) (QUOTE (-862))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 (-52))) (QUOTE (-1119)))) 
+(-645 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-373)))) 
-(-645 R) 
+((|HasCategory| |#2| (QUOTE (-374)))) 
+(-646 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4455 . T) (-4454 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) 
 NIL 
-(-646 R A) 
+(-647 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) 
-((-4457 -3763 (-3224 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) 
-((-3763 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) 
-(-647 R FE) 
+((-4459 -3739 (-3200 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) 
+((-3739 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) 
+(-648 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
 NIL 
 NIL 
-(-648 R) 
+(-649 R) 
 ((|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|))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|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 
-(-649 S R) 
+(-650 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-3213 (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-650 R) 
+((-3189 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-651 R) 
 ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
-(-651 S) 
+(-652 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
-(-652 A B) 
+(-653 A B) 
 ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
 NIL 
 NIL 
-(-653 A B) 
+(-654 A B) 
 ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) 
 NIL 
 NIL 
-(-654 A B C) 
+(-655 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 
-(-655 S) 
+(-656 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-656 T$) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-657 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-657 S) 
+(-658 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds if \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
-(-658 S) 
+(-659 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-659 R) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-660 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-660 S E |un|) 
+(-661 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 
-(-661 A S) 
+(-662 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,{}..))}.")) (|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 -4461))) 
-(-662 S) 
+((|HasAttribute| |#1| (QUOTE -4463))) 
+(-663 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,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-663 R -3027 L) 
+(-664 R -3003 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 
-(-664 A) 
+(-665 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-665 A M) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-666 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-666 S A) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-667 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-373)))) 
-(-667 A) 
+((|HasCategory| |#2| (QUOTE (-374)))) 
+(-668 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}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-668 -3027 UP) 
+(-669 -3003 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)))) 
-(-669 A -3902) 
+(-670 A -1957) 
 ((|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}}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-670 A L) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-671 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 
-(-671 S) 
+(-672 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-672) 
+(-673) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-673 M R S) 
+(-674 M R S) 
 ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4455 . T) (-4454 . T)) 
-((|HasCategory| |#1| (QUOTE (-802)))) 
-(-674 R) 
+((-4457 . T) (-4456 . T)) 
+((|HasCategory| |#1| (QUOTE (-803)))) 
+(-675 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 fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-675 |VarSet| R) 
+(-676 |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) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-676 A S) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) 
+((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-677 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 
-(-677 S) 
+(-678 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}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-678 -3027) 
+(-679 -3003) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-679 -3027 |Row| |Col| M) 
+(-680 -3003 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-680 R E OV P) 
+(-681 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 
-(-681 |n| R) 
+(-682 |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."))) 
-((-4457 . T) (-4460 . T) (-4454 . T) (-4455 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-567))) (-3763 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-682) 
+((-4459 . T) (-4462 . T) (-4456 . T) (-4457 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-3739 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-683) 
 ((|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 
-(-683 |VarSet|) 
+(-684 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-684 A S) 
+(-685 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-685 S) 
+(-686 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-686 R) 
+(-687 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 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-687) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-688) 
 ((|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 
-(-688 |VarSet|) 
+(-689 |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 
-(-689 A) 
+(-690 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 
-(-690 A C) 
+(-691 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 
-(-691 A B C) 
+(-692 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 
-(-692) 
+(-693) 
 ((|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 
-(-693 A) 
+(-694 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 
-(-694 A C) 
+(-695 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 
-(-695 A B C) 
+(-696 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 
-(-696 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-697 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 
-(-697 S R |Row| |Col|) 
+(-698 S R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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 (-4462 "*"))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-567)))) 
-(-698 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) 
+(-699 R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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"))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
-(-699 R |Row| |Col| M) 
+(-700 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 (-373))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567)))) 
-(-700 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."))) 
-((-4460 . T) (-4461 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
+((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) 
 (-701 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."))) 
+((-4462 . T) (-4463 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-702 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 
-(-702 T$) 
+(-703 T$) 
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) 
 NIL 
 NIL 
-(-703 S -3027 FLAF FLAS) 
+(-704 S -3003 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 
-(-704 R Q) 
+(-705 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 
-(-705) 
+(-706) 
 ((|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"))) 
-((-4453 . T) (-4458 |has| (-710) (-373)) (-4452 |has| (-710) (-373)) (-3501 . T) (-4459 |has| (-710) (-6 -4459)) (-4456 |has| (-710) (-6 -4456)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-710) (QUOTE (-148))) (|HasCategory| (-710) (QUOTE (-146))) (|HasCategory| (-710) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-710) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-710) (QUOTE (-378))) (|HasCategory| (-710) (QUOTE (-373))) (-3763 (|HasCategory| (-710) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-710) (QUOTE (-373)))) (|HasCategory| (-710) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-710) (QUOTE (-238))) (|HasCategory| (-710) (QUOTE (-237))) (-3763 (-12 (|HasCategory| (-710) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-710) (QUOTE (-373)))) (|HasCategory| (-710) (LIST (QUOTE -915) (QUOTE (-1194))))) (-3763 (|HasCategory| (-710) (QUOTE (-373))) (|HasCategory| (-710) (QUOTE (-359)))) (|HasCategory| (-710) (QUOTE (-359))) (|HasCategory| (-710) (LIST (QUOTE -295) (QUOTE (-710)) (QUOTE (-710)))) (|HasCategory| (-710) (LIST (QUOTE -318) (QUOTE (-710)))) (|HasCategory| (-710) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-710)))) (|HasCategory| (-710) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-710) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-710) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-710) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (-3763 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-373))) (|HasCategory| (-710) (QUOTE (-359)))) (|HasCategory| (-710) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-710) (QUOTE (-1039))) (|HasCategory| (-710) (QUOTE (-1220))) (-12 (|HasCategory| (-710) (QUOTE (-1019))) (|HasCategory| (-710) (QUOTE (-1220)))) (-3763 (-12 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (QUOTE (-373))) (-12 (|HasCategory| (-710) (QUOTE (-359))) (|HasCategory| (-710) (QUOTE (-924))))) (-3763 (-12 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (-12 (|HasCategory| (-710) (QUOTE (-373))) (|HasCategory| (-710) (QUOTE (-924)))) (-12 (|HasCategory| (-710) (QUOTE (-359))) (|HasCategory| (-710) (QUOTE (-924))))) (|HasCategory| (-710) (QUOTE (-556))) (-12 (|HasCategory| (-710) (QUOTE (-1077))) (|HasCategory| (-710) (QUOTE (-1220)))) (|HasCategory| (-710) (QUOTE (-1077))) (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924))) (-3763 (-12 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (QUOTE (-373)))) (-3763 (-12 (|HasCategory| (-710) (QUOTE (-238))) (|HasCategory| (-710) (QUOTE (-373)))) (|HasCategory| (-710) (QUOTE (-237)))) (-3763 (-12 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (QUOTE (-567)))) (-12 (|HasCategory| (-710) (QUOTE (-237))) (|HasCategory| (-710) (QUOTE (-373)))) (-12 (|HasCategory| (-710) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-710) (QUOTE (-373)))) (-12 (|HasCategory| (-710) (QUOTE (-238))) (|HasCategory| (-710) (QUOTE (-373)))) (-12 (|HasCategory| (-710) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-710) (QUOTE (-373)))) (|HasCategory| (-710) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-710) (QUOTE (-567))) (|HasAttribute| (-710) (QUOTE -4459)) (|HasAttribute| (-710) (QUOTE -4456)) (-12 (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (LIST (QUOTE -915) (QUOTE (-1194)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (QUOTE (-146)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-710) (QUOTE (-316))) (|HasCategory| (-710) (QUOTE (-924)))) (|HasCategory| (-710) (QUOTE (-359))))) 
-(-706 S) 
+((-4455 . T) (-4460 |has| (-711) (-374)) (-4454 |has| (-711) (-374)) (-3477 . T) (-4461 |has| (-711) (-6 -4461)) (-4458 |has| (-711) (-6 -4458)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-3739 (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-3739 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1196))))) (-3739 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-3739 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1041))) (|HasCategory| (-711) (QUOTE (-1222))) (-12 (|HasCategory| (-711) (QUOTE (-1021))) (|HasCategory| (-711) (QUOTE (-1222)))) (-3739 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-3739 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-1222)))) (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926))) (-3739 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-3739 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-3739 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4461)) (|HasAttribute| (-711) (QUOTE -4458)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1196)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-360))))) 
+(-707 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}."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
-(-707 U) 
+(-708 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 
-(-708) 
+(-709) 
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-709 OV E -3027 PG) 
+(-710 OV E -3003 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 
-(-710) 
+(-711) 
 ((|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}"))) 
-((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-3468 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-711 R) 
+(-712 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 
-(-712) 
+(-713) 
 ((|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}"))) 
-((-4459 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4461 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-713 S D1 D2 I) 
+(-714 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
 NIL 
 NIL 
-(-714 S) 
+(-715 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
-(-715 S) 
+(-716 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 
-(-716 S T$) 
+(-717 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 
-(-717 S -3428 I) 
+(-718 S -3404 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 
-(-718 E OV R P) 
+(-719 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 
-(-719 R) 
+(-720 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)}.}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-720 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-721 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 
-(-721) 
+(-722) 
 ((|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 
-(-722 R |Mod| -1745 -4167 |exactQuo|) 
+(-723 R |Mod| -1880 -3343 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-723 R |Rep|) 
+(-724 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4456 |has| |#1| (-373)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-724 IS E |ff|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-725 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-725 R M) 
+(-726 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) 
+((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-726 R |Mod| -1745 -4167 |exactQuo|) 
+(-727 R |Mod| -1880 -3343 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-727 S R) 
+(-728 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-728 R) 
+(-729 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-729 -3027) 
+(-730 -3003) 
 ((|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]]}."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-730 S) 
+(-731 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-731) 
+(-732) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 
-(-732 S) 
+(-733 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 
-(-733) 
+(-734) 
 ((|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 
-(-734 S R UP) 
+(-735 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 (-359))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-378)))) 
-(-735 R UP) 
+((|HasCategory| |#2| (QUOTE (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) 
+(-736 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."))) 
-((-4453 |has| |#1| (-373)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-736 S) 
+(-737 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 
-(-737) 
+(-738) 
 ((|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 
-(-738 -3027 UP) 
+(-739 -3003 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 
-(-739 |VarSet| E1 E2 R S PR PS) 
+(-740 |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 
-(-740 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-741 |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 
-(-741 E OV R PPR) 
+(-742 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 
-(-742 |vl| R) 
+(-743 |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."))) 
-(((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-743 E OV R PRF) 
+(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-926))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-744 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 
-(-744 E OV R P) 
+(-745 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 
-(-745 R S M) 
+(-746 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 
-(-746 R M) 
+(-747 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}."))) 
-((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-861)))) 
-(-747 S) 
+((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-862)))) 
+(-748 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4450 . T) (-4461 . T)) 
+((-4452 . T) (-4463 . T)) 
 NIL 
-(-748 S) 
+(-749 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}."))) 
-((-4460 . T) (-4450 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-749) 
+((-4462 . T) (-4452 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-750) 
 ((|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 
-(-750 S) 
+(-751 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 
-(-751 |Coef| |Var|) 
+(-752 |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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-752 OV E R P) 
+(-753 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 
-(-753 E OV R P) 
+(-754 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 
-(-754 S R) 
+(-755 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 
-(-755 R) 
+(-756 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}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-756) 
+(-757) 
 ((|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 
-(-757) 
+(-758) 
 ((|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 
-(-758) 
+(-759) 
 ((|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 
-(-759) 
+(-760) 
 ((|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 
-(-760) 
+(-761) 
 ((|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 
-(-761) 
+(-762) 
 ((|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 
-(-762) 
+(-763) 
 ((|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 
-(-763) 
+(-764) 
 ((|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 
-(-764) 
+(-765) 
 ((|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 
-(-765) 
+(-766) 
 ((|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 
-(-766) 
+(-767) 
 ((|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,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,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,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,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 
-(-767) 
+(-768) 
 ((|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 
-(-768) 
+(-769) 
 ((|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 
-(-769) 
+(-770) 
 ((|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 
-(-770) 
+(-771) 
 ((|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 
-(-771 S) 
+(-772 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-772) 
+(-773) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-773 S) 
+(-774 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 
-(-774) 
+(-775) 
 ((|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 
-(-775 |Par|) 
+(-776 |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 
-(-776 -3027) 
+(-777 -3003) 
 ((|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 
-(-777 P -3027) 
+(-778 P -3003) 
 ((|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 
-(-778 T$) 
+(-779 T$) 
 NIL 
 NIL 
 NIL 
-(-779 UP -3027) 
+(-780 UP -3003) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
-(-780) 
+(-781) 
 ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-781 R) 
+(-782 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 
-(-782) 
+(-783) 
 ((|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."))) 
-(((-4462 "*") . T)) 
+(((-4464 "*") . T)) 
 NIL 
-(-783 R -3027) 
+(-784 R -3003) 
 ((|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 
-(-784 S) 
+(-785 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 
-(-785) 
+(-786) 
 ((|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 
-(-786 R |PolR| E |PolE|) 
+(-787 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 
-(-787 R E V P TS) 
+(-788 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 
-(-788 -3027 |ExtF| |SUEx| |ExtP| |n|) 
+(-789 -3003 |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 
-(-789 BP E OV R P) 
+(-790 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 
-(-790 |Par|) 
+(-791 |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 
-(-791 R |VarSet|) 
+(-792 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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (QUOTE (-556)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-575))))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-575))))))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-792 R S) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
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+(-793 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-793 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)}"))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4456 |has| |#1| (-373)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-794 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)}"))) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-795 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) 
-(-795 R E V P) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
+(-796 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.}"))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-796 S) 
+(-797 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 (-567))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-174)))) 
-(-797) 
+((-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-174)))) 
+(-798) 
 ((|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 
-(-798) 
+(-799) 
 ((|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 
-(-799) 
+(-800) 
 ((|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 
-(-800) 
+(-801) 
 ((|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 
-(-801 |Curve|) 
+(-802 |Curve|) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-802) 
+(-803) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-803) 
+(-804) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-804) 
+(-805) 
 ((|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| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-805) 
+(-806) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-806) 
+(-807) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-807 S R) 
+(-808 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1077))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-378)))) 
-(-808 R) 
+((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) 
+(-809 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-809 -3763 R OS S) 
+(-810 -3739 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
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-(-810 R) 
+(-811 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-3763 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-811) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-3739 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-812) 
 ((|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 
-(-812 R -3027 L) 
+(-813 R -3003 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-813 R -3027) 
+(-814 R -3003) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-814) 
+(-815) 
 ((|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 
-(-815 R -3027) 
+(-816 R -3003) 
 ((|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 
-(-816) 
+(-817) 
 ((|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 
-(-817 -3027 UP UPUP R) 
+(-818 -3003 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 
-(-818 -3027 UP L LQ) 
+(-819 -3003 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 
-(-819) 
+(-820) 
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-820 -3027 UP L LQ) 
+(-821 -3003 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\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{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 ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\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 
-(-821 -3027 UP) 
+(-822 -3003 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-822 -3027 L UP A LO) 
+(-823 -3003 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 
-(-823 -3027 UP) 
+(-824 -3003 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{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 ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-824 -3027 LO) 
+(-825 -3003 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 
-(-825 -3027 LODO) 
+(-826 -3003 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-826 -2831 S |f|) 
+(-827 -2809 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}."))) 
-((-4454 |has| |#2| (-1066)) (-4455 |has| |#2| (-1066)) (-4457 |has| |#2| (-6 -4457)) (-4460 . T)) 
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(QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-862))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196))))) (-3739 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-738)))) (-3739 (|HasCategory| |#2| (QUOTE (-1068))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasAttribute| |#2| (QUOTE -4459)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196))))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) 
+(-828 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
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-(-828 |Kernels| R |var|) 
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+(-829 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4462 "*") |has| |#2| (-373)) (-4453 |has| |#2| (-373)) (-4458 |has| |#2| (-373)) (-4452 |has| |#2| (-373)) (-4457 . T) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#2| (QUOTE (-373)))) 
-(-829 S) 
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+((|HasCategory| |#2| (QUOTE (-374)))) 
+(-830 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 
-(-830 S) 
+(-831 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\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}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-861)))) 
-(-831) 
+((|HasCategory| |#1| (QUOTE (-862)))) 
+(-832) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-832) 
+(-833) 
 ((|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 
-(-833) 
+(-834) 
 ((|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 
-(-834) 
+(-835) 
 ((|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 
-(-835) 
+(-836) 
 ((|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 
-(-836) 
+(-837) 
 ((|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|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
 NIL 
 NIL 
-(-837 R) 
+(-838 R) 
 ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
 NIL 
 NIL 
-(-838 P R) 
+(-839 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) 
-(-839) 
+(-840) 
 ((|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 
-(-840) 
+(-841) 
 ((|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 
-(-841 S) 
+(-842 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4460 . T) (-4450 . T) (-4461 . T)) 
+((-4462 . T) (-4452 . T) (-4463 . T)) 
 NIL 
-(-842) 
+(-843) 
 ((|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 
-(-843 R S) 
+(-844 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 
-(-844 R) 
+(-845 R) 
 ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) 
-((-4457 |has| |#1| (-859))) 
-((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) 
-(-845 A S) 
+((-4459 |has| |#1| (-860))) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3739 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) 
+(-846 A S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-846 S) 
+(-847 S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-847 R) 
+(-848 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) 
+((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-848) 
+(-849) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) 
 NIL 
 NIL 
-(-849) 
+(-850) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of \\spad{`x'}."))) 
 NIL 
 NIL 
-(-850) 
+(-851) 
 ((|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 
-(-851) 
+(-852) 
 ((|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 
-(-852) 
+(-853) 
 ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-853 R S) 
+(-854 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 
-(-854 R) 
+(-855 R) 
 ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4457 |has| |#1| (-859))) 
-((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) 
-(-855) 
+((-4459 |has| |#1| (-860))) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3739 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) 
+(-856) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-856 -2831 S) 
+(-857 -2809 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-857) 
+(-858) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-858 S) 
+(-859 S) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
 NIL 
 NIL 
-(-859) 
+(-860) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-860 S) 
+(-861 S) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-861) 
+(-862) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-862 S R) 
+(-863 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-863 R) 
+((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-864 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-864 R C) 
+(-865 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 (-373))) (|HasCategory| |#1| (QUOTE (-567)))) 
-(-865 R |sigma| -3592) 
+((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) 
+(-866 R |sigma| -3568) 
 ((|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."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-866 |x| R |sigma| -3592) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-867 |x| R |sigma| -3568) 
 ((|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}."))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-373)))) 
-(-867 R) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) 
+(-868 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 -418) (QUOTE (-575)))))) 
-(-868) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
+(-869) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-869) 
+(-870) 
 ((|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 
-(-870 S) 
+(-871 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-871) 
+(-872) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-872) 
+(-873) 
 ((|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 
-(-873) 
+(-874) 
 ((|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 
-(-874) 
+(-875) 
 ((|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 
-(-875 |VariableList|) 
+(-876 |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 
-(-876) 
+(-877) 
 ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) 
 NIL 
 NIL 
-(-877 R |vl| |wl| |wtlevel|) 
+(-878 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)"))) 
-((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-878 R PS UP) 
+((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-879 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 
-(-879 R |x| |pt|) 
+(-880 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 
-(-880 |p|) 
+(-881 |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}."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-881 |p|) 
+(-882 |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)."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-882 |p|) 
+(-883 |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)."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-881 |#1|) (QUOTE (-924))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-148))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-881 |#1|) (QUOTE (-1039))) (|HasCategory| (-881 |#1|) (QUOTE (-831))) (-3763 (|HasCategory| (-881 |#1|) (QUOTE (-831))) (|HasCategory| (-881 |#1|) (QUOTE (-861)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-1169))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-237))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-238))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -881) (|devaluate| |#1|)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (QUOTE (-316))) (|HasCategory| (-881 |#1|) (QUOTE (-556))) (|HasCategory| (-881 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))))) 
-(-883 |p| PADIC) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-3739 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) 
+(-884 |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)}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-831))) (-3763 (|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -295) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-884 S T$) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-3739 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-885 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 (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) 
-(-885) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) 
+(-886) 
 ((|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 
-(-886) 
+(-887) 
 ((|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 
-(-887) 
+(-888) 
 ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) 
 NIL 
 NIL 
-(-888 CF1 CF2) 
+(-889 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-889 |ComponentFunction|) 
+(-890 |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 
-(-890 CF1 CF2) 
+(-891 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-891 |ComponentFunction|) 
+(-892 |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 
-(-892) 
+(-893) 
 ((|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 
-(-893 CF1 CF2) 
+(-894 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-894 |ComponentFunction|) 
+(-895 |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 
-(-895) 
+(-896) 
 ((|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| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-896 R) 
+(-897 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 
-(-897 R S L) 
+(-898 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 
-(-898 S) 
+(-899 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 
-(-899 |Base| |Subject| |Pat|) 
+(-900 |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 (-3213 (|HasCategory| |#2| (QUOTE (-1066)))) (-3213 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (-3213 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194))))) 
-(-900 R A B) 
+((-12 (-3189 (|HasCategory| |#2| (QUOTE (-1068)))) (-3189 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-3189 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196))))) 
+(-901 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 
-(-901 R S) 
+(-902 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 
-(-902 R -3428) 
+(-903 R -3404) 
 ((|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 
-(-903 R S) 
+(-904 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 
-(-904 R) 
+(-905 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\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 
-(-905 |VarSet|) 
+(-906 |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 
-(-906 UP R) 
+(-907 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-907 A T$ S) 
+(-908 A T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-908 T$ S) 
+(-909 T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-909) 
+(-910) 
 ((|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 
-(-910 UP -3027) 
+(-911 UP -3003) 
 ((|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 
-(-911) 
+(-912) 
 ((|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 
-(-912) 
+(-913) 
 ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-913 S) 
+(-914 R S) 
+((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
+((-4457 . T) (-4456 . T)) 
+NIL 
+(-915 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-914 A S) 
+(-916 A S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-915 S) 
+(-917 S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-916 S) 
+(-918 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-917 |n| R) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-919 |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 
-(-918 S) 
+(-920 S) 
 ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-919 S) 
+(-921 S) 
 ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-920 S) 
+(-922 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-4457 . T)) 
-((-3763 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) 
-(-921 R E |VarSet| S) 
+((-4459 . T)) 
+((-3739 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) 
+(-923 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-922 R S) 
+(-924 R S) 
 ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-923 S) 
+(-925 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 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 (-146)))) 
-(-924) 
+(-926) 
 ((|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 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}."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-925 |p|) 
+(-927 |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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-378)))) 
-(-926 R0 -3027 UP UPUP R) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) 
+(-928 R0 -3003 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 
-(-927 UP UPUP R) 
+(-929 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 
-(-928 UP UPUP) 
+(-930 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 
-(-929 R) 
+(-931 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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-930 R) 
+(-932 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 
-(-931 E OV R P) 
+(-933 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 
-(-932) 
+(-934) 
 ((|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(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) 
 NIL 
 NIL 
-(-933 -3027) 
+(-935 -3003) 
 ((|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 
-(-934 R) 
+(-936 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 
-(-935) 
+(-937) 
 ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-936) 
+(-938) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4462 "*") . T)) 
+(((-4464 "*") . T)) 
 NIL 
-(-937 -3027 P) 
+(-939 -3003 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-938 |xx| -3027) 
+(-940 |xx| -3003) 
 ((|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 
-(-939 R |Var| |Expon| GR) 
+(-941 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 
-(-940 S) 
+(-942 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 
-(-941) 
+(-943) 
 ((|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 
-(-942) 
+(-944) 
 ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) 
 NIL 
 NIL 
-(-943) 
+(-945) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-944 R -3027) 
+(-946 R -3003) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-945) 
+(-947) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-946 S A B) 
+(-948 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 
-(-947 S R -3027) 
+(-949 S R -3003) 
 ((|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 
-(-948 I) 
+(-950 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 
-(-949 S E) 
+(-951 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 
-(-950 S R L) 
+(-952 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 
-(-951 S E V R P) 
+(-953 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 -898) (|devaluate| |#1|)))) 
-(-952 R -3027 -3428) 
+((|HasCategory| |#3| (LIST (QUOTE -899) (|devaluate| |#1|)))) 
+(-954 R -3003 -3404) 
 ((|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 
-(-953 -3428) 
+(-955 -3404) 
 ((|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 
-(-954 S R Q) 
+(-956 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 
-(-955 S) 
+(-957 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 
-(-956 S R P) 
+(-958 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 
-(-957) 
+(-959) 
 ((|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 
-(-958 R) 
+(-960 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-959 |lv| R) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-961 |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 
-(-960 |TheField| |ThePols|) 
+(-962 |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 (-859)))) 
-(-961 R S) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-963 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 
-(-962 |x| R) 
+(-964 |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 
-(-963 S R E |VarSet|) 
+(-965 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 (-924))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#4| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#4| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#4| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) 
-(-964 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-926))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) 
+(-966 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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-965 E V R P -3027) 
+(-967 E V R P -3003) 
 ((|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 
-(-966 E |Vars| R P S) 
+(-968 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 
-(-967 R) 
+(-969 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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-968 E V R P -3027) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-970 E V R P -3003) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-463)))) 
-(-969) 
+((|HasCategory| |#3| (QUOTE (-464)))) 
+(-971) 
 ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) 
 NIL 
 NIL 
-(-970) 
+(-972) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-971 R L) 
+(-973 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-972 A B) 
+(-974 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
-(-973 S) 
+(-975 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-974) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-976) 
 ((|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 
-(-975 -3027) 
+(-977 -3003) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\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{ai = 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 
-(-976 I) 
+(-978 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-977) 
+(-979) 
 ((|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 
-(-978 R E) 
+(-980 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}"))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4458))) 
-(-979 A B) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4460))) 
+(-981 A B) 
 ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) 
-((-4457 -12 (|has| |#2| (-484)) (|has| |#1| (-484)))) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737))))) (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-378)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) 
-(-980) 
+((-4459 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) 
+(-982) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-981 T$) 
+(-983 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-982 T$) 
+(-984 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-983 S T$) 
+(-985 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-984) 
+(-986) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-985 S) 
+(-987 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
-(-986 R |polR|) 
+(-988 R |polR|) 
 ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-463)))) 
-(-987) 
+((|HasCategory| |#1| (QUOTE (-464)))) 
+(-989) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-988) 
+(-990) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-989 S |Coef| |Expon| |Var|) 
+(-991 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 
-(-990 |Coef| |Expon| |Var|) 
+(-992 |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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-991) 
+(-993) 
 ((|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 
-(-992 S R E |VarSet| P) 
+(-994 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 (-567)))) 
-(-993 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-568)))) 
+(-995 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."))) 
-((-4460 . T)) 
+((-4462 . T)) 
 NIL 
-(-994 R E V P) 
+(-996 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 (-148))) (|HasCategory| |#1| (QUOTE (-316)))) (|HasCategory| |#1| (QUOTE (-463)))) 
-(-995 K) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-464)))) 
+(-997 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."))) 
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-(-996 |VarSet| E RC P) 
+(-998 |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."))) 
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-(-997 R) 
+(-999 R) 
 ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-998 R1 R2) 
+(-1000 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
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-(-999 R) 
+(-1001 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."))) 
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-(-1000 K) 
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 ((|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."))) 
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-(-1001 R E OV PPR) 
+(-1003 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"))) 
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-(-1002 K R UP -3027) 
+(-1004 K R UP -3003) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1003 |vl| |nv|) 
+(-1005 |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 
-(-1004 R |Var| |Expon| |Dpoly|) 
+(-1006 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-316))))) 
-(-1005 R E V P TS) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317))))) 
+(-1007 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 
-(-1006) 
+(-1008) 
 ((|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 
-(-1007 A B R S) 
+(-1009 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 
-(-1008 A S) 
+(-1010 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 (-924))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1169)))) 
-(-1009 S) 
+((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171)))) 
+(-1011 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}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1010 |n| K) 
+(-1012 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1011) 
+(-1013) 
 ((|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 
-(-1012 S) 
+(-1014 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."))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
-(-1013 S R) 
+(-1015 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 (-556))) (|HasCategory| |#2| (QUOTE (-1077))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-299)))) 
-(-1014 R) 
+((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-300)))) 
+(-1016 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-4453 |has| |#1| (-299)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1015 QR R QS S) 
+(-1017 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-1016 R) 
+(-1018 R) 
 ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) 
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-(-1017 S) 
+((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) 
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+(-1019 S) 
 ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1018 S) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1020 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1019) 
+(-1021) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-1020 -3027 UP UPUP |radicnd| |n|) 
+(-1022 -3003 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
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-(-1021 |bb|) 
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+((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3739 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3739 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3739 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3739 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3739 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3739 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) 
+(-1023 |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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) 
-(-1022) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-3739 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) 
+(-1024) 
 ((|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 
-(-1023) 
+(-1025) 
 ((|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 
-(-1024 RP) 
+(-1026 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 
-(-1025 S) 
+(-1027 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 
-(-1026 A S) 
+(-1028 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 -4461)) (|HasCategory| |#2| (QUOTE (-1117)))) 
-(-1027 S) 
+((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-1119)))) 
+(-1029 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
 NIL 
-(-1028 S) 
+(-1030 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 
-(-1029) 
+(-1031) 
 ((|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}}"))) 
-((-4453 . T) (-4458 . T) (-4452 . T) (-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4457 . T)) 
+((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) 
 NIL 
-(-1030 R -3027) 
+(-1032 R -3003) 
 ((|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 
-(-1031 R -3027) 
+(-1033 R -3003) 
 ((|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 
-(-1032 -3027 UP) 
+(-1034 -3003 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 
-(-1033 -3027 UP) 
+(-1035 -3003 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 
-(-1034 S) 
+(-1036 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 
-(-1035 F1 UP UPUP R F2) 
+(-1037 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 
-(-1036) 
+(-1038) 
 ((|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 
-(-1037 |Pol|) 
+(-1039 |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 
-(-1038 |Pol|) 
+(-1040 |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 
-(-1039) 
+(-1041) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1040) 
+(-1042) 
 ((|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 
-(-1041 |TheField|) 
+(-1043 |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"))) 
-((-4453 . T) (-4458 . T) (-4452 . T) (-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4457 . T)) 
-((-3763 (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575))))) 
-(-1042 -3027 L) 
+((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) 
+((-3739 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) 
+(-1044 -3003 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
-(-1043 S) 
+(-1045 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 (-1117)))) 
-(-1044 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1119)))) 
+(-1046 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."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1045 R) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1047 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(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\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 ai} and {\\em 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 (-4462 "*")))) 
-(-1046 R) 
+((|HasAttribute| |#1| (QUOTE (-4464 "*")))) 
+(-1048 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 (-373))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-316)))) 
-(-1047 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317)))) 
+(-1049 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 
-(-1048) 
+(-1050) 
 ((|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 
-(-1049 S) 
+(-1051 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 
-(-1050 S) 
+(-1052 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 
-(-1051 -3027 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1053 -3003 |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"))) 
-(((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1052) 
+(-1054) 
 ((|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.}"))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1053) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -3153) (QUOTE (-52))))))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-1196) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1055) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1054 A S) 
+(-1056 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-1055 S) 
+(-1057 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-1056 Q R) 
+(-1058 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 
-(-1057) 
+(-1059) 
 ((|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 
-(-1058 UP) 
+(-1060 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 
-(-1059 R) 
+(-1061 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 
-(-1060 R) 
+(-1062 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 
-(-1061 T$) 
+(-1063 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| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) 
 NIL 
 NIL 
-(-1062 T$) 
+(-1064 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 
-(-1063 R |ls|) 
+(-1065 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}."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| (-791 |#1| (-875 |#2|)) (QUOTE (-1117))) (|HasCategory| (-791 |#1| (-875 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -791) (|devaluate| |#1|) (LIST (QUOTE -875) (|devaluate| |#2|)))))) (|HasCategory| (-791 |#1| (-875 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-791 |#1| (-875 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| (-875 |#2|) (QUOTE (-378))) (|HasCategory| (-791 |#1| (-875 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1064) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -876) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-876 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1066) 
 ((|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 
-(-1065 S) 
+(-1067 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-1066) 
+(-1068) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
-((-4457 . T)) 
+((-4459 . T)) 
 NIL 
-(-1067 |xx| -3027) 
+(-1069 |xx| -3003) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1068 S) 
+(-1070 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds if \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
-(-1069 S |m| |n| R |Row| |Col|) 
+(-1071 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 (-316))) (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (QUOTE (-567))) (|HasCategory| |#4| (QUOTE (-174)))) 
-(-1070 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) 
+(-1072 |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"))) 
-((-4460 . T) (-4455 . T) (-4454 . T)) 
+((-4462 . T) (-4457 . T) (-4456 . T)) 
 NIL 
-(-1071 |m| |n| R) 
+(-1073 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-4460 . T) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#3| (QUOTE (-174))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (QUOTE (-316))) (|HasCategory| |#3| (QUOTE (-567))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1072 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4462 . T) (-4457 . T) (-4456 . T)) 
+((|HasCategory| |#3| (QUOTE (-174))) (-3739 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1074 |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 
-(-1073 R) 
+(-1075 R) 
 ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-1074 S T$) 
+(-1076 S T$) 
 ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1117)))) 
-(-1075) 
+((|HasCategory| |#1| (QUOTE (-1119)))) 
+(-1077) 
 ((|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 
-(-1076 S) 
+(-1078 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1077) 
+(-1079) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1078 |TheField| |ThePolDom|) 
+(-1080 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1079) 
+(-1081) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4448 . T) (-4452 . T) (-4447 . T) (-4458 . T) (-4459 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1080) 
+(-1082) 
 ((|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}"))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1081 S R E V) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -3153) (QUOTE (-52))))))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (QUOTE (-1119))) (|HasCategory| (-1196) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1196)) (|:| -3153 (-52))) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1083 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-1194))))) 
-(-1082 R E V) 
+((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1196))))) 
+(-1084 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-1083) 
+(-1085) 
 ((|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 
-(-1084 S |TheField| |ThePols|) 
+(-1086 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 
-(-1085 |TheField| |ThePols|) 
+(-1087 |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 
-(-1086 R E V P TS) 
+(-1088 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 
-(-1087 S R E V P) 
+(-1089 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\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 
-(-1088 R E V P) 
+(-1090 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\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}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1089 R E V P TS) 
+(-1091 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 
-(-1090) 
+(-1092) 
 ((|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 
-(-1091) 
+(-1093) 
 ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) 
 NIL 
 NIL 
-(-1092 |f|) 
+(-1094 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1093 |Base| R -3027) 
+(-1095 |Base| R -3003) 
 ((|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 
-(-1094 |Base| R -3027) 
+(-1096 |Base| R -3003) 
 ((|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 
-(-1095 R |ls|) 
+(-1097 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 
-(-1096 UP SAE UPA) 
+(-1098 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 
-(-1097 R UP M) 
+(-1099 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."))) 
-((-4453 |has| |#1| (-373)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-359))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) 
-(-1098 UP SAE UPA) 
+((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))))) 
+(-1100 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 
-(-1099) 
+(-1101) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1100) 
+(-1102) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1101 S) 
+(-1103 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 
-(-1102) 
+(-1104) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-1103 R) 
+(-1105 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 
-(-1104 R) 
+(-1106 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"))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1105 S) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1107 (-1196)) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1107 (-1196)) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1107 (-1196)) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1107 (-1196)) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1107 (-1196)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1107 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 
-(-1106 R S) 
+(-1108 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 (-859)))) 
-(-1107) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1109) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1108 R S) 
+(-1110 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1109 S) 
+(-1111 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1111 |#1|) (QUOTE (-1117)))) 
-(-1110 S) 
+((|HasCategory| (-1113 |#1|) (QUOTE (-1119)))) 
+(-1112 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
 NIL 
 NIL 
-(-1111 S) 
+(-1113 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-1117)))) 
-(-1112 S L) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1119)))) 
+(-1114 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) 
 NIL 
 NIL 
-(-1113) 
+(-1115) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1114 A S) 
+(-1116 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1115 S) 
+(-1117 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-4450 . T)) 
+((-4452 . T)) 
 NIL 
-(-1116 S) 
+(-1118 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1117) 
+(-1119) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1118 |m| |n|) 
+(-1120 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1119 S) 
+(-1121 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)}}"))) 
-((-4460 . T) (-4450 . T) (-4461 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-1120 |Str| |Sym| |Int| |Flt| |Expr|) 
+((-4462 . T) (-4452 . T) (-4463 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-1122 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
 NIL 
-(-1121) 
+(-1123) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1122 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1124 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1123 R FS) 
+(-1125 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 
-(-1124 R E V P TS) 
+(-1126 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 
-(-1125 R E V P TS) 
+(-1127 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 
-(-1126 R E V P) 
+(-1128 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.}"))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1127) 
+(-1129) 
 ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1128 S) 
+(-1130 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1129) 
+(-1131) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1130 |dimtot| |dim1| S) 
+(-1132 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(-1068)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119))))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1068))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-862))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1196))))) (-3739 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-738)))) (-3739 (|HasCategory| |#3| (QUOTE (-1068))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1119)))) (|HasAttribute| |#3| (QUOTE -4459)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1068)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -915) (QUOTE (-1196))))) (|HasCategory| |#3| (QUOTE (-862))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) 
+(-1133 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 (-463)))) 
-(-1132) 
+((|HasCategory| |#1| (QUOTE (-464)))) 
+(-1134) 
 ((|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 
-(-1133 R -3027) 
+(-1135 R -3003) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1134 R) 
+(-1136 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1135) 
+(-1137) 
 ((|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 
-(-1136) 
+(-1138) 
 ((|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 
-(-1137) 
+(-1139) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) 
-((-4448 . T) (-4452 . T) (-4447 . T) (-4458 . T) (-4459 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1138 S) 
+(-1140 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4460 . T) (-4461 . T)) 
+((-4462 . T) (-4463 . T)) 
 NIL 
-(-1139 S |ndim| R |Row| |Col|) 
+(-1141 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-373))) (|HasAttribute| |#3| (QUOTE (-4462 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
-(-1140 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4464 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
+(-1142 |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."))) 
-((-4460 . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4462 . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1141 R |Row| |Col| M) 
+(-1143 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 
-(-1142 R |VarSet|) 
+(-1144 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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1143 |Coef| |Var| SMP) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1145 |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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-1144 R E V P) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-1146 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}"))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1145 UP -3027) 
+(-1147 UP -3003) 
 ((|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 
-(-1146 R) 
+(-1148 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 
-(-1147 R) 
+(-1149 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 
-(-1148 R) 
+(-1150 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 
-(-1149 S A) 
+(-1151 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 (-861)))) 
-(-1150 R) 
+((|HasCategory| |#1| (QUOTE (-862)))) 
+(-1152 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 
-(-1151 R) 
+(-1153 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 
-(-1152) 
+(-1154) 
 ((|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 
-(-1153) 
+(-1155) 
 ((|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 
-(-1154) 
+(-1156) 
 ((|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.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\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.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\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|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|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|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) 
 NIL 
 NIL 
-(-1155) 
+(-1157) 
 ((|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 
-(-1156) 
+(-1158) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1157 V C) 
+(-1159 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 
-(-1158 V C) 
+(-1160 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))) (-3763 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))))) (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1159 |ndim| R) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-3739 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1161 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
-((-4457 . T) (-4449 |has| |#2| (-6 (-4462 "*"))) (-4460 . T) (-4454 . T) (-4455 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (-3763 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-1160 S) 
+((-4459 . T) (-4451 |has| |#2| (-6 (-4464 "*"))) (-4462 . T) (-4456 . T) (-4457 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (-3739 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-1162 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1161) 
+(-1163) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1162 R E V P TS) 
+(-1164 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 
-(-1163 R E V P) 
+(-1165 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."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1164 S) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1166 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}."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1165 A S) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1167 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 
-(-1166 S) 
+(-1168 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 
-(-1167 |Key| |Ent| |dent|) 
+(-1169 |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."))) 
-((-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) 
-(-1168) 
+((-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119)))) 
+(-1170) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1169) 
+(-1171) 
 ((|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 
-(-1170 |Coef|) 
+(-1172 |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 
-(-1171 S) 
+(-1173 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 
-(-1172 A B) 
+(-1174 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 
-(-1173 A B C) 
+(-1175 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 
-(-1174 S) 
+(-1176 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
-((-4461 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1175) 
+((-4463 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1177) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1176) 
+(-1178) 
 NIL 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) 
-(-1177 |Entry|) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) 
+(-1179 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#1|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-1176) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1178 A) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#1|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (QUOTE (-1119))) (|HasCategory| (-1178) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 (-1178)) (|:| -3153 |#1|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1180 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\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,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 (-373))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) 
-(-1179 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
+(-1181 |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 
-(-1180 |Coef|) 
+(-1182 |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 
-(-1181 R UP) 
+(-1183 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 (-316)))) 
-(-1182 |n| R) 
+((|HasCategory| |#1| (QUOTE (-317)))) 
+(-1184 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\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,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 
-(-1183 S1 S2) 
+(-1185 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 
-(-1184) 
+(-1186) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1185 |Coef| |var| |cen|) 
+(-1187 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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(|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1194 |#1| |#2| |#3|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1194 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1194 |#1| |#2| |#3|) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1194 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1194 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1194 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1188 R -3003) 
 ((|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 
-(-1187 R) 
+(-1189 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 
-(-1188 R S) 
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 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1189 E OV R P) 
+(-1191 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 
-(-1190 R) 
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 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1191 |Coef| |var| |cen|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1193 |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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) 
-(-1192 |Coef| |var| |cen|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) 
+(-1194 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) 
-(-1193) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) 
+(-1195) 
 ((|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 
-(-1194) 
+(-1196) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1195 R) 
+(-1197 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1196 R) 
+(-1198 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| (-988) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasAttribute| |#1| (QUOTE -4458))) 
-(-1197) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3739 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-990) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4460))) 
+(-1199) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1198) 
+(-1200) 
 ((|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 
-(-1199) 
+(-1201) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1200 N) 
+(-1202 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1201 N) 
+(-1203 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) 
 NIL 
 NIL 
-(-1202) 
+(-1204) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1203 R) 
+(-1205 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 
-(-1204) 
+(-1206) 
 ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) 
 NIL 
 NIL 
-(-1205 S) 
+(-1207 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 
-(-1206 S) 
+(-1208 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 
-(-1207 |Key| |Entry|) 
+(-1209 |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}"))) 
-((-4460 . T) (-4461 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1208 S) 
+((-4462 . T) (-4463 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4147) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3153) (|devaluate| |#2|)))))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-3739 (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1210 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
 NIL 
-(-1209 R) 
+(-1211 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1210 S |Key| |Entry|) 
+(-1212 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 
-(-1211 |Key| |Entry|) 
+(-1213 |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})}."))) 
-((-4461 . T)) 
+((-4463 . T)) 
 NIL 
-(-1212 |Key| |Entry|) 
+(-1214 |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 
-(-1213) 
+(-1215) 
 ((|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 
-(-1214 S) 
+(-1216 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 
-(-1215) 
+(-1217) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1216) 
+(-1218) 
 ((|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 
-(-1217 R) 
+(-1219 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 
-(-1218) 
+(-1220) 
 ((|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 
-(-1219 S) 
+(-1221 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1220) 
+(-1222) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1221 S) 
+(-1223 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1222 S) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1224 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1223) 
+(-1225) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1224 R -3027) 
+(-1226 R -3003) 
 ((|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 
-(-1225 R |Row| |Col| M) 
+(-1227 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 
-(-1226 R -3027) 
+(-1228 R -3003) 
 ((|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 -625) (LIST (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -898) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -898) (|devaluate| |#1|))))) 
-(-1227 S R E V P) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -899) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -899) (|devaluate| |#1|))))) 
+(-1229 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 (-378)))) 
-(-1228 R E V P) 
+((|HasCategory| |#4| (QUOTE (-379)))) 
+(-1230 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1229 |Coef|) 
+(-1231 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-1230 |Curve|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-1232 |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 
-(-1231) 
+(-1233) 
 ((|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 
-(-1232 S) 
+(-1234 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1233 -3027) 
+((|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1235 -3003) 
 ((|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 
-(-1234) 
+(-1236) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1235) 
+(-1237) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1236 S) 
+(-1238 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 < 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 < 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 (-861)))) 
-(-1237) 
+((|HasCategory| |#1| (QUOTE (-862)))) 
+(-1239) 
 ((|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 
-(-1238 S) 
+(-1240 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 
-(-1239) 
+(-1241) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1240) 
+(-1242) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1241) 
+(-1243) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1242) 
+(-1244) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1243) 
+(-1245) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1244 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1246 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1245 |Coef|) 
+(-1247 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1246 S |Coef| UTS) 
+(-1248 S |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-373)))) 
-(-1247 |Coef| UTS) 
+((|HasCategory| |#2| (QUOTE (-374)))) 
+(-1249 |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1248 |Coef| UTS) 
+(-1250 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -295) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-861)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-924)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-1169)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1055) 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(LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-3739 (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1279 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1252 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1251 R S) 
+(-1253 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-859)))) 
-(-1252 S) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1254 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-1117)))) 
-(-1253 |x| R |y| S) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1119)))) 
+(-1255 |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 
-(-1254 R Q UP) 
+(-1256 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 
-(-1255 R UP) 
+(-1257 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 
-(-1256 R UP) 
+(-1258 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 
-(-1257 R U) 
+(-1259 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 
-(-1258 |x| R) 
+(-1260 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4456 |has| |#2| (-373)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-1259 R PR S PS) 
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+((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-3739 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-3739 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-3739 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-1261 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 
-(-1260 S R) 
+(-1262 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 -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1169)))) 
-(-1261 R) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1171)))) 
+(-1263 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}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4456 |has| |#1| (-373)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-1262 S |Coef| |Expon|) 
+(-1264 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}.")) (|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 -913) (QUOTE (-1194)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1129))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2882) (LIST (|devaluate| |#2|) (QUOTE (-1194)))))) 
-(-1263 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2858) (LIST (|devaluate| |#2|) (QUOTE (-1196)))))) 
+(-1265 |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}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1264 RC P) 
+(-1266 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1265 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1267 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1266 |Coef|) 
+(-1268 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1267 S |Coef| ULS) 
+(-1269 S |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
 NIL 
 NIL 
-(-1268 |Coef| ULS) 
+(-1270 |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1269 |Coef| ULS) 
+(-1271 |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)}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
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-(-1270 |Coef| |var| |cen|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
+(-1272 |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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) 
-(-1271 R FE |var| |cen|) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3739 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) 
+(-1273 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))}."))) 
-(((-4462 "*") |has| (-1270 |#2| |#3| |#4|) (-174)) (-4453 |has| (-1270 |#2| |#3| |#4|) (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-174))) (-3763 (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-373))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-463))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-567)))) 
-(-1272 A S) 
+(((-4464 "*") |has| (-1272 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1272 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-174))) (-3739 (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-568)))) 
+(-1274 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4461))) 
-(-1273 S) 
+((|HasAttribute| |#1| (QUOTE -4463))) 
+(-1275 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1274 |Coef1| |Coef2| UTS1 UTS2) 
+(-1276 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1275 S |Coef|) 
+(-1277 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-575)))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-1220))) (|HasSignature| |#2| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4388) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1194))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373)))) 
-(-1276 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1222))) (|HasSignature| |#2| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1850) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1196))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) 
+(-1278 |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."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1277 |Coef| |var| |cen|) 
+(-1279 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) 
-(-1278 |Coef| UTS) 
+(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3739 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -2858) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3739 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1850) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1634) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) 
+(-1280 |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 
-(-1279 -3027 UP L UTS) 
+(-1281 -3003 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 (-567)))) 
-(-1280) 
+((|HasCategory| |#1| (QUOTE (-568)))) 
+(-1282) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
 NIL 
 NIL 
-(-1281 |sym|) 
+(-1283 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1282 S R) 
+(-1284 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 (-1019))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1283 R) 
+((|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1285 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4461 . T) (-4460 . T)) 
+((-4463 . T) (-4462 . T)) 
 NIL 
-(-1284 A B) 
+(-1286 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1285 R) 
+(-1287 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4461 . T) (-4460 . T)) 
-((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) 
-(-1286) 
+((-4463 . T) (-4462 . T)) 
+((-3739 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3739 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3739 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+(-1288) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\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(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1287) 
+(-1289) 
 ((|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."))) 
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-(-1288) 
+(-1290) 
 ((|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."))) 
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-(-1289) 
+(-1291) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\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 
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-(-1290) 
+(-1292) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
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-(-1291 A S) 
+(-1293 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1292 S) 
+(-1294 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}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1293 R) 
+(-1295 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."))) 
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-(-1294 K R UP -3027) 
+(-1296 K R UP -3003) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1295) 
+(-1297) 
 ((|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 
-(-1296) 
+(-1298) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1297 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1299 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)"))) 
-((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373)))) 
-(-1298 R E V P) 
+((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) 
+(-1300 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}}."))) 
-((-4461 . T) (-4460 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#4| (LIST (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-873))))) 
-(-1299 R) 
+((-4463 . T) (-4462 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874))))) 
+(-1301 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})"))) 
-((-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1300 |vl| R) 
+(-1302 |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."))) 
-((-4457 . T) (-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4453))) 
-(-1301 R |VarSet| XPOLY) 
+((-4459 . T) (-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) 
+(-1303 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 
-(-1302 |vl| R) 
+(-1304 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-1303 S -3027) 
+(-1305 S -3003) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-1304 -3027) 
+((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
+(-1306 -3003) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
-(-1305 |VarSet| R) 
+(-1307 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) 
-((-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -728) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasAttribute| |#2| (QUOTE -4453))) 
-(-1306 |vl| R) 
+((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4455))) 
+(-1308 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) 
+((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) 
 NIL 
-(-1307 R) 
+(-1309 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4453 |has| |#1| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4453))) 
-(-1308 R E) 
+((-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4455))) 
+(-1310 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-4457 . T) (-4458 |has| |#1| (-6 -4458)) (-4453 |has| |#1| (-6 -4453)) (-4455 . T) (-4454 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4453))) 
-(-1309 |VarSet| R) 
+((-4459 . T) (-4460 |has| |#1| (-6 -4460)) (-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4455))) 
+(-1311 |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."))) 
-((-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4453))) 
-(-1310) 
+((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) 
+(-1312) 
 ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) 
 NIL 
 NIL 
-(-1311 A) 
+(-1313 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 
-(-1312 R |ls| |ls2|) 
+(-1314 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 
-(-1313 R) 
+(-1315 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 
-(-1314 |p|) 
+(-1316 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) 
+(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5204,4 +5212,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2279571 2279576 2279581 2279586) (-2 NIL 2279551 2279556 2279561 2279566) (-1 NIL 2279531 2279536 2279541 2279546) (0 NIL 2279511 2279516 2279521 2279526) (-1314 "ZMOD.spad" 2279320 2279333 2279449 2279506) (-1313 "ZLINDEP.spad" 2278386 2278397 2279310 2279315) (-1312 "ZDSOLVE.spad" 2268331 2268353 2278376 2278381) (-1311 "YSTREAM.spad" 2267826 2267837 2268321 2268326) (-1310 "YDIAGRAM.spad" 2267460 2267469 2267816 2267821) (-1309 "XRPOLY.spad" 2266680 2266700 2267316 2267385) (-1308 "XPR.spad" 2264475 2264488 2266398 2266497) (-1307 "XPOLY.spad" 2264030 2264041 2264331 2264400) (-1306 "XPOLYC.spad" 2263349 2263365 2263956 2264025) (-1305 "XPBWPOLY.spad" 2261786 2261806 2263129 2263198) (-1304 "XF.spad" 2260249 2260264 2261688 2261781) (-1303 "XF.spad" 2258692 2258709 2260133 2260138) (-1302 "XFALG.spad" 2255740 2255756 2258618 2258687) (-1301 "XEXPPKG.spad" 2254991 2255017 2255730 2255735) (-1300 "XDPOLY.spad" 2254605 2254621 2254847 2254916) (-1299 "XALG.spad" 2254265 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2158586 2160673 2160678) (-1261 "UPOLYC.spad" 2153600 2153611 2158402 2158555) (-1260 "UPOLYC.spad" 2148532 2148545 2153336 2153341) (-1259 "UPOLYC2.spad" 2148003 2148022 2148522 2148527) (-1258 "UP.spad" 2145109 2145124 2145496 2145649) (-1257 "UPMP.spad" 2144009 2144022 2145099 2145104) (-1256 "UPDIVP.spad" 2143574 2143588 2143999 2144004) (-1255 "UPDECOMP.spad" 2141819 2141833 2143564 2143569) (-1254 "UPCDEN.spad" 2141028 2141044 2141809 2141814) (-1253 "UP2.spad" 2140392 2140413 2141018 2141023) (-1252 "UNISEG.spad" 2139745 2139756 2140311 2140316) (-1251 "UNISEG2.spad" 2139242 2139255 2139701 2139706) (-1250 "UNIFACT.spad" 2138345 2138357 2139232 2139237) (-1249 "ULS.spad" 2128129 2128157 2129074 2129503) (-1248 "ULSCONS.spad" 2119263 2119283 2119633 2119782) (-1247 "ULSCCAT.spad" 2117000 2117020 2119109 2119258) (-1246 "ULSCCAT.spad" 2114845 2114867 2116956 2116961) (-1245 "ULSCAT.spad" 2113077 2113093 2114691 2114840) (-1244 "ULS2.spad" 2112591 2112644 2113067 2113072) (-1243 "UINT8.spad" 2112468 2112477 2112581 2112586) (-1242 "UINT64.spad" 2112344 2112353 2112458 2112463) (-1241 "UINT32.spad" 2112220 2112229 2112334 2112339) (-1240 "UINT16.spad" 2112096 2112105 2112210 2112215) (-1239 "UFD.spad" 2111161 2111170 2112022 2112091) (-1238 "UFD.spad" 2110288 2110299 2111151 2111156) (-1237 "UDVO.spad" 2109169 2109178 2110278 2110283) (-1236 "UDPO.spad" 2106662 2106673 2109125 2109130) (-1235 "TYPE.spad" 2106594 2106603 2106652 2106657) (-1234 "TYPEAST.spad" 2106513 2106522 2106584 2106589) (-1233 "TWOFACT.spad" 2105165 2105180 2106503 2106508) (-1232 "TUPLE.spad" 2104651 2104662 2105064 2105069) (-1231 "TUBETOOL.spad" 2101518 2101527 2104641 2104646) (-1230 "TUBE.spad" 2100165 2100182 2101508 2101513) (-1229 "TS.spad" 2098764 2098780 2099730 2099827) (-1228 "TSETCAT.spad" 2085891 2085908 2098732 2098759) (-1227 "TSETCAT.spad" 2073004 2073023 2085847 2085852) (-1226 "TRMANIP.spad" 2067370 2067387 2072710 2072715) (-1225 "TRIMAT.spad" 2066333 2066358 2067360 2067365) (-1224 "TRIGMNIP.spad" 2064860 2064877 2066323 2066328) (-1223 "TRIGCAT.spad" 2064372 2064381 2064850 2064855) (-1222 "TRIGCAT.spad" 2063882 2063893 2064362 2064367) (-1221 "TREE.spad" 2062457 2062468 2063489 2063516) (-1220 "TRANFUN.spad" 2062296 2062305 2062447 2062452) (-1219 "TRANFUN.spad" 2062133 2062144 2062286 2062291) (-1218 "TOPSP.spad" 2061807 2061816 2062123 2062128) (-1217 "TOOLSIGN.spad" 2061470 2061481 2061797 2061802) (-1216 "TEXTFILE.spad" 2060031 2060040 2061460 2061465) (-1215 "TEX.spad" 2057177 2057186 2060021 2060026) (-1214 "TEX1.spad" 2056733 2056744 2057167 2057172) (-1213 "TEMUTL.spad" 2056288 2056297 2056723 2056728) (-1212 "TBCMPPK.spad" 2054381 2054404 2056278 2056283) (-1211 "TBAGG.spad" 2053431 2053454 2054361 2054376) (-1210 "TBAGG.spad" 2052489 2052514 2053421 2053426) (-1209 "TANEXP.spad" 2051897 2051908 2052479 2052484) (-1208 "TALGOP.spad" 2051621 2051632 2051887 2051892) (-1207 "TABLE.spad" 2050032 2050055 2050302 2050329) (-1206 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2014737 2014742) (-1187 "SUMRF.spad" 2013113 2013124 2014129 2014134) (-1186 "SUMFS.spad" 2012750 2012767 2013103 2013108) (-1185 "SULS.spad" 2002521 2002549 2003479 2003908) (-1184 "SUCHTAST.spad" 2002290 2002299 2002511 2002516) (-1183 "SUCH.spad" 2001972 2001987 2002280 2002285) (-1182 "SUBSPACE.spad" 1994087 1994102 2001962 2001967) (-1181 "SUBRESP.spad" 1993257 1993271 1994043 1994048) (-1180 "STTF.spad" 1989356 1989372 1993247 1993252) (-1179 "STTFNC.spad" 1985824 1985840 1989346 1989351) (-1178 "STTAYLOR.spad" 1978459 1978470 1985705 1985710) (-1177 "STRTBL.spad" 1976964 1976981 1977113 1977140) (-1176 "STRING.spad" 1976373 1976382 1976387 1976414) (-1175 "STRICAT.spad" 1976161 1976170 1976341 1976368) (-1174 "STREAM.spad" 1973079 1973090 1975686 1975701) (-1173 "STREAM3.spad" 1972652 1972667 1973069 1973074) (-1172 "STREAM2.spad" 1971780 1971793 1972642 1972647) (-1171 "STREAM1.spad" 1971486 1971497 1971770 1971775) (-1170 "STINPROD.spad" 1970422 1970438 1971476 1971481) (-1169 "STEP.spad" 1969623 1969632 1970412 1970417) (-1168 "STEPAST.spad" 1968857 1968866 1969613 1969618) (-1167 "STBL.spad" 1967383 1967411 1967550 1967565) (-1166 "STAGG.spad" 1966458 1966469 1967373 1967378) (-1165 "STAGG.spad" 1965531 1965544 1966448 1966453) (-1164 "STACK.spad" 1964888 1964899 1965138 1965165) (-1163 "SREGSET.spad" 1962592 1962609 1964534 1964561) (-1162 "SRDCMPK.spad" 1961153 1961173 1962582 1962587) (-1161 "SRAGG.spad" 1956296 1956305 1961121 1961148) (-1160 "SRAGG.spad" 1951459 1951470 1956286 1956291) (-1159 "SQMATRIX.spad" 1949038 1949056 1949954 1950041) (-1158 "SPLTREE.spad" 1943590 1943603 1948474 1948501) (-1157 "SPLNODE.spad" 1940178 1940191 1943580 1943585) (-1156 "SPFCAT.spad" 1938987 1938996 1940168 1940173) (-1155 "SPECOUT.spad" 1937539 1937548 1938977 1938982) (-1154 "SPADXPT.spad" 1929134 1929143 1937529 1937534) (-1153 "spad-parser.spad" 1928599 1928608 1929124 1929129) (-1152 "SPADAST.spad" 1928300 1928309 1928589 1928594) (-1151 "SPACEC.spad" 1912499 1912510 1928290 1928295) (-1150 "SPACE3.spad" 1912275 1912286 1912489 1912494) (-1149 "SORTPAK.spad" 1911824 1911837 1912231 1912236) (-1148 "SOLVETRA.spad" 1909587 1909598 1911814 1911819) (-1147 "SOLVESER.spad" 1908115 1908126 1909577 1909582) (-1146 "SOLVERAD.spad" 1904141 1904152 1908105 1908110) (-1145 "SOLVEFOR.spad" 1902603 1902621 1904131 1904136) (-1144 "SNTSCAT.spad" 1902203 1902220 1902571 1902598) (-1143 "SMTS.spad" 1900475 1900501 1901768 1901865) (-1142 "SMP.spad" 1897950 1897970 1898340 1898467) (-1141 "SMITH.spad" 1896795 1896820 1897940 1897945) (-1140 "SMATCAT.spad" 1894905 1894935 1896739 1896790) (-1139 "SMATCAT.spad" 1892947 1892979 1894783 1894788) (-1138 "SKAGG.spad" 1891910 1891921 1892915 1892942) (-1137 "SINT.spad" 1890850 1890859 1891776 1891905) (-1136 "SIMPAN.spad" 1890578 1890587 1890840 1890845) (-1135 "SIG.spad" 1889908 1889917 1890568 1890573) (-1134 "SIGNRF.spad" 1889026 1889037 1889898 1889903) (-1133 "SIGNEF.spad" 1888305 1888322 1889016 1889021) (-1132 "SIGAST.spad" 1887690 1887699 1888295 1888300) (-1131 "SHP.spad" 1885618 1885633 1887646 1887651) (-1130 "SHDP.spad" 1873821 1873848 1874330 1874429) (-1129 "SGROUP.spad" 1873429 1873438 1873811 1873816) (-1128 "SGROUP.spad" 1873035 1873046 1873419 1873424) (-1127 "SGCF.spad" 1866174 1866183 1873025 1873030) (-1126 "SFRTCAT.spad" 1865104 1865121 1866142 1866169) (-1125 "SFRGCD.spad" 1864167 1864187 1865094 1865099) (-1124 "SFQCMPK.spad" 1858804 1858824 1864157 1864162) (-1123 "SFORT.spad" 1858243 1858257 1858794 1858799) (-1122 "SEXOF.spad" 1858086 1858126 1858233 1858238) (-1121 "SEX.spad" 1857978 1857987 1858076 1858081) (-1120 "SEXCAT.spad" 1855759 1855799 1857968 1857973) (-1119 "SET.spad" 1854083 1854094 1855180 1855219) (-1118 "SETMN.spad" 1852533 1852550 1854073 1854078) (-1117 "SETCAT.spad" 1851855 1851864 1852523 1852528) (-1116 "SETCAT.spad" 1851175 1851186 1851845 1851850) (-1115 "SETAGG.spad" 1847724 1847735 1851155 1851170) (-1114 "SETAGG.spad" 1844281 1844294 1847714 1847719) (-1113 "SEQAST.spad" 1843984 1843993 1844271 1844276) (-1112 "SEGXCAT.spad" 1843140 1843153 1843974 1843979) (-1111 "SEG.spad" 1842953 1842964 1843059 1843064) (-1110 "SEGCAT.spad" 1841878 1841889 1842943 1842948) (-1109 "SEGBIND.spad" 1841636 1841647 1841825 1841830) (-1108 "SEGBIND2.spad" 1841334 1841347 1841626 1841631) (-1107 "SEGAST.spad" 1841048 1841057 1841324 1841329) (-1106 "SEG2.spad" 1840483 1840496 1841004 1841009) (-1105 "SDVAR.spad" 1839759 1839770 1840473 1840478) (-1104 "SDPOL.spad" 1837092 1837103 1837383 1837510) (-1103 "SCPKG.spad" 1835181 1835192 1837082 1837087) (-1102 "SCOPE.spad" 1834334 1834343 1835171 1835176) (-1101 "SCACHE.spad" 1833030 1833041 1834324 1834329) (-1100 "SASTCAT.spad" 1832939 1832948 1833020 1833025) (-1099 "SAOS.spad" 1832811 1832820 1832929 1832934) (-1098 "SAERFFC.spad" 1832524 1832544 1832801 1832806) (-1097 "SAE.spad" 1829994 1830010 1830605 1830740) (-1096 "SAEFACT.spad" 1829695 1829715 1829984 1829989) (-1095 "RURPK.spad" 1827354 1827370 1829685 1829690) (-1094 "RULESET.spad" 1826807 1826831 1827344 1827349) (-1093 "RULE.spad" 1825047 1825071 1826797 1826802) (-1092 "RULECOLD.spad" 1824899 1824912 1825037 1825042) (-1091 "RTVALUE.spad" 1824634 1824643 1824889 1824894) (-1090 "RSTRCAST.spad" 1824351 1824360 1824624 1824629) (-1089 "RSETGCD.spad" 1820729 1820749 1824341 1824346) (-1088 "RSETCAT.spad" 1810665 1810682 1820697 1820724) (-1087 "RSETCAT.spad" 1800621 1800640 1810655 1810660) (-1086 "RSDCMPK.spad" 1799073 1799093 1800611 1800616) (-1085 "RRCC.spad" 1797457 1797487 1799063 1799068) (-1084 "RRCC.spad" 1795839 1795871 1797447 1797452) (-1083 "RPTAST.spad" 1795541 1795550 1795829 1795834) (-1082 "RPOLCAT.spad" 1774901 1774916 1795409 1795536) (-1081 "RPOLCAT.spad" 1753974 1753991 1774484 1774489) (-1080 "ROUTINE.spad" 1749857 1749866 1752621 1752648) (-1079 "ROMAN.spad" 1749185 1749194 1749723 1749852) (-1078 "ROIRC.spad" 1748265 1748297 1749175 1749180) (-1077 "RNS.spad" 1747168 1747177 1748167 1748260) (-1076 "RNS.spad" 1746157 1746168 1747158 1747163) (-1075 "RNG.spad" 1745892 1745901 1746147 1746152) (-1074 "RNGBIND.spad" 1745052 1745066 1745847 1745852) (-1073 "RMODULE.spad" 1744817 1744828 1745042 1745047) (-1072 "RMCAT2.spad" 1744237 1744294 1744807 1744812) (-1071 "RMATRIX.spad" 1743061 1743080 1743404 1743443) (-1070 "RMATCAT.spad" 1738640 1738671 1743017 1743056) (-1069 "RMATCAT.spad" 1734109 1734142 1738488 1738493) (-1068 "RLINSET.spad" 1733664 1733675 1734099 1734104) (-1067 "RINTERP.spad" 1733552 1733572 1733654 1733659) (-1066 "RING.spad" 1733022 1733031 1733532 1733547) (-1065 "RING.spad" 1732500 1732511 1733012 1733017) (-1064 "RIDIST.spad" 1731892 1731901 1732490 1732495) (-1063 "RGCHAIN.spad" 1730475 1730491 1731377 1731404) (-1062 "RGBCSPC.spad" 1730256 1730268 1730465 1730470) (-1061 "RGBCMDL.spad" 1729786 1729798 1730246 1730251) (-1060 "RF.spad" 1727428 1727439 1729776 1729781) (-1059 "RFFACTOR.spad" 1726890 1726901 1727418 1727423) (-1058 "RFFACT.spad" 1726625 1726637 1726880 1726885) (-1057 "RFDIST.spad" 1725621 1725630 1726615 1726620) (-1056 "RETSOL.spad" 1725040 1725053 1725611 1725616) (-1055 "RETRACT.spad" 1724468 1724479 1725030 1725035) (-1054 "RETRACT.spad" 1723894 1723907 1724458 1724463) (-1053 "RETAST.spad" 1723706 1723715 1723884 1723889) (-1052 "RESULT.spad" 1721766 1721775 1722353 1722380) (-1051 "RESRING.spad" 1721113 1721160 1721704 1721761) (-1050 "RESLATC.spad" 1720437 1720448 1721103 1721108) (-1049 "REPSQ.spad" 1720168 1720179 1720427 1720432) (-1048 "REP.spad" 1717722 1717731 1720158 1720163) (-1047 "REPDB.spad" 1717429 1717440 1717712 1717717) (-1046 "REP2.spad" 1707087 1707098 1717271 1717276) (-1045 "REP1.spad" 1701283 1701294 1707037 1707042) (-1044 "REGSET.spad" 1699080 1699097 1700929 1700956) (-1043 "REF.spad" 1698415 1698426 1699035 1699040) (-1042 "REDORDER.spad" 1697621 1697638 1698405 1698410) (-1041 "RECLOS.spad" 1696404 1696424 1697108 1697201) (-1040 "REALSOLV.spad" 1695544 1695553 1696394 1696399) (-1039 "REAL.spad" 1695416 1695425 1695534 1695539) (-1038 "REAL0Q.spad" 1692714 1692729 1695406 1695411) (-1037 "REAL0.spad" 1689558 1689573 1692704 1692709) (-1036 "RDUCEAST.spad" 1689279 1689288 1689548 1689553) (-1035 "RDIV.spad" 1688934 1688959 1689269 1689274) (-1034 "RDIST.spad" 1688501 1688512 1688924 1688929) (-1033 "RDETRS.spad" 1687365 1687383 1688491 1688496) (-1032 "RDETR.spad" 1685504 1685522 1687355 1687360) (-1031 "RDEEFS.spad" 1684603 1684620 1685494 1685499) (-1030 "RDEEF.spad" 1683613 1683630 1684593 1684598) (-1029 "RCFIELD.spad" 1680799 1680808 1683515 1683608) (-1028 "RCFIELD.spad" 1678071 1678082 1680789 1680794) (-1027 "RCAGG.spad" 1675999 1676010 1678061 1678066) (-1026 "RCAGG.spad" 1673854 1673867 1675918 1675923) (-1025 "RATRET.spad" 1673214 1673225 1673844 1673849) (-1024 "RATFACT.spad" 1672906 1672918 1673204 1673209) (-1023 "RANDSRC.spad" 1672225 1672234 1672896 1672901) (-1022 "RADUTIL.spad" 1671981 1671990 1672215 1672220) (-1021 "RADIX.spad" 1668805 1668819 1670351 1670444) (-1020 "RADFF.spad" 1666544 1666581 1666663 1666819) (-1019 "RADCAT.spad" 1666139 1666148 1666534 1666539) (-1018 "RADCAT.spad" 1665732 1665743 1666129 1666134) (-1017 "QUEUE.spad" 1665080 1665091 1665339 1665366) (-1016 "QUAT.spad" 1663568 1663579 1663911 1663976) (-1015 "QUATCT2.spad" 1663188 1663207 1663558 1663563) (-1014 "QUATCAT.spad" 1661358 1661369 1663118 1663183) (-1013 "QUATCAT.spad" 1659279 1659292 1661041 1661046) (-1012 "QUAGG.spad" 1658106 1658117 1659247 1659274) (-1011 "QQUTAST.spad" 1657874 1657883 1658096 1658101) (-1010 "QFORM.spad" 1657492 1657507 1657864 1657869) (-1009 "QFCAT.spad" 1656194 1656205 1657394 1657487) (-1008 "QFCAT.spad" 1654487 1654500 1655689 1655694) (-1007 "QFCAT2.spad" 1654179 1654196 1654477 1654482) (-1006 "QEQUAT.spad" 1653737 1653746 1654169 1654174) (-1005 "QCMPACK.spad" 1648483 1648503 1653727 1653732) (-1004 "QALGSET.spad" 1644561 1644594 1648397 1648402) (-1003 "QALGSET2.spad" 1642556 1642575 1644551 1644556) (-1002 "PWFFINTB.spad" 1639971 1639993 1642546 1642551) (-1001 "PUSHVAR.spad" 1639309 1639329 1639961 1639966) (-1000 "PTRANFN.spad" 1635436 1635447 1639299 1639304) (-999 "PTPACK.spad" 1632524 1632534 1635426 1635431) (-998 "PTFUNC2.spad" 1632347 1632361 1632514 1632519) (-997 "PTCAT.spad" 1631602 1631612 1632315 1632342) (-996 "PSQFR.spad" 1630909 1630933 1631592 1631597) (-995 "PSEUDLIN.spad" 1629795 1629805 1630899 1630904) (-994 "PSETPK.spad" 1615228 1615244 1629673 1629678) (-993 "PSETCAT.spad" 1609148 1609171 1615208 1615223) (-992 "PSETCAT.spad" 1603042 1603067 1609104 1609109) (-991 "PSCURVE.spad" 1602025 1602033 1603032 1603037) (-990 "PSCAT.spad" 1600808 1600837 1601923 1602020) (-989 "PSCAT.spad" 1599681 1599712 1600798 1600803) (-988 "PRTITION.spad" 1598379 1598387 1599671 1599676) (-987 "PRTDAST.spad" 1598098 1598106 1598369 1598374) (-986 "PRS.spad" 1587660 1587677 1598054 1598059) (-985 "PRQAGG.spad" 1587095 1587105 1587628 1587655) (-984 "PROPLOG.spad" 1586667 1586675 1587085 1587090) (-983 "PROPFUN2.spad" 1586290 1586303 1586657 1586662) (-982 "PROPFUN1.spad" 1585688 1585699 1586280 1586285) (-981 "PROPFRML.spad" 1584256 1584267 1585678 1585683) (-980 "PROPERTY.spad" 1583744 1583752 1584246 1584251) (-979 "PRODUCT.spad" 1581426 1581438 1581710 1581765) (-978 "PR.spad" 1579818 1579830 1580517 1580644) (-977 "PRINT.spad" 1579570 1579578 1579808 1579813) (-976 "PRIMES.spad" 1577823 1577833 1579560 1579565) (-975 "PRIMELT.spad" 1575904 1575918 1577813 1577818) (-974 "PRIMCAT.spad" 1575531 1575539 1575894 1575899) (-973 "PRIMARR.spad" 1574536 1574546 1574714 1574741) (-972 "PRIMARR2.spad" 1573303 1573315 1574526 1574531) (-971 "PREASSOC.spad" 1572685 1572697 1573293 1573298) (-970 "PPCURVE.spad" 1571822 1571830 1572675 1572680) (-969 "PORTNUM.spad" 1571597 1571605 1571812 1571817) (-968 "POLYROOT.spad" 1570446 1570468 1571553 1571558) (-967 "POLY.spad" 1567781 1567791 1568296 1568423) (-966 "POLYLIFT.spad" 1567046 1567069 1567771 1567776) (-965 "POLYCATQ.spad" 1565164 1565186 1567036 1567041) (-964 "POLYCAT.spad" 1558634 1558655 1565032 1565159) (-963 "POLYCAT.spad" 1551442 1551465 1557842 1557847) (-962 "POLY2UP.spad" 1550894 1550908 1551432 1551437) (-961 "POLY2.spad" 1550491 1550503 1550884 1550889) (-960 "POLUTIL.spad" 1549432 1549461 1550447 1550452) (-959 "POLTOPOL.spad" 1548180 1548195 1549422 1549427) (-958 "POINT.spad" 1547018 1547028 1547105 1547132) (-957 "PNTHEORY.spad" 1543720 1543728 1547008 1547013) (-956 "PMTOOLS.spad" 1542495 1542509 1543710 1543715) (-955 "PMSYM.spad" 1542044 1542054 1542485 1542490) (-954 "PMQFCAT.spad" 1541635 1541649 1542034 1542039) (-953 "PMPRED.spad" 1541114 1541128 1541625 1541630) (-952 "PMPREDFS.spad" 1540568 1540590 1541104 1541109) (-951 "PMPLCAT.spad" 1539648 1539666 1540500 1540505) (-950 "PMLSAGG.spad" 1539233 1539247 1539638 1539643) (-949 "PMKERNEL.spad" 1538812 1538824 1539223 1539228) (-948 "PMINS.spad" 1538392 1538402 1538802 1538807) (-947 "PMFS.spad" 1537969 1537987 1538382 1538387) (-946 "PMDOWN.spad" 1537259 1537273 1537959 1537964) (-945 "PMASS.spad" 1536269 1536277 1537249 1537254) (-944 "PMASSFS.spad" 1535236 1535252 1536259 1536264) (-943 "PLOTTOOL.spad" 1535016 1535024 1535226 1535231) (-942 "PLOT.spad" 1529939 1529947 1535006 1535011) (-941 "PLOT3D.spad" 1526403 1526411 1529929 1529934) (-940 "PLOT1.spad" 1525560 1525570 1526393 1526398) (-939 "PLEQN.spad" 1512850 1512877 1525550 1525555) (-938 "PINTERP.spad" 1512472 1512491 1512840 1512845) (-937 "PINTERPA.spad" 1512256 1512272 1512462 1512467) (-936 "PI.spad" 1511865 1511873 1512230 1512251) (-935 "PID.spad" 1510835 1510843 1511791 1511860) (-934 "PICOERCE.spad" 1510492 1510502 1510825 1510830) (-933 "PGROEB.spad" 1509093 1509107 1510482 1510487) (-932 "PGE.spad" 1500710 1500718 1509083 1509088) (-931 "PGCD.spad" 1499600 1499617 1500700 1500705) (-930 "PFRPAC.spad" 1498749 1498759 1499590 1499595) (-929 "PFR.spad" 1495412 1495422 1498651 1498744) (-928 "PFOTOOLS.spad" 1494670 1494686 1495402 1495407) (-927 "PFOQ.spad" 1494040 1494058 1494660 1494665) (-926 "PFO.spad" 1493459 1493486 1494030 1494035) (-925 "PF.spad" 1493033 1493045 1493264 1493357) (-924 "PFECAT.spad" 1490715 1490723 1492959 1493028) (-923 "PFECAT.spad" 1488425 1488435 1490671 1490676) (-922 "PFBRU.spad" 1486313 1486325 1488415 1488420) (-921 "PFBR.spad" 1483873 1483896 1486303 1486308) (-920 "PERM.spad" 1479680 1479690 1483703 1483718) (-919 "PERMGRP.spad" 1474450 1474460 1479670 1479675) (-918 "PERMCAT.spad" 1473111 1473121 1474430 1474445) (-917 "PERMAN.spad" 1471643 1471657 1473101 1473106) (-916 "PENDTREE.spad" 1470984 1470994 1471272 1471277) (-915 "PDSPC.spad" 1469797 1469807 1470974 1470979) (-914 "PDSPC.spad" 1468608 1468620 1469787 1469792) (-913 "PDRING.spad" 1468450 1468460 1468588 1468603) (-912 "PDEPROB.spad" 1467465 1467473 1468440 1468445) (-911 "PDEPACK.spad" 1461505 1461513 1467455 1467460) (-910 "PDECOMP.spad" 1460975 1460992 1461495 1461500) (-909 "PDECAT.spad" 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380644) (-278 "E04GCFA.spad" 379721 379729 380175 380180) (-277 "E04FDFA.spad" 379257 379265 379711 379716) (-276 "E04DGFA.spad" 378793 378801 379247 379252) (-275 "E04AGNT.spad" 374643 374651 378783 378788) (-274 "DVARCAT.spad" 371533 371543 374633 374638) (-273 "DVARCAT.spad" 368421 368433 371523 371528) (-272 "DSMP.spad" 365795 365809 366100 366227) (-271 "DSEXT.spad" 365097 365107 365785 365790) (-270 "DSEXT.spad" 364306 364318 364996 365001) (-269 "DROPT.spad" 358265 358273 364296 364301) (-268 "DROPT1.spad" 357930 357940 358255 358260) (-267 "DROPT0.spad" 352787 352795 357920 357925) (-266 "DRAWPT.spad" 350960 350968 352777 352782) (-265 "DRAW.spad" 343836 343849 350950 350955) (-264 "DRAWHACK.spad" 343144 343154 343826 343831) (-263 "DRAWCX.spad" 340614 340622 343134 343139) (-262 "DRAWCURV.spad" 340161 340176 340604 340609) (-261 "DRAWCFUN.spad" 329693 329701 340151 340156) (-260 "DQAGG.spad" 327871 327881 329661 329688) (-259 "DPOLCAT.spad" 323220 323236 327739 327866) (-258 "DPOLCAT.spad" 318655 318673 323176 323181) (-257 "DPMO.spad" 310451 310467 310589 310802) (-256 "DPMM.spad" 302260 302278 302385 302598) (-255 "DOMTMPLT.spad" 302031 302039 302250 302255) (-254 "DOMCTOR.spad" 301786 301794 302021 302026) (-253 "DOMAIN.spad" 300873 300881 301776 301781) (-252 "DMP.spad" 298133 298148 298703 298830) (-251 "DLP.spad" 297485 297495 298123 298128) (-250 "DLIST.spad" 296064 296074 296668 296695) (-249 "DLAGG.spad" 294481 294491 296054 296059) (-248 "DIVRING.spad" 294023 294031 294425 294476) (-247 "DIVRING.spad" 293609 293619 294013 294018) (-246 "DISPLAY.spad" 291799 291807 293599 293604) (-245 "DIRPROD.spad" 279871 279887 280511 280610) (-244 "DIRPROD2.spad" 278689 278707 279861 279866) (-243 "DIRPCAT.spad" 277882 277898 278585 278684) (-242 "DIRPCAT.spad" 276702 276720 277407 277412) (-241 "DIOSP.spad" 275527 275535 276692 276697) (-240 "DIOPS.spad" 274523 274533 275507 275522) (-239 "DIOPS.spad" 273493 273505 274479 274484) (-238 "DIFRING.spad" 273331 273339 273473 273488) (-237 "DIFFSPC.spad" 272910 272918 273321 273326) (-236 "DIFFSPC.spad" 272487 272497 272900 272905) (-235 "DIFFMOD.spad" 271976 271986 272455 272482) (-234 "DIFFDOM.spad" 271141 271152 271966 271971) (-233 "DIFFDOM.spad" 270304 270317 271131 271136) (-232 "DIFEXT.spad" 270123 270133 270284 270299) (-231 "DIAGG.spad" 269753 269763 270103 270118) (-230 "DIAGG.spad" 269391 269403 269743 269748) (-229 "DHMATRIX.spad" 267703 267713 268848 268875) (-228 "DFSFUN.spad" 261343 261351 267693 267698) (-227 "DFLOAT.spad" 258074 258082 261233 261338) (-226 "DFINTTLS.spad" 256305 256321 258064 258069) (-225 "DERHAM.spad" 254219 254251 256285 256300) (-224 "DEQUEUE.spad" 253543 253553 253826 253853) (-223 "DEGRED.spad" 253160 253174 253533 253538) (-222 "DEFINTRF.spad" 250697 250707 253150 253155) (-221 "DEFINTEF.spad" 249207 249223 250687 250692) (-220 "DEFAST.spad" 248575 248583 249197 249202) (-219 "DECIMAL.spad" 246584 246592 246945 247038) (-218 "DDFACT.spad" 244397 244414 246574 246579) (-217 "DBLRESP.spad" 243997 244021 244387 244392) (-216 "DBASE.spad" 242661 242671 243987 243992) (-215 "DATAARY.spad" 242123 242136 242651 242656) (-214 "D03FAFA.spad" 241951 241959 242113 242118) (-213 "D03EEFA.spad" 241771 241779 241941 241946) (-212 "D03AGNT.spad" 240857 240865 241761 241766) (-211 "D02EJFA.spad" 240319 240327 240847 240852) (-210 "D02CJFA.spad" 239797 239805 240309 240314) (-209 "D02BHFA.spad" 239287 239295 239787 239792) (-208 "D02BBFA.spad" 238777 238785 239277 239282) (-207 "D02AGNT.spad" 233591 233599 238767 238772) (-206 "D01WGTS.spad" 231910 231918 233581 233586) (-205 "D01TRNS.spad" 231887 231895 231900 231905) (-204 "D01GBFA.spad" 231409 231417 231877 231882) (-203 "D01FCFA.spad" 230931 230939 231399 231404) (-202 "D01ASFA.spad" 230399 230407 230921 230926) (-201 "D01AQFA.spad" 229845 229853 230389 230394) (-200 "D01APFA.spad" 229269 229277 229835 229840) (-199 "D01ANFA.spad" 228763 228771 229259 229264) (-198 "D01AMFA.spad" 228273 228281 228753 228758) (-197 "D01ALFA.spad" 227813 227821 228263 228268) (-196 "D01AKFA.spad" 227339 227347 227803 227808) (-195 "D01AJFA.spad" 226862 226870 227329 227334) (-194 "D01AGNT.spad" 222929 222937 226852 226857) (-193 "CYCLOTOM.spad" 222435 222443 222919 222924) (-192 "CYCLES.spad" 219227 219235 222425 222430) (-191 "CVMP.spad" 218644 218654 219217 219222) (-190 "CTRIGMNP.spad" 217144 217160 218634 218639) (-189 "CTOR.spad" 216835 216843 217134 217139) (-188 "CTORKIND.spad" 216438 216446 216825 216830) (-187 "CTORCAT.spad" 215687 215695 216428 216433) (-186 "CTORCAT.spad" 214934 214944 215677 215682) (-185 "CTORCALL.spad" 214523 214533 214924 214929) (-184 "CSTTOOLS.spad" 213768 213781 214513 214518) (-183 "CRFP.spad" 207492 207505 213758 213763) (-182 "CRCEAST.spad" 207212 207220 207482 207487) (-181 "CRAPACK.spad" 206263 206273 207202 207207) (-180 "CPMATCH.spad" 205767 205782 206188 206193) (-179 "CPIMA.spad" 205472 205491 205757 205762) (-178 "COORDSYS.spad" 200481 200491 205462 205467) (-177 "CONTOUR.spad" 199892 199900 200471 200476) (-176 "CONTFRAC.spad" 195642 195652 199794 199887) (-175 "CONDUIT.spad" 195400 195408 195632 195637) (-174 "COMRING.spad" 195074 195082 195338 195395) (-173 "COMPPROP.spad" 194592 194600 195064 195069) (-172 "COMPLPAT.spad" 194359 194374 194582 194587) (-171 "COMPLEX.spad" 189736 189746 189980 190241) (-170 "COMPLEX2.spad" 189451 189463 189726 189731) (-169 "COMPILER.spad" 189000 189008 189441 189446) (-168 "COMPFACT.spad" 188602 188616 188990 188995) (-167 "COMPCAT.spad" 186674 186684 188336 188597) (-166 "COMPCAT.spad" 184474 184486 186138 186143) (-165 "COMMUPC.spad" 184222 184240 184464 184469) (-164 "COMMONOP.spad" 183755 183763 184212 184217) (-163 "COMM.spad" 183566 183574 183745 183750) (-162 "COMMAAST.spad" 183329 183337 183556 183561) (-161 "COMBOPC.spad" 182244 182252 183319 183324) (-160 "COMBINAT.spad" 181011 181021 182234 182239) (-159 "COMBF.spad" 178393 178409 181001 181006) (-158 "COLOR.spad" 177230 177238 178383 178388) (-157 "COLONAST.spad" 176896 176904 177220 177225) (-156 "CMPLXRT.spad" 176607 176624 176886 176891) (-155 "CLLCTAST.spad" 176269 176277 176597 176602) (-154 "CLIP.spad" 172377 172385 176259 176264) (-153 "CLIF.spad" 171032 171048 172333 172372) (-152 "CLAGG.spad" 167537 167547 171022 171027) (-151 "CLAGG.spad" 163913 163925 167400 167405) (-150 "CINTSLPE.spad" 163244 163257 163903 163908) (-149 "CHVAR.spad" 161382 161404 163234 163239) (-148 "CHARZ.spad" 161297 161305 161362 161377) (-147 "CHARPOL.spad" 160807 160817 161287 161292) (-146 "CHARNZ.spad" 160560 160568 160787 160802) (-145 "CHAR.spad" 158434 158442 160550 160555) (-144 "CFCAT.spad" 157762 157770 158424 158429) (-143 "CDEN.spad" 156958 156972 157752 157757) (-142 "CCLASS.spad" 155107 155115 156369 156408) (-141 "CATEGORY.spad" 154149 154157 155097 155102) (-140 "CATCTOR.spad" 154040 154048 154139 154144) (-139 "CATAST.spad" 153658 153666 154030 154035) (-138 "CASEAST.spad" 153372 153380 153648 153653) (-137 "CARTEN.spad" 148739 148763 153362 153367) (-136 "CARTEN2.spad" 148129 148156 148729 148734) (-135 "CARD.spad" 145424 145432 148103 148124) (-134 "CAPSLAST.spad" 145198 145206 145414 145419) (-133 "CACHSET.spad" 144822 144830 145188 145193) (-132 "CABMON.spad" 144377 144385 144812 144817) (-131 "BYTEORD.spad" 144052 144060 144367 144372) (-130 "BYTE.spad" 143479 143487 144042 144047) (-129 "BYTEBUF.spad" 141338 141346 142648 142675) (-128 "BTREE.spad" 140411 140421 140945 140972) (-127 "BTOURN.spad" 139416 139426 140018 140045) (-126 "BTCAT.spad" 138808 138818 139384 139411) (-125 "BTCAT.spad" 138220 138232 138798 138803) (-124 "BTAGG.spad" 137686 137694 138188 138215) (-123 "BTAGG.spad" 137172 137182 137676 137681) (-122 "BSTREE.spad" 135913 135923 136779 136806) (-121 "BRILL.spad" 134110 134121 135903 135908) (-120 "BRAGG.spad" 133050 133060 134100 134105) (-119 "BRAGG.spad" 131954 131966 133006 133011) (-118 "BPADICRT.spad" 129828 129840 130083 130176) (-117 "BPADIC.spad" 129492 129504 129754 129823) (-116 "BOUNDZRO.spad" 129148 129165 129482 129487) (-115 "BOP.spad" 124330 124338 129138 129143) (-114 "BOP1.spad" 121796 121806 124320 124325) (-113 "BOOLE.spad" 121446 121454 121786 121791) (-112 "BOOLEAN.spad" 120884 120892 121436 121441) (-111 "BMODULE.spad" 120596 120608 120852 120879) (-110 "BITS.spad" 120017 120025 120232 120259) (-109 "BINDING.spad" 119430 119438 120007 120012) (-108 "BINARY.spad" 117444 117452 117800 117893) (-107 "BGAGG.spad" 116649 116659 117424 117439) (-106 "BGAGG.spad" 115862 115874 116639 116644) (-105 "BFUNCT.spad" 115426 115434 115842 115857) (-104 "BEZOUT.spad" 114566 114593 115376 115381) (-103 "BBTREE.spad" 111411 111421 114173 114200) (-102 "BASTYPE.spad" 111083 111091 111401 111406) (-101 "BASTYPE.spad" 110753 110763 111073 111078) (-100 "BALFACT.spad" 110212 110225 110743 110748) (-99 "AUTOMOR.spad" 109663 109672 110192 110207) (-98 "ATTREG.spad" 106386 106393 109415 109658) (-97 "ATTRBUT.spad" 102409 102416 106366 106381) (-96 "ATTRAST.spad" 102126 102133 102399 102404) (-95 "ATRIG.spad" 101596 101603 102116 102121) (-94 "ATRIG.spad" 101064 101073 101586 101591) (-93 "ASTCAT.spad" 100968 100975 101054 101059) (-92 "ASTCAT.spad" 100870 100879 100958 100963) (-91 "ASTACK.spad" 100209 100218 100477 100504) (-90 "ASSOCEQ.spad" 99035 99046 100165 100170) (-89 "ASP9.spad" 98116 98129 99025 99030) (-88 "ASP8.spad" 97159 97172 98106 98111) (-87 "ASP80.spad" 96481 96494 97149 97154) (-86 "ASP7.spad" 95641 95654 96471 96476) (-85 "ASP78.spad" 95092 95105 95631 95636) (-84 "ASP77.spad" 94461 94474 95082 95087) (-83 "ASP74.spad" 93553 93566 94451 94456) (-82 "ASP73.spad" 92824 92837 93543 93548) (-81 "ASP6.spad" 91691 91704 92814 92819) (-80 "ASP55.spad" 90200 90213 91681 91686) (-79 "ASP50.spad" 88017 88030 90190 90195) (-78 "ASP4.spad" 87312 87325 88007 88012) (-77 "ASP49.spad" 86311 86324 87302 87307) (-76 "ASP42.spad" 84718 84757 86301 86306) (-75 "ASP41.spad" 83297 83336 84708 84713) (-74 "ASP35.spad" 82285 82298 83287 83292) (-73 "ASP34.spad" 81586 81599 82275 82280) (-72 "ASP33.spad" 81146 81159 81576 81581) (-71 "ASP31.spad" 80286 80299 81136 81141) (-70 "ASP30.spad" 79178 79191 80276 80281) (-69 "ASP29.spad" 78644 78657 79168 79173) (-68 "ASP28.spad" 69917 69930 78634 78639) (-67 "ASP27.spad" 68814 68827 69907 69912) (-66 "ASP24.spad" 67901 67914 68804 68809) (-65 "ASP20.spad" 67365 67378 67891 67896) (-64 "ASP1.spad" 66746 66759 67355 67360) (-63 "ASP19.spad" 61432 61445 66736 66741) (-62 "ASP12.spad" 60846 60859 61422 61427) (-61 "ASP10.spad" 60117 60130 60836 60841) (-60 "ARRAY2.spad" 59477 59486 59724 59751) (-59 "ARRAY1.spad" 58314 58323 58660 58687) (-58 "ARRAY12.spad" 57027 57038 58304 58309) (-57 "ARR2CAT.spad" 52801 52822 56995 57022) (-56 "ARR2CAT.spad" 48595 48618 52791 52796) (-55 "ARITY.spad" 47967 47974 48585 48590) (-54 "APPRULE.spad" 47227 47249 47957 47962) (-53 "APPLYORE.spad" 46846 46859 47217 47222) (-52 "ANY.spad" 45705 45712 46836 46841) (-51 "ANY1.spad" 44776 44785 45695 45700) (-50 "ANTISYM.spad" 43221 43237 44756 44771) (-49 "ANON.spad" 42914 42921 43211 43216) (-48 "AN.spad" 41223 41230 42730 42823) (-47 "AMR.spad" 39408 39419 41121 41218) (-46 "AMR.spad" 37430 37443 39145 39150) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-3 NIL 2279891 2279896 2279901 2279906) (-2 NIL 2279871 2279876 2279881 2279886) (-1 NIL 2279851 2279856 2279861 2279866) (0 NIL 2279831 2279836 2279841 2279846) (-1316 "ZMOD.spad" 2279640 2279653 2279769 2279826) (-1315 "ZLINDEP.spad" 2278706 2278717 2279630 2279635) (-1314 "ZDSOLVE.spad" 2268651 2268673 2278696 2278701) (-1313 "YSTREAM.spad" 2268146 2268157 2268641 2268646) (-1312 "YDIAGRAM.spad" 2267780 2267789 2268136 2268141) (-1311 "XRPOLY.spad" 2267000 2267020 2267636 2267705) (-1310 "XPR.spad" 2264795 2264808 2266718 2266817) (-1309 "XPOLY.spad" 2264350 2264361 2264651 2264720) (-1308 "XPOLYC.spad" 2263669 2263685 2264276 2264345) (-1307 "XPBWPOLY.spad" 2262106 2262126 2263449 2263518) (-1306 "XF.spad" 2260569 2260584 2262008 2262101) (-1305 "XF.spad" 2259012 2259029 2260453 2260458) (-1304 "XFALG.spad" 2256060 2256076 2258938 2259007) (-1303 "XEXPPKG.spad" 2255311 2255337 2256050 2256055) (-1302 "XDPOLY.spad" 2254925 2254941 2255167 2255236) (-1301 "XALG.spad" 2254585 2254596 2254881 2254920) (-1300 "WUTSET.spad" 2250424 2250441 2254231 2254258) (-1299 "WP.spad" 2249623 2249667 2250282 2250349) (-1298 "WHILEAST.spad" 2249421 2249430 2249613 2249618) (-1297 "WHEREAST.spad" 2249092 2249101 2249411 2249416) (-1296 "WFFINTBS.spad" 2246755 2246777 2249082 2249087) (-1295 "WEIER.spad" 2244977 2244988 2246745 2246750) (-1294 "VSPACE.spad" 2244650 2244661 2244945 2244972) (-1293 "VSPACE.spad" 2244343 2244356 2244640 2244645) (-1292 "VOID.spad" 2244020 2244029 2244333 2244338) (-1291 "VIEW.spad" 2241700 2241709 2244010 2244015) (-1290 "VIEWDEF.spad" 2236901 2236910 2241690 2241695) (-1289 "VIEW3D.spad" 2220862 2220871 2236891 2236896) (-1288 "VIEW2D.spad" 2208753 2208762 2220852 2220857) (-1287 "VECTOR.spad" 2207427 2207438 2207678 2207705) (-1286 "VECTOR2.spad" 2206066 2206079 2207417 2207422) (-1285 "VECTCAT.spad" 2203970 2203981 2206034 2206061) (-1284 "VECTCAT.spad" 2201681 2201694 2203747 2203752) (-1283 "VARIABLE.spad" 2201461 2201476 2201671 2201676) (-1282 "UTYPE.spad" 2201105 2201114 2201451 2201456) (-1281 "UTSODETL.spad" 2200400 2200424 2201061 2201066) (-1280 "UTSODE.spad" 2198616 2198636 2200390 2200395) (-1279 "UTS.spad" 2193563 2193591 2197083 2197180) (-1278 "UTSCAT.spad" 2191042 2191058 2193461 2193558) (-1277 "UTSCAT.spad" 2188165 2188183 2190586 2190591) (-1276 "UTS2.spad" 2187760 2187795 2188155 2188160) (-1275 "URAGG.spad" 2182433 2182444 2187750 2187755) (-1274 "URAGG.spad" 2177070 2177083 2182389 2182394) (-1273 "UPXSSING.spad" 2174715 2174741 2176151 2176284) (-1272 "UPXS.spad" 2172011 2172039 2172847 2172996) (-1271 "UPXSCONS.spad" 2169770 2169790 2170143 2170292) (-1270 "UPXSCCA.spad" 2168341 2168361 2169616 2169765) (-1269 "UPXSCCA.spad" 2167054 2167076 2168331 2168336) (-1268 "UPXSCAT.spad" 2165643 2165659 2166900 2167049) (-1267 "UPXS2.spad" 2165186 2165239 2165633 2165638) (-1266 "UPSQFREE.spad" 2163600 2163614 2165176 2165181) (-1265 "UPSCAT.spad" 2161387 2161411 2163498 2163595) (-1264 "UPSCAT.spad" 2158880 2158906 2160993 2160998) (-1263 "UPOLYC.spad" 2153920 2153931 2158722 2158875) (-1262 "UPOLYC.spad" 2148852 2148865 2153656 2153661) (-1261 "UPOLYC2.spad" 2148323 2148342 2148842 2148847) (-1260 "UP.spad" 2145429 2145444 2145816 2145969) (-1259 "UPMP.spad" 2144329 2144342 2145419 2145424) (-1258 "UPDIVP.spad" 2143894 2143908 2144319 2144324) (-1257 "UPDECOMP.spad" 2142139 2142153 2143884 2143889) (-1256 "UPCDEN.spad" 2141348 2141364 2142129 2142134) (-1255 "UP2.spad" 2140712 2140733 2141338 2141343) (-1254 "UNISEG.spad" 2140065 2140076 2140631 2140636) (-1253 "UNISEG2.spad" 2139562 2139575 2140021 2140026) (-1252 "UNIFACT.spad" 2138665 2138677 2139552 2139557) (-1251 "ULS.spad" 2128449 2128477 2129394 2129823) (-1250 "ULSCONS.spad" 2119583 2119603 2119953 2120102) (-1249 "ULSCCAT.spad" 2117320 2117340 2119429 2119578) (-1248 "ULSCCAT.spad" 2115165 2115187 2117276 2117281) (-1247 "ULSCAT.spad" 2113397 2113413 2115011 2115160) (-1246 "ULS2.spad" 2112911 2112964 2113387 2113392) (-1245 "UINT8.spad" 2112788 2112797 2112901 2112906) (-1244 "UINT64.spad" 2112664 2112673 2112778 2112783) (-1243 "UINT32.spad" 2112540 2112549 2112654 2112659) (-1242 "UINT16.spad" 2112416 2112425 2112530 2112535) (-1241 "UFD.spad" 2111481 2111490 2112342 2112411) (-1240 "UFD.spad" 2110608 2110619 2111471 2111476) (-1239 "UDVO.spad" 2109489 2109498 2110598 2110603) (-1238 "UDPO.spad" 2106982 2106993 2109445 2109450) (-1237 "TYPE.spad" 2106914 2106923 2106972 2106977) (-1236 "TYPEAST.spad" 2106833 2106842 2106904 2106909) (-1235 "TWOFACT.spad" 2105485 2105500 2106823 2106828) (-1234 "TUPLE.spad" 2104971 2104982 2105384 2105389) (-1233 "TUBETOOL.spad" 2101838 2101847 2104961 2104966) (-1232 "TUBE.spad" 2100485 2100502 2101828 2101833) (-1231 "TS.spad" 2099084 2099100 2100050 2100147) (-1230 "TSETCAT.spad" 2086211 2086228 2099052 2099079) (-1229 "TSETCAT.spad" 2073324 2073343 2086167 2086172) (-1228 "TRMANIP.spad" 2067690 2067707 2073030 2073035) (-1227 "TRIMAT.spad" 2066653 2066678 2067680 2067685) (-1226 "TRIGMNIP.spad" 2065180 2065197 2066643 2066648) (-1225 "TRIGCAT.spad" 2064692 2064701 2065170 2065175) (-1224 "TRIGCAT.spad" 2064202 2064213 2064682 2064687) (-1223 "TREE.spad" 2062777 2062788 2063809 2063836) (-1222 "TRANFUN.spad" 2062616 2062625 2062767 2062772) (-1221 "TRANFUN.spad" 2062453 2062464 2062606 2062611) (-1220 "TOPSP.spad" 2062127 2062136 2062443 2062448) (-1219 "TOOLSIGN.spad" 2061790 2061801 2062117 2062122) (-1218 "TEXTFILE.spad" 2060351 2060360 2061780 2061785) (-1217 "TEX.spad" 2057497 2057506 2060341 2060346) (-1216 "TEX1.spad" 2057053 2057064 2057487 2057492) (-1215 "TEMUTL.spad" 2056608 2056617 2057043 2057048) (-1214 "TBCMPPK.spad" 2054701 2054724 2056598 2056603) (-1213 "TBAGG.spad" 2053751 2053774 2054681 2054696) (-1212 "TBAGG.spad" 2052809 2052834 2053741 2053746) (-1211 "TANEXP.spad" 2052217 2052228 2052799 2052804) (-1210 "TALGOP.spad" 2051941 2051952 2052207 2052212) (-1209 "TABLE.spad" 2050352 2050375 2050622 2050649) (-1208 "TABLEAU.spad" 2049833 2049844 2050342 2050347) (-1207 "TABLBUMP.spad" 2046636 2046647 2049823 2049828) (-1206 "SYSTEM.spad" 2045864 2045873 2046626 2046631) (-1205 "SYSSOLP.spad" 2043347 2043358 2045854 2045859) (-1204 "SYSPTR.spad" 2043246 2043255 2043337 2043342) (-1203 "SYSNNI.spad" 2042428 2042439 2043236 2043241) (-1202 "SYSINT.spad" 2041832 2041843 2042418 2042423) (-1201 "SYNTAX.spad" 2038038 2038047 2041822 2041827) (-1200 "SYMTAB.spad" 2036106 2036115 2038028 2038033) (-1199 "SYMS.spad" 2032129 2032138 2036096 2036101) (-1198 "SYMPOLY.spad" 2031136 2031147 2031218 2031345) (-1197 "SYMFUNC.spad" 2030637 2030648 2031126 2031131) (-1196 "SYMBOL.spad" 2028140 2028149 2030627 2030632) (-1195 "SWITCH.spad" 2024911 2024920 2028130 2028135) (-1194 "SUTS.spad" 2021959 2021987 2023378 2023475) (-1193 "SUPXS.spad" 2019242 2019270 2020091 2020240) (-1192 "SUP.spad" 2015962 2015973 2016735 2016888) (-1191 "SUPFRACF.spad" 2015067 2015085 2015952 2015957) (-1190 "SUP2.spad" 2014459 2014472 2015057 2015062) (-1189 "SUMRF.spad" 2013433 2013444 2014449 2014454) (-1188 "SUMFS.spad" 2013070 2013087 2013423 2013428) (-1187 "SULS.spad" 2002841 2002869 2003799 2004228) (-1186 "SUCHTAST.spad" 2002610 2002619 2002831 2002836) (-1185 "SUCH.spad" 2002292 2002307 2002600 2002605) (-1184 "SUBSPACE.spad" 1994407 1994422 2002282 2002287) (-1183 "SUBRESP.spad" 1993577 1993591 1994363 1994368) (-1182 "STTF.spad" 1989676 1989692 1993567 1993572) (-1181 "STTFNC.spad" 1986144 1986160 1989666 1989671) (-1180 "STTAYLOR.spad" 1978779 1978790 1986025 1986030) (-1179 "STRTBL.spad" 1977284 1977301 1977433 1977460) (-1178 "STRING.spad" 1976693 1976702 1976707 1976734) (-1177 "STRICAT.spad" 1976481 1976490 1976661 1976688) (-1176 "STREAM.spad" 1973399 1973410 1976006 1976021) (-1175 "STREAM3.spad" 1972972 1972987 1973389 1973394) (-1174 "STREAM2.spad" 1972100 1972113 1972962 1972967) (-1173 "STREAM1.spad" 1971806 1971817 1972090 1972095) (-1172 "STINPROD.spad" 1970742 1970758 1971796 1971801) (-1171 "STEP.spad" 1969943 1969952 1970732 1970737) (-1170 "STEPAST.spad" 1969177 1969186 1969933 1969938) (-1169 "STBL.spad" 1967703 1967731 1967870 1967885) (-1168 "STAGG.spad" 1966778 1966789 1967693 1967698) (-1167 "STAGG.spad" 1965851 1965864 1966768 1966773) (-1166 "STACK.spad" 1965208 1965219 1965458 1965485) (-1165 "SREGSET.spad" 1962912 1962929 1964854 1964881) (-1164 "SRDCMPK.spad" 1961473 1961493 1962902 1962907) (-1163 "SRAGG.spad" 1956616 1956625 1961441 1961468) (-1162 "SRAGG.spad" 1951779 1951790 1956606 1956611) (-1161 "SQMATRIX.spad" 1949358 1949376 1950274 1950361) (-1160 "SPLTREE.spad" 1943910 1943923 1948794 1948821) (-1159 "SPLNODE.spad" 1940498 1940511 1943900 1943905) (-1158 "SPFCAT.spad" 1939307 1939316 1940488 1940493) (-1157 "SPECOUT.spad" 1937859 1937868 1939297 1939302) (-1156 "SPADXPT.spad" 1929454 1929463 1937849 1937854) (-1155 "spad-parser.spad" 1928919 1928928 1929444 1929449) (-1154 "SPADAST.spad" 1928620 1928629 1928909 1928914) (-1153 "SPACEC.spad" 1912819 1912830 1928610 1928615) (-1152 "SPACE3.spad" 1912595 1912606 1912809 1912814) (-1151 "SORTPAK.spad" 1912144 1912157 1912551 1912556) (-1150 "SOLVETRA.spad" 1909907 1909918 1912134 1912139) (-1149 "SOLVESER.spad" 1908435 1908446 1909897 1909902) (-1148 "SOLVERAD.spad" 1904461 1904472 1908425 1908430) (-1147 "SOLVEFOR.spad" 1902923 1902941 1904451 1904456) (-1146 "SNTSCAT.spad" 1902523 1902540 1902891 1902918) (-1145 "SMTS.spad" 1900795 1900821 1902088 1902185) (-1144 "SMP.spad" 1898270 1898290 1898660 1898787) (-1143 "SMITH.spad" 1897115 1897140 1898260 1898265) (-1142 "SMATCAT.spad" 1895225 1895255 1897059 1897110) (-1141 "SMATCAT.spad" 1893267 1893299 1895103 1895108) (-1140 "SKAGG.spad" 1892230 1892241 1893235 1893262) (-1139 "SINT.spad" 1891170 1891179 1892096 1892225) (-1138 "SIMPAN.spad" 1890898 1890907 1891160 1891165) (-1137 "SIG.spad" 1890228 1890237 1890888 1890893) (-1136 "SIGNRF.spad" 1889346 1889357 1890218 1890223) (-1135 "SIGNEF.spad" 1888625 1888642 1889336 1889341) (-1134 "SIGAST.spad" 1888010 1888019 1888615 1888620) (-1133 "SHP.spad" 1885938 1885953 1887966 1887971) (-1132 "SHDP.spad" 1874141 1874168 1874650 1874749) (-1131 "SGROUP.spad" 1873749 1873758 1874131 1874136) (-1130 "SGROUP.spad" 1873355 1873366 1873739 1873744) (-1129 "SGCF.spad" 1866494 1866503 1873345 1873350) (-1128 "SFRTCAT.spad" 1865424 1865441 1866462 1866489) (-1127 "SFRGCD.spad" 1864487 1864507 1865414 1865419) (-1126 "SFQCMPK.spad" 1859124 1859144 1864477 1864482) (-1125 "SFORT.spad" 1858563 1858577 1859114 1859119) (-1124 "SEXOF.spad" 1858406 1858446 1858553 1858558) (-1123 "SEX.spad" 1858298 1858307 1858396 1858401) (-1122 "SEXCAT.spad" 1856079 1856119 1858288 1858293) (-1121 "SET.spad" 1854403 1854414 1855500 1855539) (-1120 "SETMN.spad" 1852853 1852870 1854393 1854398) (-1119 "SETCAT.spad" 1852175 1852184 1852843 1852848) (-1118 "SETCAT.spad" 1851495 1851506 1852165 1852170) (-1117 "SETAGG.spad" 1848044 1848055 1851475 1851490) (-1116 "SETAGG.spad" 1844601 1844614 1848034 1848039) (-1115 "SEQAST.spad" 1844304 1844313 1844591 1844596) (-1114 "SEGXCAT.spad" 1843460 1843473 1844294 1844299) (-1113 "SEG.spad" 1843273 1843284 1843379 1843384) (-1112 "SEGCAT.spad" 1842198 1842209 1843263 1843268) (-1111 "SEGBIND.spad" 1841956 1841967 1842145 1842150) (-1110 "SEGBIND2.spad" 1841654 1841667 1841946 1841951) (-1109 "SEGAST.spad" 1841368 1841377 1841644 1841649) (-1108 "SEG2.spad" 1840803 1840816 1841324 1841329) (-1107 "SDVAR.spad" 1840079 1840090 1840793 1840798) (-1106 "SDPOL.spad" 1837412 1837423 1837703 1837830) (-1105 "SCPKG.spad" 1835501 1835512 1837402 1837407) (-1104 "SCOPE.spad" 1834654 1834663 1835491 1835496) (-1103 "SCACHE.spad" 1833350 1833361 1834644 1834649) (-1102 "SASTCAT.spad" 1833259 1833268 1833340 1833345) (-1101 "SAOS.spad" 1833131 1833140 1833249 1833254) (-1100 "SAERFFC.spad" 1832844 1832864 1833121 1833126) (-1099 "SAE.spad" 1830314 1830330 1830925 1831060) (-1098 "SAEFACT.spad" 1830015 1830035 1830304 1830309) (-1097 "RURPK.spad" 1827674 1827690 1830005 1830010) (-1096 "RULESET.spad" 1827127 1827151 1827664 1827669) (-1095 "RULE.spad" 1825367 1825391 1827117 1827122) (-1094 "RULECOLD.spad" 1825219 1825232 1825357 1825362) (-1093 "RTVALUE.spad" 1824954 1824963 1825209 1825214) (-1092 "RSTRCAST.spad" 1824671 1824680 1824944 1824949) (-1091 "RSETGCD.spad" 1821049 1821069 1824661 1824666) (-1090 "RSETCAT.spad" 1810985 1811002 1821017 1821044) (-1089 "RSETCAT.spad" 1800941 1800960 1810975 1810980) (-1088 "RSDCMPK.spad" 1799393 1799413 1800931 1800936) (-1087 "RRCC.spad" 1797777 1797807 1799383 1799388) (-1086 "RRCC.spad" 1796159 1796191 1797767 1797772) (-1085 "RPTAST.spad" 1795861 1795870 1796149 1796154) (-1084 "RPOLCAT.spad" 1775221 1775236 1795729 1795856) (-1083 "RPOLCAT.spad" 1754294 1754311 1774804 1774809) (-1082 "ROUTINE.spad" 1750177 1750186 1752941 1752968) (-1081 "ROMAN.spad" 1749505 1749514 1750043 1750172) (-1080 "ROIRC.spad" 1748585 1748617 1749495 1749500) (-1079 "RNS.spad" 1747488 1747497 1748487 1748580) (-1078 "RNS.spad" 1746477 1746488 1747478 1747483) (-1077 "RNG.spad" 1746212 1746221 1746467 1746472) (-1076 "RNGBIND.spad" 1745372 1745386 1746167 1746172) (-1075 "RMODULE.spad" 1745137 1745148 1745362 1745367) (-1074 "RMCAT2.spad" 1744557 1744614 1745127 1745132) (-1073 "RMATRIX.spad" 1743381 1743400 1743724 1743763) (-1072 "RMATCAT.spad" 1738960 1738991 1743337 1743376) (-1071 "RMATCAT.spad" 1734429 1734462 1738808 1738813) (-1070 "RLINSET.spad" 1733984 1733995 1734419 1734424) (-1069 "RINTERP.spad" 1733872 1733892 1733974 1733979) (-1068 "RING.spad" 1733342 1733351 1733852 1733867) (-1067 "RING.spad" 1732820 1732831 1733332 1733337) (-1066 "RIDIST.spad" 1732212 1732221 1732810 1732815) (-1065 "RGCHAIN.spad" 1730795 1730811 1731697 1731724) (-1064 "RGBCSPC.spad" 1730576 1730588 1730785 1730790) (-1063 "RGBCMDL.spad" 1730106 1730118 1730566 1730571) (-1062 "RF.spad" 1727748 1727759 1730096 1730101) (-1061 "RFFACTOR.spad" 1727210 1727221 1727738 1727743) (-1060 "RFFACT.spad" 1726945 1726957 1727200 1727205) (-1059 "RFDIST.spad" 1725941 1725950 1726935 1726940) (-1058 "RETSOL.spad" 1725360 1725373 1725931 1725936) (-1057 "RETRACT.spad" 1724788 1724799 1725350 1725355) (-1056 "RETRACT.spad" 1724214 1724227 1724778 1724783) (-1055 "RETAST.spad" 1724026 1724035 1724204 1724209) (-1054 "RESULT.spad" 1722086 1722095 1722673 1722700) (-1053 "RESRING.spad" 1721433 1721480 1722024 1722081) (-1052 "RESLATC.spad" 1720757 1720768 1721423 1721428) (-1051 "REPSQ.spad" 1720488 1720499 1720747 1720752) (-1050 "REP.spad" 1718042 1718051 1720478 1720483) (-1049 "REPDB.spad" 1717749 1717760 1718032 1718037) (-1048 "REP2.spad" 1707407 1707418 1717591 1717596) (-1047 "REP1.spad" 1701603 1701614 1707357 1707362) (-1046 "REGSET.spad" 1699400 1699417 1701249 1701276) (-1045 "REF.spad" 1698735 1698746 1699355 1699360) (-1044 "REDORDER.spad" 1697941 1697958 1698725 1698730) (-1043 "RECLOS.spad" 1696724 1696744 1697428 1697521) (-1042 "REALSOLV.spad" 1695864 1695873 1696714 1696719) (-1041 "REAL.spad" 1695736 1695745 1695854 1695859) (-1040 "REAL0Q.spad" 1693034 1693049 1695726 1695731) (-1039 "REAL0.spad" 1689878 1689893 1693024 1693029) (-1038 "RDUCEAST.spad" 1689599 1689608 1689868 1689873) (-1037 "RDIV.spad" 1689254 1689279 1689589 1689594) (-1036 "RDIST.spad" 1688821 1688832 1689244 1689249) (-1035 "RDETRS.spad" 1687685 1687703 1688811 1688816) (-1034 "RDETR.spad" 1685824 1685842 1687675 1687680) (-1033 "RDEEFS.spad" 1684923 1684940 1685814 1685819) (-1032 "RDEEF.spad" 1683933 1683950 1684913 1684918) (-1031 "RCFIELD.spad" 1681119 1681128 1683835 1683928) (-1030 "RCFIELD.spad" 1678391 1678402 1681109 1681114) (-1029 "RCAGG.spad" 1676319 1676330 1678381 1678386) (-1028 "RCAGG.spad" 1674174 1674187 1676238 1676243) (-1027 "RATRET.spad" 1673534 1673545 1674164 1674169) (-1026 "RATFACT.spad" 1673226 1673238 1673524 1673529) (-1025 "RANDSRC.spad" 1672545 1672554 1673216 1673221) (-1024 "RADUTIL.spad" 1672301 1672310 1672535 1672540) (-1023 "RADIX.spad" 1669125 1669139 1670671 1670764) (-1022 "RADFF.spad" 1666864 1666901 1666983 1667139) (-1021 "RADCAT.spad" 1666459 1666468 1666854 1666859) (-1020 "RADCAT.spad" 1666052 1666063 1666449 1666454) (-1019 "QUEUE.spad" 1665400 1665411 1665659 1665686) (-1018 "QUAT.spad" 1663888 1663899 1664231 1664296) (-1017 "QUATCT2.spad" 1663508 1663527 1663878 1663883) (-1016 "QUATCAT.spad" 1661678 1661689 1663438 1663503) (-1015 "QUATCAT.spad" 1659599 1659612 1661361 1661366) (-1014 "QUAGG.spad" 1658426 1658437 1659567 1659594) (-1013 "QQUTAST.spad" 1658194 1658203 1658416 1658421) (-1012 "QFORM.spad" 1657812 1657827 1658184 1658189) (-1011 "QFCAT.spad" 1656514 1656525 1657714 1657807) (-1010 "QFCAT.spad" 1654807 1654820 1656009 1656014) (-1009 "QFCAT2.spad" 1654499 1654516 1654797 1654802) (-1008 "QEQUAT.spad" 1654057 1654066 1654489 1654494) (-1007 "QCMPACK.spad" 1648803 1648823 1654047 1654052) (-1006 "QALGSET.spad" 1644881 1644914 1648717 1648722) (-1005 "QALGSET2.spad" 1642876 1642895 1644871 1644876) (-1004 "PWFFINTB.spad" 1640291 1640313 1642866 1642871) (-1003 "PUSHVAR.spad" 1639629 1639649 1640281 1640286) (-1002 "PTRANFN.spad" 1635756 1635767 1639619 1639624) (-1001 "PTPACK.spad" 1632843 1632854 1635746 1635751) (-1000 "PTFUNC2.spad" 1632665 1632680 1632833 1632838) (-999 "PTCAT.spad" 1631920 1631930 1632633 1632660) (-998 "PSQFR.spad" 1631227 1631251 1631910 1631915) (-997 "PSEUDLIN.spad" 1630113 1630123 1631217 1631222) (-996 "PSETPK.spad" 1615546 1615562 1629991 1629996) (-995 "PSETCAT.spad" 1609466 1609489 1615526 1615541) (-994 "PSETCAT.spad" 1603360 1603385 1609422 1609427) (-993 "PSCURVE.spad" 1602343 1602351 1603350 1603355) (-992 "PSCAT.spad" 1601126 1601155 1602241 1602338) (-991 "PSCAT.spad" 1599999 1600030 1601116 1601121) (-990 "PRTITION.spad" 1598697 1598705 1599989 1599994) (-989 "PRTDAST.spad" 1598416 1598424 1598687 1598692) (-988 "PRS.spad" 1587978 1587995 1598372 1598377) (-987 "PRQAGG.spad" 1587413 1587423 1587946 1587973) (-986 "PROPLOG.spad" 1586985 1586993 1587403 1587408) (-985 "PROPFUN2.spad" 1586608 1586621 1586975 1586980) (-984 "PROPFUN1.spad" 1586006 1586017 1586598 1586603) (-983 "PROPFRML.spad" 1584574 1584585 1585996 1586001) (-982 "PROPERTY.spad" 1584062 1584070 1584564 1584569) (-981 "PRODUCT.spad" 1581744 1581756 1582028 1582083) (-980 "PR.spad" 1580136 1580148 1580835 1580962) (-979 "PRINT.spad" 1579888 1579896 1580126 1580131) (-978 "PRIMES.spad" 1578141 1578151 1579878 1579883) (-977 "PRIMELT.spad" 1576222 1576236 1578131 1578136) (-976 "PRIMCAT.spad" 1575849 1575857 1576212 1576217) (-975 "PRIMARR.spad" 1574854 1574864 1575032 1575059) (-974 "PRIMARR2.spad" 1573621 1573633 1574844 1574849) (-973 "PREASSOC.spad" 1573003 1573015 1573611 1573616) (-972 "PPCURVE.spad" 1572140 1572148 1572993 1572998) (-971 "PORTNUM.spad" 1571915 1571923 1572130 1572135) (-970 "POLYROOT.spad" 1570764 1570786 1571871 1571876) (-969 "POLY.spad" 1568099 1568109 1568614 1568741) (-968 "POLYLIFT.spad" 1567364 1567387 1568089 1568094) (-967 "POLYCATQ.spad" 1565482 1565504 1567354 1567359) (-966 "POLYCAT.spad" 1558952 1558973 1565350 1565477) (-965 "POLYCAT.spad" 1551760 1551783 1558160 1558165) (-964 "POLY2UP.spad" 1551212 1551226 1551750 1551755) (-963 "POLY2.spad" 1550809 1550821 1551202 1551207) (-962 "POLUTIL.spad" 1549750 1549779 1550765 1550770) (-961 "POLTOPOL.spad" 1548498 1548513 1549740 1549745) (-960 "POINT.spad" 1547336 1547346 1547423 1547450) (-959 "PNTHEORY.spad" 1544038 1544046 1547326 1547331) (-958 "PMTOOLS.spad" 1542813 1542827 1544028 1544033) (-957 "PMSYM.spad" 1542362 1542372 1542803 1542808) (-956 "PMQFCAT.spad" 1541953 1541967 1542352 1542357) (-955 "PMPRED.spad" 1541432 1541446 1541943 1541948) (-954 "PMPREDFS.spad" 1540886 1540908 1541422 1541427) (-953 "PMPLCAT.spad" 1539966 1539984 1540818 1540823) (-952 "PMLSAGG.spad" 1539551 1539565 1539956 1539961) (-951 "PMKERNEL.spad" 1539130 1539142 1539541 1539546) (-950 "PMINS.spad" 1538710 1538720 1539120 1539125) (-949 "PMFS.spad" 1538287 1538305 1538700 1538705) (-948 "PMDOWN.spad" 1537577 1537591 1538277 1538282) (-947 "PMASS.spad" 1536587 1536595 1537567 1537572) (-946 "PMASSFS.spad" 1535554 1535570 1536577 1536582) (-945 "PLOTTOOL.spad" 1535334 1535342 1535544 1535549) (-944 "PLOT.spad" 1530257 1530265 1535324 1535329) (-943 "PLOT3D.spad" 1526721 1526729 1530247 1530252) (-942 "PLOT1.spad" 1525878 1525888 1526711 1526716) (-941 "PLEQN.spad" 1513168 1513195 1525868 1525873) (-940 "PINTERP.spad" 1512790 1512809 1513158 1513163) (-939 "PINTERPA.spad" 1512574 1512590 1512780 1512785) (-938 "PI.spad" 1512183 1512191 1512548 1512569) (-937 "PID.spad" 1511153 1511161 1512109 1512178) (-936 "PICOERCE.spad" 1510810 1510820 1511143 1511148) (-935 "PGROEB.spad" 1509411 1509425 1510800 1510805) (-934 "PGE.spad" 1501028 1501036 1509401 1509406) (-933 "PGCD.spad" 1499918 1499935 1501018 1501023) (-932 "PFRPAC.spad" 1499067 1499077 1499908 1499913) (-931 "PFR.spad" 1495730 1495740 1498969 1499062) (-930 "PFOTOOLS.spad" 1494988 1495004 1495720 1495725) (-929 "PFOQ.spad" 1494358 1494376 1494978 1494983) (-928 "PFO.spad" 1493777 1493804 1494348 1494353) (-927 "PF.spad" 1493351 1493363 1493582 1493675) (-926 "PFECAT.spad" 1491033 1491041 1493277 1493346) (-925 "PFECAT.spad" 1488743 1488753 1490989 1490994) (-924 "PFBRU.spad" 1486631 1486643 1488733 1488738) (-923 "PFBR.spad" 1484191 1484214 1486621 1486626) (-922 "PERM.spad" 1479998 1480008 1484021 1484036) (-921 "PERMGRP.spad" 1474768 1474778 1479988 1479993) (-920 "PERMCAT.spad" 1473429 1473439 1474748 1474763) (-919 "PERMAN.spad" 1471961 1471975 1473419 1473424) (-918 "PENDTREE.spad" 1471302 1471312 1471590 1471595) (-917 "PDSPC.spad" 1470115 1470125 1471292 1471297) (-916 "PDSPC.spad" 1468926 1468938 1470105 1470110) (-915 "PDRING.spad" 1468768 1468778 1468906 1468921) (-914 "PDMOD.spad" 1468584 1468596 1468736 1468763) (-913 "PDEPROB.spad" 1467599 1467607 1468574 1468579) (-912 "PDEPACK.spad" 1461639 1461647 1467589 1467594) (-911 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(-836 "OMERRK.spad" 1365543 1365551 1366499 1366504) (-835 "OMENC.spad" 1364887 1364895 1365533 1365538) (-834 "OMDEV.spad" 1359196 1359204 1364877 1364882) (-833 "OMCONN.spad" 1358605 1358613 1359186 1359191) (-832 "OINTDOM.spad" 1358368 1358376 1358531 1358600) (-831 "OFMONOID.spad" 1356491 1356501 1358324 1358329) (-830 "ODVAR.spad" 1355752 1355762 1356481 1356486) (-829 "ODR.spad" 1355396 1355422 1355564 1355713) (-828 "ODPOL.spad" 1352685 1352695 1353025 1353152) (-827 "ODP.spad" 1341024 1341044 1341397 1341496) (-826 "ODETOOLS.spad" 1339673 1339692 1341014 1341019) (-825 "ODESYS.spad" 1337367 1337384 1339663 1339668) (-824 "ODERTRIC.spad" 1333376 1333393 1337324 1337329) (-823 "ODERED.spad" 1332775 1332799 1333366 1333371) (-822 "ODERAT.spad" 1330390 1330407 1332765 1332770) (-821 "ODEPRRIC.spad" 1327427 1327449 1330380 1330385) (-820 "ODEPROB.spad" 1326684 1326692 1327417 1327422) (-819 "ODEPRIM.spad" 1324018 1324040 1326674 1326679) (-818 "ODEPAL.spad" 1323404 1323428 1324008 1324013) (-817 "ODEPACK.spad" 1310070 1310078 1323394 1323399) (-816 "ODEINT.spad" 1309505 1309521 1310060 1310065) (-815 "ODEIFTBL.spad" 1306900 1306908 1309495 1309500) (-814 "ODEEF.spad" 1302391 1302407 1306890 1306895) (-813 "ODECONST.spad" 1301928 1301946 1302381 1302386) (-812 "ODECAT.spad" 1300526 1300534 1301918 1301923) (-811 "OCT.spad" 1298662 1298672 1299376 1299415) (-810 "OCTCT2.spad" 1298308 1298329 1298652 1298657) (-809 "OC.spad" 1296104 1296114 1298264 1298303) (-808 "OC.spad" 1293625 1293637 1295787 1295792) (-807 "OCAMON.spad" 1293473 1293481 1293615 1293620) (-806 "OASGP.spad" 1293288 1293296 1293463 1293468) (-805 "OAMONS.spad" 1292810 1292818 1293278 1293283) (-804 "OAMON.spad" 1292671 1292679 1292800 1292805) (-803 "OAGROUP.spad" 1292533 1292541 1292661 1292666) (-802 "NUMTUBE.spad" 1292124 1292140 1292523 1292528) (-801 "NUMQUAD.spad" 1280100 1280108 1292114 1292119) (-800 "NUMODE.spad" 1271454 1271462 1280090 1280095) (-799 "NUMINT.spad" 1269020 1269028 1271444 1271449) (-798 "NUMFMT.spad" 1267860 1267868 1269010 1269015) (-797 "NUMERIC.spad" 1259974 1259984 1267665 1267670) (-796 "NTSCAT.spad" 1258482 1258498 1259942 1259969) (-795 "NTPOLFN.spad" 1258033 1258043 1258399 1258404) (-794 "NSUP.spad" 1250986 1250996 1255526 1255679) (-793 "NSUP2.spad" 1250378 1250390 1250976 1250981) (-792 "NSMP.spad" 1246608 1246627 1246916 1247043) (-791 "NREP.spad" 1244986 1245000 1246598 1246603) (-790 "NPCOEF.spad" 1244232 1244252 1244976 1244981) (-789 "NORMRETR.spad" 1243830 1243869 1244222 1244227) (-788 "NORMPK.spad" 1241732 1241751 1243820 1243825) (-787 "NORMMA.spad" 1241420 1241446 1241722 1241727) (-786 "NONE.spad" 1241161 1241169 1241410 1241415) (-785 "NONE1.spad" 1240837 1240847 1241151 1241156) (-784 "NODE1.spad" 1240324 1240340 1240827 1240832) (-783 "NNI.spad" 1239219 1239227 1240298 1240319) (-782 "NLINSOL.spad" 1237845 1237855 1239209 1239214) (-781 "NIPROB.spad" 1236386 1236394 1237835 1237840) (-780 "NFINTBAS.spad" 1233946 1233963 1236376 1236381) (-779 "NETCLT.spad" 1233920 1233931 1233936 1233941) (-778 "NCODIV.spad" 1232136 1232152 1233910 1233915) (-777 "NCNTFRAC.spad" 1231778 1231792 1232126 1232131) (-776 "NCEP.spad" 1229944 1229958 1231768 1231773) (-775 "NASRING.spad" 1229540 1229548 1229934 1229939) (-774 "NASRING.spad" 1229134 1229144 1229530 1229535) (-773 "NARNG.spad" 1228486 1228494 1229124 1229129) (-772 "NARNG.spad" 1227836 1227846 1228476 1228481) (-771 "NAGSP.spad" 1226913 1226921 1227826 1227831) (-770 "NAGS.spad" 1216574 1216582 1226903 1226908) (-769 "NAGF07.spad" 1215005 1215013 1216564 1216569) (-768 "NAGF04.spad" 1209407 1209415 1214995 1215000) (-767 "NAGF02.spad" 1203476 1203484 1209397 1209402) (-766 "NAGF01.spad" 1199237 1199245 1203466 1203471) (-765 "NAGE04.spad" 1192937 1192945 1199227 1199232) (-764 "NAGE02.spad" 1183597 1183605 1192927 1192932) (-763 "NAGE01.spad" 1179599 1179607 1183587 1183592) (-762 "NAGD03.spad" 1177603 1177611 1179589 1179594) (-761 "NAGD02.spad" 1170350 1170358 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380782 380790 381192 381197) (-280 "E04JAFA.spad" 380318 380326 380772 380777) (-279 "E04GCFA.spad" 379854 379862 380308 380313) (-278 "E04FDFA.spad" 379390 379398 379844 379849) (-277 "E04DGFA.spad" 378926 378934 379380 379385) (-276 "E04AGNT.spad" 374776 374784 378916 378921) (-275 "DVARCAT.spad" 371666 371676 374766 374771) (-274 "DVARCAT.spad" 368554 368566 371656 371661) (-273 "DSMP.spad" 365928 365942 366233 366360) (-272 "DSEXT.spad" 365230 365240 365918 365923) (-271 "DSEXT.spad" 364439 364451 365129 365134) (-270 "DROPT.spad" 358398 358406 364429 364434) (-269 "DROPT1.spad" 358063 358073 358388 358393) (-268 "DROPT0.spad" 352920 352928 358053 358058) (-267 "DRAWPT.spad" 351093 351101 352910 352915) (-266 "DRAW.spad" 343969 343982 351083 351088) (-265 "DRAWHACK.spad" 343277 343287 343959 343964) (-264 "DRAWCX.spad" 340747 340755 343267 343272) (-263 "DRAWCURV.spad" 340294 340309 340737 340742) (-262 "DRAWCFUN.spad" 329826 329834 340284 340289) (-261 "DQAGG.spad" 328004 328014 329794 329821) (-260 "DPOLCAT.spad" 323353 323369 327872 327999) (-259 "DPOLCAT.spad" 318788 318806 323309 323314) (-258 "DPMO.spad" 310584 310600 310722 310935) (-257 "DPMM.spad" 302393 302411 302518 302731) (-256 "DOMTMPLT.spad" 302164 302172 302383 302388) (-255 "DOMCTOR.spad" 301919 301927 302154 302159) (-254 "DOMAIN.spad" 301006 301014 301909 301914) (-253 "DMP.spad" 298266 298281 298836 298963) (-252 "DMEXT.spad" 298133 298143 298234 298261) (-251 "DLP.spad" 297485 297495 298123 298128) (-250 "DLIST.spad" 296064 296074 296668 296695) (-249 "DLAGG.spad" 294481 294491 296054 296059) (-248 "DIVRING.spad" 294023 294031 294425 294476) (-247 "DIVRING.spad" 293609 293619 294013 294018) (-246 "DISPLAY.spad" 291799 291807 293599 293604) (-245 "DIRPROD.spad" 279871 279887 280511 280610) (-244 "DIRPROD2.spad" 278689 278707 279861 279866) (-243 "DIRPCAT.spad" 277882 277898 278585 278684) (-242 "DIRPCAT.spad" 276702 276720 277407 277412) (-241 "DIOSP.spad" 275527 275535 276692 276697) (-240 "DIOPS.spad" 274523 274533 275507 275522) (-239 "DIOPS.spad" 273493 273505 274479 274484) (-238 "DIFRING.spad" 273331 273339 273473 273488) (-237 "DIFFSPC.spad" 272910 272918 273321 273326) (-236 "DIFFSPC.spad" 272487 272497 272900 272905) (-235 "DIFFMOD.spad" 271976 271986 272455 272482) (-234 "DIFFDOM.spad" 271141 271152 271966 271971) (-233 "DIFFDOM.spad" 270304 270317 271131 271136) (-232 "DIFEXT.spad" 270123 270133 270284 270299) (-231 "DIAGG.spad" 269753 269763 270103 270118) (-230 "DIAGG.spad" 269391 269403 269743 269748) (-229 "DHMATRIX.spad" 267703 267713 268848 268875) (-228 "DFSFUN.spad" 261343 261351 267693 267698) (-227 "DFLOAT.spad" 258074 258082 261233 261338) (-226 "DFINTTLS.spad" 256305 256321 258064 258069) (-225 "DERHAM.spad" 254219 254251 256285 256300) (-224 "DEQUEUE.spad" 253543 253553 253826 253853) (-223 "DEGRED.spad" 253160 253174 253533 253538) (-222 "DEFINTRF.spad" 250697 250707 253150 253155) (-221 "DEFINTEF.spad" 249207 249223 250687 250692) (-220 "DEFAST.spad" 248575 248583 249197 249202) (-219 "DECIMAL.spad" 246584 246592 246945 247038) (-218 "DDFACT.spad" 244397 244414 246574 246579) (-217 "DBLRESP.spad" 243997 244021 244387 244392) (-216 "DBASE.spad" 242661 242671 243987 243992) (-215 "DATAARY.spad" 242123 242136 242651 242656) (-214 "D03FAFA.spad" 241951 241959 242113 242118) (-213 "D03EEFA.spad" 241771 241779 241941 241946) (-212 "D03AGNT.spad" 240857 240865 241761 241766) (-211 "D02EJFA.spad" 240319 240327 240847 240852) (-210 "D02CJFA.spad" 239797 239805 240309 240314) (-209 "D02BHFA.spad" 239287 239295 239787 239792) (-208 "D02BBFA.spad" 238777 238785 239277 239282) (-207 "D02AGNT.spad" 233591 233599 238767 238772) (-206 "D01WGTS.spad" 231910 231918 233581 233586) (-205 "D01TRNS.spad" 231887 231895 231900 231905) (-204 "D01GBFA.spad" 231409 231417 231877 231882) (-203 "D01FCFA.spad" 230931 230939 231399 231404) (-202 "D01ASFA.spad" 230399 230407 230921 230926) (-201 "D01AQFA.spad" 229845 229853 230389 230394) (-200 "D01APFA.spad" 229269 229277 229835 229840) (-199 "D01ANFA.spad" 228763 228771 229259 229264) (-198 "D01AMFA.spad" 228273 228281 228753 228758) (-197 "D01ALFA.spad" 227813 227821 228263 228268) (-196 "D01AKFA.spad" 227339 227347 227803 227808) (-195 "D01AJFA.spad" 226862 226870 227329 227334) (-194 "D01AGNT.spad" 222929 222937 226852 226857) (-193 "CYCLOTOM.spad" 222435 222443 222919 222924) (-192 "CYCLES.spad" 219227 219235 222425 222430) (-191 "CVMP.spad" 218644 218654 219217 219222) (-190 "CTRIGMNP.spad" 217144 217160 218634 218639) (-189 "CTOR.spad" 216835 216843 217134 217139) (-188 "CTORKIND.spad" 216438 216446 216825 216830) (-187 "CTORCAT.spad" 215687 215695 216428 216433) (-186 "CTORCAT.spad" 214934 214944 215677 215682) (-185 "CTORCALL.spad" 214523 214533 214924 214929) (-184 "CSTTOOLS.spad" 213768 213781 214513 214518) (-183 "CRFP.spad" 207492 207505 213758 213763) (-182 "CRCEAST.spad" 207212 207220 207482 207487) (-181 "CRAPACK.spad" 206263 206273 207202 207207) (-180 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(-160 "COMBINAT.spad" 181011 181021 182234 182239) (-159 "COMBF.spad" 178393 178409 181001 181006) (-158 "COLOR.spad" 177230 177238 178383 178388) (-157 "COLONAST.spad" 176896 176904 177220 177225) (-156 "CMPLXRT.spad" 176607 176624 176886 176891) (-155 "CLLCTAST.spad" 176269 176277 176597 176602) (-154 "CLIP.spad" 172377 172385 176259 176264) (-153 "CLIF.spad" 171032 171048 172333 172372) (-152 "CLAGG.spad" 167537 167547 171022 171027) (-151 "CLAGG.spad" 163913 163925 167400 167405) (-150 "CINTSLPE.spad" 163244 163257 163903 163908) (-149 "CHVAR.spad" 161382 161404 163234 163239) (-148 "CHARZ.spad" 161297 161305 161362 161377) (-147 "CHARPOL.spad" 160807 160817 161287 161292) (-146 "CHARNZ.spad" 160560 160568 160787 160802) (-145 "CHAR.spad" 158434 158442 160550 160555) (-144 "CFCAT.spad" 157762 157770 158424 158429) (-143 "CDEN.spad" 156958 156972 157752 157757) (-142 "CCLASS.spad" 155107 155115 156369 156408) (-141 "CATEGORY.spad" 154149 154157 155097 155102) (-140 "CATCTOR.spad" 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134105) (-119 "BRAGG.spad" 131954 131966 133006 133011) (-118 "BPADICRT.spad" 129828 129840 130083 130176) (-117 "BPADIC.spad" 129492 129504 129754 129823) (-116 "BOUNDZRO.spad" 129148 129165 129482 129487) (-115 "BOP.spad" 124330 124338 129138 129143) (-114 "BOP1.spad" 121796 121806 124320 124325) (-113 "BOOLE.spad" 121446 121454 121786 121791) (-112 "BOOLEAN.spad" 120884 120892 121436 121441) (-111 "BMODULE.spad" 120596 120608 120852 120879) (-110 "BITS.spad" 120017 120025 120232 120259) (-109 "BINDING.spad" 119430 119438 120007 120012) (-108 "BINARY.spad" 117444 117452 117800 117893) (-107 "BGAGG.spad" 116649 116659 117424 117439) (-106 "BGAGG.spad" 115862 115874 116639 116644) (-105 "BFUNCT.spad" 115426 115434 115842 115857) (-104 "BEZOUT.spad" 114566 114593 115376 115381) (-103 "BBTREE.spad" 111411 111421 114173 114200) (-102 "BASTYPE.spad" 111083 111091 111401 111406) (-101 "BASTYPE.spad" 110753 110763 111073 111078) (-100 "BALFACT.spad" 110212 110225 110743 110748) (-99 "AUTOMOR.spad" 109663 109672 110192 110207) (-98 "ATTREG.spad" 106386 106393 109415 109658) (-97 "ATTRBUT.spad" 102409 102416 106366 106381) (-96 "ATTRAST.spad" 102126 102133 102399 102404) (-95 "ATRIG.spad" 101596 101603 102116 102121) (-94 "ATRIG.spad" 101064 101073 101586 101591) (-93 "ASTCAT.spad" 100968 100975 101054 101059) (-92 "ASTCAT.spad" 100870 100879 100958 100963) (-91 "ASTACK.spad" 100209 100218 100477 100504) (-90 "ASSOCEQ.spad" 99035 99046 100165 100170) (-89 "ASP9.spad" 98116 98129 99025 99030) (-88 "ASP8.spad" 97159 97172 98106 98111) (-87 "ASP80.spad" 96481 96494 97149 97154) (-86 "ASP7.spad" 95641 95654 96471 96476) (-85 "ASP78.spad" 95092 95105 95631 95636) (-84 "ASP77.spad" 94461 94474 95082 95087) (-83 "ASP74.spad" 93553 93566 94451 94456) (-82 "ASP73.spad" 92824 92837 93543 93548) (-81 "ASP6.spad" 91691 91704 92814 92819) (-80 "ASP55.spad" 90200 90213 91681 91686) (-79 "ASP50.spad" 88017 88030 90190 90195) (-78 "ASP4.spad" 87312 87325 88007 88012) (-77 "ASP49.spad" 86311 86324 87302 87307) (-76 "ASP42.spad" 84718 84757 86301 86306) (-75 "ASP41.spad" 83297 83336 84708 84713) (-74 "ASP35.spad" 82285 82298 83287 83292) (-73 "ASP34.spad" 81586 81599 82275 82280) (-72 "ASP33.spad" 81146 81159 81576 81581) (-71 "ASP31.spad" 80286 80299 81136 81141) (-70 "ASP30.spad" 79178 79191 80276 80281) (-69 "ASP29.spad" 78644 78657 79168 79173) (-68 "ASP28.spad" 69917 69930 78634 78639) (-67 "ASP27.spad" 68814 68827 69907 69912) (-66 "ASP24.spad" 67901 67914 68804 68809) (-65 "ASP20.spad" 67365 67378 67891 67896) (-64 "ASP1.spad" 66746 66759 67355 67360) (-63 "ASP19.spad" 61432 61445 66736 66741) (-62 "ASP12.spad" 60846 60859 61422 61427) (-61 "ASP10.spad" 60117 60130 60836 60841) (-60 "ARRAY2.spad" 59477 59486 59724 59751) (-59 "ARRAY1.spad" 58314 58323 58660 58687) (-58 "ARRAY12.spad" 57027 57038 58304 58309) (-57 "ARR2CAT.spad" 52801 52822 56995 57022) (-56 "ARR2CAT.spad" 48595 48618 52791 52796) (-55 "ARITY.spad" 47967 47974 48585 48590) (-54 "APPRULE.spad" 47227 47249 47957 47962) (-53 "APPLYORE.spad" 46846 46859 47217 47222) (-52 "ANY.spad" 45705 45712 46836 46841) (-51 "ANY1.spad" 44776 44785 45695 45700) (-50 "ANTISYM.spad" 43221 43237 44756 44771) (-49 "ANON.spad" 42914 42921 43211 43216) (-48 "AN.spad" 41223 41230 42730 42823) (-47 "AMR.spad" 39408 39419 41121 41218) (-46 "AMR.spad" 37430 37443 39145 39150) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index d15cee09..b7593426 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,1148 +1,1148 @@
 
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. -1235) T) ((-1017 . -624) 190642) ((-705 . -271) 190624) ((-705 . -232) 190606) ((-725 . -111) 190571) ((-655 . -34) T) ((-250 . -500) 190555) ((-1314 . -1169) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-1307 . -132) T) ((-1119 . -1115) 190539) ((-173 . -1117) T) ((-1305 . -132) T) ((-1298 . -102) T) ((-1281 . -624) 190505) ((-1277 . -1235) T) ((-1270 . -1235) T) ((-967 . -924) 190484) ((-1270 . -1055) 190419) ((-1249 . -1235) T) ((-1249 . -898) NIL) ((-526 . -627) 190403) ((-1249 . -896) 190355) ((-1249 . -1055) 190321) ((-1229 . -525) 190288) ((-492 . -924) 190267) ((-1207 . -625) NIL) ((-1207 . -624) 190249) ((-1104 . -728) 190098) ((-1079 . -659) 190070) ((-967 . -659) 189959) ((-608 . -501) 189940) ((-596 . -501) 189921) ((-793 . -728) 189750) ((-608 . -624) 189716) ((-596 . -624) 189682) ((-547 . -624) 189664) ((-547 . -625) 189645) ((-791 . -728) 189494) ((-1094 . -102) T) ((-391 . -25) T) ((-634 . -657) 189466) ((-391 . -21) T) ((-492 . -659) 189355) ((-472 . -728) 189326) ((-465 . -728) 189175) ((-1004 . -102) T) ((-1159 . -1140) 189120) ((-1063 . -1228) 189049) ((-916 . -318) 188987) ((-748 . -102) T) ((-118 . -657) 188917) ((-616 . -627) 188899) ((-887 . -93) T) ((-725 . -627) 188853) ((-542 . -25) T) ((-692 . -93) T) ((-687 . -93) T) ((-675 . -624) 188835) ((-656 . -501) 188816) ((-142 . -102) T) ((-44 . -132) T) ((-656 . -624) 188769) ((-606 . -1235) T) ((-353 . -1075) T) ((-298 . -1129) T) ((-489 . -93) T) ((-418 . -237) 188720) ((-365 . -624) 188702) ((-362 . -624) 188684) ((-354 . -624) 188666) ((-272 . -625) 188414) ((-272 . -624) 188396) ((-252 . -624) 188378) ((-252 . -625) 188239) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1158 . -624) 188221) ((-1137 . -651) 188208) ((-1137 . -1068) 188195) ((-830 . -737) T) ((-830 . -868) T) ((-613 . -297) 188172) ((-592 . -728) 188137) ((-490 . -625) NIL) ((-490 . -624) 188119) ((-529 . -728) 188064) ((-325 . -102) T) ((-322 . -102) T) ((-298 . -23) T) ((-153 . -132) T) ((-925 . -624) 188046) ((-925 . -625) 188028) ((-397 . -737) T) ((-883 . -1073) 187980) ((-883 . -111) 187918) ((-725 . -1066) T) ((-723 . -1261) 187902) ((-705 . -359) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-530 . -624) 187834) ((-389 . -806) T) ((-225 . -1117) T) ((-169 . -1235) T) ((-389 . -803) T) ((-227 . -805) T) ((-227 . -802) T) ((-59 . -625) 187795) ((-59 . -624) 187707) ((-227 . -737) T) ((-527 . -625) 187668) ((-527 . -624) 187580) ((-508 . -624) 187512) ((-507 . -625) 187473) ((-507 . -624) 187385) ((-1097 . -373) 187336) ((-40 . -422) 187313) ((-77 . -1235) T) ((-882 . -924) NIL) ((-369 . -338) 187297) ((-369 . -373) T) ((-363 . -338) 187281) ((-363 . -373) T) ((-355 . -338) 187265) ((-355 . -373) T) ((-325 . -293) 187244) ((-108 . -373) T) ((-70 . -1235) T) ((-1249 . -348) 187196) ((-882 . -659) 187141) ((-1249 . -387) 187093) ((-979 . -132) 186948) ((-826 . -132) 186819) ((-973 . -662) 186803) ((-1104 . -174) 186714) ((-973 . -383) 186698) ((-1079 . -805) T) ((-1079 . -802) T) ((-883 . -627) 186596) ((-793 . -174) 186487) ((-791 . -174) 186398) ((-827 . -47) 186360) ((-1079 . -737) T) ((-336 . -500) 186344) ((-967 . -737) T) ((-1298 . -318) 186282) ((-1277 . -913) 186195) ((-465 . -174) 186106) ((-250 . -295) 186058) ((-1270 . -913) 185964) ((-1269 . -1073) 185799) ((-1249 . -913) 185632) ((-492 . -737) T) ((-1248 . -1073) 185440) ((-1229 . -299) 185419) ((-1204 . -1235) T) ((-1201 . -378) T) ((-1200 . -378) T) ((-1163 . -152) 185403) ((-1137 . -102) T) ((-1135 . -1117) T) ((-1097 . -23) T) ((-1097 . -1129) T) ((-1092 . -102) T) ((-1074 . -624) 185370) ((-1020 . -420) 185342) ((-942 . -970) T) ((-748 . -318) 185280) ((-75 . -1235) T) ((-675 . -392) 185252) ((-171 . -924) 185205) ((-30 . -970) T) ((-112 . -855) T) ((-1 . -624) 185187) ((-1016 . -908) 185108) ((-129 . -662) 185090) ((-50 . -631) 185074) ((-705 . -657) 185009) ((-606 . -913) 184922) ((-449 . -102) T) ((-129 . -383) 184904) ((-142 . -318) NIL) ((-883 . -1066) T) ((-844 . -861) 184883) ((-81 . -1235) T) ((-722 . -299) T) ((-40 . -1075) T) ((-592 . -174) T) ((-529 . -174) T) ((-522 . -624) 184865) ((-171 . -659) 184739) ((-518 . -624) 184721) ((-361 . -148) 184703) ((-361 . -146) T) ((-369 . -1129) T) ((-363 . -1129) T) ((-355 . -1129) T) ((-1021 . -316) T) ((-929 . -316) T) ((-883 . -248) T) ((-108 . -1129) T) ((-883 . -238) 184682) ((-1269 . -111) 184503) ((-1248 . -111) 184292) ((-250 . -1273) 184276) ((-575 . -859) T) ((-369 . -23) T) ((-364 . -359) T) ((-325 . -318) 184263) ((-322 . -318) 184204) ((-363 . -23) T) ((-328 . -132) T) ((-355 . -23) T) ((-1021 . -1039) T) ((-31 . -627) 184185) ((-108 . -23) T) ((-665 . -1068) 184169) ((-250 . -615) 184146) ((-342 . -1117) T) ((-665 . -651) 184116) ((-1271 . -38) 184008) ((-1258 . -924) 183987) ((-112 . -1117) T) ((-827 . -1235) T) ((-1052 . -102) T) ((-1258 . -659) 183876) ((-882 . -805) NIL) ((-866 . -659) 183850) ((-882 . -802) NIL) ((-827 . -898) NIL) ((-882 . -737) T) ((-1104 . -525) 183723) ((-793 . -525) 183670) ((-791 . -525) 183622) ((-582 . -659) 183609) ((-827 . -1055) 183437) ((-465 . -525) 183380) ((-399 . -400) T) ((-1269 . -627) 183193) ((-1248 . -627) 182941) ((-60 . -1235) T) ((-632 . -861) 182920) ((-511 . -672) T) ((-1163 . -993) 182889) ((-1041 . -657) 182826) ((-1020 . -463) T) ((-710 . -859) T) ((-521 . -803) T) ((-485 . -1073) 182661) ((-511 . -113) T) ((-353 . -1117) T) ((-322 . -1169) NIL) ((-298 . -132) T) ((-405 . -1117) T) ((-881 . -1075) T) ((-705 . -380) 182628) ((-364 . -657) 182558) ((-225 . -631) 182535) ((-336 . -295) 182487) ((-485 . -111) 182308) ((-1269 . -1066) T) ((-1248 . -1066) T) ((-827 . -387) 182292) ((-171 . -737) T) ((-665 . -102) T) ((-1269 . -248) 182271) ((-1269 . -238) 182223) ((-1248 . -238) 182128) ((-1248 . -248) 182107) ((-1020 . -413) NIL) ((-681 . -650) 182055) ((-325 . -38) 181965) ((-322 . -38) 181894) ((-69 . -624) 181876) ((-328 . -504) 181842) ((-48 . -657) 181792) ((-1207 . -297) 181771) ((-1243 . -861) T) ((-1130 . -1129) 181749) ((-83 . -1235) T) ((-61 . -624) 181731) ((-490 . -297) 181710) ((-1300 . -1055) 181687) ((-1182 . -1117) T) ((-1130 . -23) 181539) ((-827 . -913) 181475) ((-1258 . -737) T) ((-1119 . -1235) T) ((-485 . -627) 181301) ((-361 . -237) T) ((-1104 . -299) 181232) ((-981 . -1117) T) ((-905 . -102) T) ((-793 . -299) 181143) ((-336 . -19) 181127) ((-59 . -297) 181104) ((-791 . -299) 181035) ((-866 . -737) T) ((-118 . -859) NIL) ((-527 . -297) 181012) ((-336 . -615) 180989) ((-507 . -297) 180966) ((-465 . -299) 180897) ((-1052 . -318) 180748) ((-887 . -501) 180729) ((-887 . -624) 180695) ((-692 . -501) 180676) ((-582 . -737) T) ((-687 . -501) 180657) ((-692 . -624) 180607) ((-687 . -624) 180573) ((-673 . -624) 180555) ((-489 . -501) 180536) ((-489 . -624) 180502) ((-250 . -625) 180463) ((-250 . -501) 180440) ((-139 . -501) 180421) ((-138 . -501) 180402) ((-134 . -501) 180383) ((-250 . -624) 180275) ((-215 . -102) T) ((-139 . -624) 180241) ((-138 . -624) 180207) ((-134 . -624) 180173) ((-1164 . -34) T) 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((-511 . -861) T) ((-365 . -1073) 179347) ((-362 . -1073) 179299) ((-354 . -1073) 179251) ((-257 . -1235) T) ((-256 . -1235) T) ((-272 . -1073) 179094) ((-252 . -1073) 178937) ((-675 . -111) 178916) ((-828 . -1239) 178895) ((-558 . -855) T) ((-325 . -915) 178861) ((-365 . -111) 178799) ((-362 . -111) 178737) ((-354 . -111) 178675) ((-272 . -111) 178504) ((-252 . -111) 178333) ((-322 . -915) NIL) ((-634 . -422) 178317) ((-44 . -21) T) ((-44 . -25) T) ((-826 . -650) 178223) ((-828 . -567) 178202) ((-257 . -1055) 178029) ((-256 . -1055) 177856) ((-127 . -120) 177840) ((-925 . -1073) 177805) ((-723 . -102) T) ((-710 . -1075) T) ((-608 . -627) 177786) ((-596 . -627) 177767) ((-547 . -629) 177670) ((-353 . -174) T) ((-88 . -624) 177652) ((-153 . -21) T) ((-153 . -25) T) ((-925 . -111) 177608) ((-40 . -728) 177553) ((-881 . -1117) T) ((-675 . -627) 177530) ((-656 . -627) 177511) ((-365 . -627) 177448) ((-362 . -627) 177385) ((-558 . -1117) T) ((-354 . -627) 177322) ((-336 . -625) 177283) ((-336 . -624) 177195) ((-272 . -627) 176948) ((-252 . -627) 176733) ((-1248 . -803) 176686) ((-1248 . -806) 176639) ((-257 . -387) 176608) ((-256 . -387) 176577) ((-665 . -38) 176547) ((-619 . -34) T) ((-493 . -1129) 176525) ((-486 . -34) T) ((-1130 . -132) 176396) ((-979 . -25) 176207) ((-925 . -627) 176157) ((-885 . -624) 176139) ((-979 . -21) 176094) ((-826 . -25) 175927) ((-826 . -21) 175838) ((-1241 . -378) T) ((-634 . -1075) T) ((-1196 . -567) 175817) ((-1190 . -47) 175794) ((-365 . -1066) T) ((-362 . -1066) T) ((-493 . -23) 175646) ((-354 . -1066) T) ((-272 . -1066) T) ((-252 . -1066) T) ((-1142 . -47) 175618) ((-118 . -1075) T) ((-1051 . -659) 175592) ((-973 . -34) T) ((-365 . -238) 175571) ((-365 . -248) T) ((-362 . -238) 175550) ((-362 . -248) T) ((-354 . -238) 175529) ((-354 . -248) T) ((-272 . -335) 175501) ((-252 . -335) 175458) ((-272 . -238) 175437) ((-1174 . -152) 175421) ((-257 . -913) 175353) ((-256 . -913) 175285) ((-1159 . -908) 175206) ((-1099 . -861) T) ((-425 . -1129) T) ((-1071 . -23) T) ((-1041 . -859) T) ((-925 . -1066) T) ((-331 . -659) 175188) ((-712 . -237) T) ((-681 . -234) 175133) ((-1229 . -1019) 175099) ((-1191 . -935) 175078) ((-1185 . -935) 175057) ((-1185 . -831) NIL) ((-1016 . -1068) 174953) ((-982 . -1235) T) ((-925 . -248) T) ((-828 . -373) 174932) ((-395 . -23) T) ((-128 . -1117) 174910) ((-122 . -1117) 174888) ((-925 . -238) T) ((-129 . -34) T) ((-389 . -659) 174853) ((-1016 . -651) 174801) ((-881 . -728) 174788) ((-1314 . -657) 174760) ((-1063 . -152) 174725) ((-1010 . -1235) T) ((-40 . -174) T) ((-705 . -422) 174707) ((-723 . -318) 174694) ((-847 . -659) 174654) ((-838 . -659) 174628) ((-328 . -25) T) ((-328 . -21) T) ((-669 . -295) 174607) ((-591 . -1117) T) ((-575 . -1117) T) ((-506 . -1117) T) ((-250 . -297) 174584) ((-1190 . -1235) T) ((-1142 . -1235) T) ((-322 . -271) 174545) ((-322 . -232) 174506) ((-1190 . -898) NIL) ((-55 . -1117) T) ((-1142 . -898) 174365) ((-130 . -861) T) ((-1190 . -1055) 174245) ((-1142 . -1055) 174128) ((-185 . -624) 174110) ((-865 . -1055) 174006) ((-793 . -295) 173933) ((-828 . -1129) T) ((-1051 . -737) T) ((-1063 . -993) 173862) ((-613 . -662) 173846) ((-1020 . -908) 173753) ((-1016 . -102) T) ((-828 . -23) T) ((-723 . -1169) 173731) ((-705 . -1075) T) ((-613 . -383) 173715) ((-361 . -463) T) ((-353 . -299) T) ((-1286 . -1117) T) ((-253 . -1117) T) ((-410 . -102) T) ((-298 . -21) T) ((-298 . -25) T) ((-371 . -737) T) ((-721 . -1117) T) ((-710 . -1117) T) ((-371 . -484) T) ((-1229 . -624) 173697) ((-1190 . -387) 173681) ((-1142 . -387) 173665) ((-1041 . -422) 173627) ((-142 . -231) 173609) ((-389 . -805) T) ((-389 . -802) T) ((-881 . -174) T) ((-389 . -737) T) ((-722 . -624) 173591) ((-723 . -38) 173420) ((-1285 . -1283) 173404) ((-361 . -413) T) ((-1285 . -1117) 173354) ((-1208 . -1117) T) ((-591 . -728) 173341) ((-575 . -728) 173328) ((-506 . -728) 173293) ((-1271 . -657) 173183) ((-325 . -640) 173162) ((-847 . -737) T) ((-838 . -737) T) ((-655 . -1235) T) ((-1097 . -650) 173110) ((-1190 . -913) 173053) ((-1142 . -913) 173037) ((-826 . -234) 172928) ((-673 . -1073) 172912) ((-108 . -650) 172894) ((-493 . -132) 172765) ((-1196 . -1129) T) ((-967 . -47) 172734) ((-634 . -1117) T) ((-673 . -111) 172713) ((-502 . -624) 172679) ((-336 . -297) 172656) ((-492 . -47) 172613) ((-1196 . -23) T) ((-118 . -1117) T) ((-103 . -102) 172591) ((-1297 . -1129) T) ((-559 . -861) T) ((-227 . -1235) T) ((-1071 . -132) T) ((-1041 . -1075) T) ((-1297 . -23) T) ((-830 . -1055) 172575) ((-1215 . -624) 172557) ((-1020 . -735) 172529) ((-1137 . -839) T) ((-710 . -728) 172494) ((-597 . -624) 172476) ((-397 . -1055) 172460) ((-364 . -1075) T) ((-395 . -132) T) ((-333 . -1055) 172444) ((-1122 . -1117) T) ((-1097 . -21) T) ((-1097 . -25) T) ((-227 . -898) 172426) ((-1021 . -935) T) ((-91 . -34) T) ((-1021 . -831) T) ((-929 . -935) T) ((-1016 . -318) 172391) ((-887 . -627) 172372) ((-498 . -1239) T) ((-725 . -659) 172332) ((-692 . -627) 172313) ((-687 . -627) 172294) ((-219 . -1239) T) ((-418 . -908) 172215) ((-227 . -1055) 172175) ((-40 . -299) T) ((-498 . -567) T) ((-489 . -627) 172156) ((-369 . -25) T) ((-325 . -657) 171811) ((-322 . -657) 171725) ((-369 . -21) T) ((-363 . -25) T) ((-363 . -21) T) ((-219 . -567) T) ((-355 . -25) T) ((-355 . -21) T) ((-328 . -234) 171671) ((-250 . -627) 171648) ((-139 . -627) 171629) ((-138 . -627) 171610) ((-134 . -627) 171591) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1075) T) ((-591 . -174) T) ((-575 . -174) T) ((-506 . -174) T) ((-1079 . -1235) T) ((-967 . -1235) T) ((-669 . -624) 171573) ((-492 . -1235) T) ((-748 . -747) 171557) ((-346 . -624) 171539) ((-68 . -393) T) ((-68 . -406) T) ((-1119 . -107) 171523) ((-1079 . -898) 171505) ((-967 . -898) 171430) ((-664 . -1129) T) ((-634 . -728) 171417) ((-492 . -898) NIL) ((-1163 . -102) T) ((-1111 . -629) 171401) ((-1079 . -1055) 171383) ((-97 . -624) 171365) ((-488 . -148) T) ((-967 . -1055) 171245) ((-118 . -728) 171190) ((-723 . -915) 171097) ((-664 . -23) T) ((-492 . -1055) 170973) ((-1104 . -625) NIL) ((-1104 . -624) 170955) ((-793 . -625) NIL) ((-793 . -624) 170916) ((-791 . -625) 170550) ((-791 . -624) 170464) ((-1130 . -650) 170370) ((-472 . -624) 170352) ((-465 . -624) 170334) ((-465 . -625) 170195) ((-1052 . -231) 170141) ((-883 . -924) 170120) ((-127 . -34) T) ((-828 . -132) T) ((-660 . -624) 170102) ((-589 . -102) T) ((-365 . -1304) 170086) ((-362 . -1304) 170070) ((-354 . -1304) 170054) ((-128 . -525) 169987) ((-122 . -525) 169920) ((-522 . -803) T) ((-522 . -806) T) ((-521 . -805) T) ((-103 . -318) 169858) ((-224 . -102) 169836) ((-710 . -174) T) ((-705 . -1117) T) ((-883 . -659) 169752) ((-65 . -394) T) ((-283 . -624) 169734) ((-65 . -406) T) ((-967 . -387) 169718) ((-881 . -299) T) ((-50 . -624) 169700) ((-1016 . -38) 169648) ((-1137 . -657) 169620) ((-592 . -624) 169602) ((-492 . -387) 169586) ((-592 . -625) 169568) ((-529 . -624) 169550) ((-925 . -1304) 169537) ((-882 . -1235) T) ((-712 . -463) T) ((-506 . -525) 169503) ((-498 . -373) T) ((-365 . -378) 169482) ((-362 . -378) 169461) ((-354 . -378) 169440) ((-725 . -737) T) ((-219 . -373) T) ((-117 . -463) T) ((-1308 . -1299) 169424) ((-882 . -896) 169401) ((-882 . -898) NIL) ((-979 . -861) 169300) ((-826 . -861) 169251) ((-1242 . -102) T) ((-665 . -667) 169235) ((-1221 . -34) T) ((-173 . -624) 169217) ((-1130 . -25) 169050) ((-1130 . -21) 168961) ((-882 . -1055) 168938) ((-967 . -913) 168919) ((-1258 . -47) 168896) ((-925 . -378) T) ((-59 . -662) 168880) ((-527 . -662) 168864) ((-492 . -913) 168841) ((-71 . -452) T) ((-71 . -406) T) ((-507 . -662) 168825) ((-59 . -383) 168809) ((-634 . -174) T) ((-527 . -383) 168793) ((-507 . -383) 168777) ((-838 . -719) 168761) ((-1190 . -316) 168740) ((-1196 . -132) T) ((-1159 . -1068) 168724) ((-118 . -174) T) ((-1159 . -651) 168656) ((-1163 . -318) 168594) ((-171 . -1235) T) ((-1297 . -132) T) ((-877 . -1068) 168564) ((-646 . -755) 168548) ((-618 . -755) 168532) ((-1270 . -935) 168511) ((-1249 . -935) 168490) ((-1249 . -831) NIL) ((-877 . -651) 168460) ((-705 . -728) 168410) ((-1248 . -924) 168363) ((-1041 . -1117) T) ((-882 . -387) 168340) ((-882 . -348) 168317) ((-920 . -1129) T) ((-171 . -896) 168301) ((-171 . -898) 168226) ((-1285 . -525) 168159) ((-1269 . -659) 168056) ((-1097 . -234) 167929) ((-498 . -1129) T) ((-364 . -1117) T) ((-219 . -1129) T) ((-76 . -452) T) ((-76 . -406) T) ((-171 . -1055) 167825) ((-303 . -908) 167782) ((-328 . -861) T) ((-1248 . -659) 167590) ((-883 . -805) 167569) ((-883 . -802) 167548) ((-883 . -737) T) ((-498 . -23) T) ((-369 . -234) 167521) ((-363 . -234) 167494) ((-355 . -234) 167467) ((-225 . -624) 167449) ((-176 . -463) T) ((-224 . -318) 167387) ((-86 . -452) T) ((-86 . -406) T) ((-108 . -234) 167374) ((-219 . -23) T) ((-1309 . -1302) 167353) ((-688 . -1055) 167337) ((-591 . -299) T) ((-575 . -299) T) ((-506 . -299) T) ((-137 . -481) 167292) ((-1258 . -1235) T) ((-665 . -657) 167251) ((-48 . -1117) T) ((-723 . -271) 167235) ((-723 . -232) 167219) ((-882 . -913) NIL) ((-1258 . -898) NIL) ((-901 . -102) T) ((-897 . -102) T) ((-399 . -1117) T) ((-171 . -387) 167203) ((-171 . -348) 167187) ((-1258 . -1055) 167067) ((-866 . -1055) 166963) ((-1159 . -102) T) ((-1016 . -915) 166886) ((-673 . -803) 166865) ((-664 . -132) T) ((-673 . -806) 166844) ((-118 . -525) 166752) ((-582 . -1055) 166734) ((-303 . -1292) 166704) ((-877 . -102) T) ((-978 . -567) 166683) ((-1229 . -1073) 166566) ((-1020 . -1068) 166511) ((-493 . -650) 166417) ((-919 . -1117) T) ((-1041 . -728) 166354) ((-722 . -1073) 166319) ((-1020 . -651) 166264) ((-628 . -102) T) ((-613 . -34) T) ((-1164 . -1235) T) ((-1229 . -111) 166133) ((-485 . -659) 166030) ((-364 . -728) 165975) ((-171 . -913) 165934) ((-710 . -299) T) ((-705 . -174) T) ((-722 . -111) 165890) ((-1314 . -1075) T) ((-1258 . -387) 165874) ((-429 . -1239) 165852) ((-1135 . -624) 165834) ((-322 . -859) NIL) ((-429 . -567) T) ((-227 . -316) T) ((-1248 . -802) 165787) ((-1248 . -805) 165740) ((-1269 . -737) T) ((-1248 . -737) T) ((-48 . -728) 165705) ((-227 . -1039) T) ((-1271 . -422) 165671) ((-361 . -1292) 165648) ((-1258 . -913) 165591) ((-729 . -737) T) ((-342 . -624) 165573) ((-1229 . -627) 165455) ((-1130 . -234) 165346) ((-112 . -624) 165328) ((-112 . -625) 165310) ((-729 . -484) T) ((-722 . -627) 165260) ((-1308 . -1068) 165244) ((-493 . -25) 165077) ((-128 . -500) 165061) ((-122 . -500) 165045) ((-493 . -21) 164956) ((-1308 . -651) 164926) ((-634 . -299) T) ((-597 . -1073) 164901) ((-448 . -1117) T) ((-1079 . -316) T) ((-118 . -299) T) ((-1121 . -102) T) ((-1020 . -102) T) ((-597 . -111) 164869) ((-1159 . -318) 164807) ((-1229 . -1066) T) ((-1079 . -1039) T) ((-66 . -1235) T) ((-1071 . -25) T) ((-1071 . -21) T) ((-722 . -1066) T) ((-395 . -21) T) ((-395 . -25) T) ((-705 . -525) NIL) ((-1041 . -174) T) ((-722 . -248) T) ((-1079 . -556) T) ((-723 . -657) 164717) ((-517 . -102) T) ((-513 . -102) T) ((-364 . -174) T) ((-353 . -624) 164699) ((-418 . -1068) 164651) ((-405 . -624) 164633) ((-1137 . -859) T) ((-485 . -737) T) ((-904 . -1055) 164601) ((-418 . -651) 164553) ((-108 . -861) T) ((-669 . -1073) 164537) ((-498 . -132) T) ((-1271 . -1075) T) ((-219 . -132) T) ((-1174 . -102) 164515) ((-99 . -1117) T) ((-250 . -677) 164499) ((-250 . -662) 164483) ((-669 . -111) 164462) ((-597 . -627) 164446) ((-325 . -422) 164430) ((-250 . -383) 164414) ((-1177 . -240) 164361) ((-1016 . -271) 164345) ((-1016 . -232) 164329) ((-74 . -1235) T) ((-48 . -174) T) ((-712 . -398) T) ((-712 . -144) T) ((-1308 . -102) T) ((-1215 . -627) 164311) ((-1105 . -1235) T) ((-1104 . -1073) 164154) ((-1093 . -1235) T) ((-272 . -924) 164133) ((-252 . -924) 164112) ((-793 . -1073) 163935) ((-791 . -1073) 163778) ((-619 . -1235) T) ((-1182 . -624) 163760) ((-1104 . -111) 163589) ((-1063 . -102) T) ((-486 . -1235) T) ((-472 . -1073) 163560) ((-465 . -1073) 163403) ((-675 . -659) 163387) ((-882 . -316) T) ((-793 . -111) 163196) ((-791 . -111) 163025) ((-365 . -659) 162977) ((-362 . -659) 162929) ((-354 . -659) 162881) ((-272 . -659) 162770) ((-252 . -659) 162659) ((-1176 . -861) T) ((-1105 . -1055) 162643) ((-472 . -111) 162604) ((-465 . -111) 162433) ((-1093 . -1055) 162410) ((-1017 . -34) T) ((-981 . -624) 162392) ((-973 . -1235) T) ((-127 . -1027) 162376) ((-978 . -1129) T) ((-882 . -1039) NIL) ((-746 . -1129) T) ((-726 . -1129) T) ((-669 . -627) 162294) ((-1285 . -500) 162278) ((-1159 . -38) 162238) ((-978 . -23) T) ((-925 . -659) 162203) ((-876 . -1117) T) ((-854 . -102) T) ((-828 . -21) T) ((-646 . -1068) 162187) ((-618 . -1068) 162171) ((-828 . -25) T) ((-746 . -23) T) ((-726 . -23) T) ((-646 . -651) 162155) ((-110 . -672) T) ((-618 . -651) 162139) ((-592 . -1073) 162104) ((-529 . -1073) 162049) ((-229 . -57) 162007) ((-464 . -23) T) ((-418 . -102) T) ((-269 . -102) T) ((-110 . -113) T) ((-705 . -299) T) ((-877 . -38) 161977) ((-592 . -111) 161933) ((-529 . -111) 161862) ((-1104 . -627) 161598) ((-429 . -1129) T) ((-325 . -1075) 161488) ((-322 . -1075) T) ((-129 . -1235) T) ((-793 . -627) 161236) ((-791 . -627) 161002) ((-669 . -1066) T) ((-1314 . -1117) T) ((-465 . -627) 160787) ((-171 . -316) 160718) ((-429 . -23) T) ((-40 . -624) 160700) ((-40 . -625) 160684) ((-108 . -1009) 160666) ((-117 . -880) 160650) ((-660 . -627) 160634) ((-48 . -525) 160600) ((-1221 . -1027) 160584) ((-1199 . -624) 160551) ((-1207 . -34) T) ((-969 . -624) 160517) ((-936 . -624) 160499) ((-1130 . -861) 160450) ((-782 . -624) 160432) ((-683 . -624) 160414) ((-1174 . -318) 160352) ((-490 . -34) T) ((-1109 . -1235) T) ((-488 . -463) T) ((-1158 . -34) T) ((-1104 . -1066) T) ((-50 . -627) 160321) ((-793 . -1066) T) ((-791 . -1066) T) ((-658 . -240) 160305) ((-643 . -240) 160251) ((-592 . -627) 160201) ((-529 . -627) 160131) ((-493 . -234) 160022) ((-1258 . -316) 160001) ((-1104 . -335) 159962) ((-465 . -1066) T) ((-1196 . -21) T) ((-1104 . -238) 159941) ((-793 . -335) 159918) ((-793 . -238) T) ((-791 . -335) 159890) ((-742 . -1239) 159869) ((-336 . -662) 159853) ((-1196 . -25) T) ((-59 . -34) T) ((-530 . -34) T) ((-527 . -34) T) ((-465 . -335) 159832) ((-336 . -383) 159816) ((-508 . -34) T) ((-507 . -34) T) ((-1020 . -1169) NIL) ((-742 . -567) 159747) ((-646 . -102) T) ((-618 . -102) T) ((-365 . -737) T) ((-362 . -737) T) ((-354 . -737) T) ((-272 . -737) T) ((-252 . -737) T) ((-389 . -1235) T) ((-1063 . -318) 159655) ((-1297 . -21) T) ((-916 . -1117) 159633) ((-829 . -234) 159620) ((-50 . -1066) T) ((-1297 . -25) T) ((-1192 . -567) 159599) ((-1191 . -1239) 159578) ((-1191 . -567) 159529) ((-1185 . -1239) 159508) ((-1185 . -567) 159459) ((-592 . -1066) T) ((-529 . -1066) T) ((-1041 . -299) T) ((-371 . -1055) 159443) ((-331 . -1055) 159427) ((-1020 . -38) 159372) ((-389 . -898) 159354) ((-1016 . -657) 159277) ((-847 . -1235) T) ((-838 . -1235) 159256) ((-810 . -1129) T) ((-925 . -737) T) ((-592 . -248) T) ((-592 . -238) T) ((-529 . -238) T) ((-529 . -248) T) ((-1143 . -567) 159235) ((-364 . -299) T) ((-658 . -706) 159219) ((-389 . -1055) 159179) ((-303 . -1068) 159100) ((-349 . -908) 159079) ((-1137 . -1075) T) ((-103 . -126) 159063) ((-303 . -651) 159005) ((-810 . -23) T) ((-1307 . -1302) 158981) ((-1305 . -1302) 158960) ((-1285 . -295) 158912) ((-418 . -318) 158877) ((-1271 . -1117) T) ((-1159 . -915) 158800) ((-881 . -624) 158782) ((-847 . -1055) 158751) ((-205 . -798) T) ((-204 . -798) T) ((-203 . -798) T) ((-202 . -798) T) ((-201 . -798) T) ((-200 . -798) T) ((-199 . -798) T) ((-198 . -798) T) ((-197 . -798) T) ((-196 . -798) T) ((-558 . -624) 158733) ((-506 . -1019) T) ((-282 . -850) T) ((-281 . -850) T) ((-280 . -850) T) ((-279 . -850) T) ((-48 . -299) T) ((-278 . -850) T) ((-277 . -850) T) ((-276 . -850) T) ((-195 . -798) T) ((-623 . -861) T) ((-665 . -422) 158717) ((-681 . -237) 158668) ((-225 . -627) 158630) ((-110 . -861) T) ((-664 . -21) T) ((-664 . -25) T) ((-1308 . -38) 158600) ((-118 . -295) 158551) ((-1285 . -19) 158535) ((-1285 . -615) 158512) ((-1298 . -1117) T) ((-361 . -1068) 158457) ((-1094 . -1117) T) ((-1004 . -1117) T) ((-978 . -132) T) ((-828 . -234) 158444) ((-748 . -1117) T) ((-361 . -651) 158389) ((-746 . -132) T) ((-726 . -132) T) ((-522 . -804) T) ((-522 . -805) T) ((-464 . -132) T) ((-418 . -1169) 158367) ((-225 . -1066) T) ((-303 . -102) 158149) ((-142 . -1117) T) ((-710 . -1019) T) ((-1122 . -295) 158105) ((-91 . -1235) T) ((-128 . -624) 158037) ((-122 . -624) 157969) ((-1314 . -174) T) ((-1191 . -373) 157948) ((-1185 . -373) 157927) ((-325 . -1117) T) ((-429 . -132) T) ((-322 . -1117) T) ((-418 . -38) 157879) ((-1150 . -102) T) ((-1271 . -728) 157771) ((-665 . -1075) T) ((-1152 . -1280) T) ((-328 . -146) 157750) ((-328 . -148) 157729) ((-140 . -1117) T) ((-137 . -1117) T) ((-115 . -1117) T) ((-869 . -102) T) ((-591 . -624) 157711) ((-575 . -625) 157610) ((-575 . -624) 157592) ((-506 . -624) 157574) ((-506 . -625) 157519) ((-496 . -23) T) ((-493 . -861) 157470) ((-498 . -650) 157452) ((-980 . -624) 157434) ((-1020 . -915) 157343) ((-219 . -650) 157325) ((-227 . -415) T) ((-673 . -659) 157309) ((-55 . -624) 157291) ((-1190 . -935) 157270) ((-742 . -1129) T) ((-361 . -102) T) ((-1234 . -1100) T) ((-1137 . -855) T) ((-829 . -861) T) ((-742 . -23) T) ((-353 . -1073) 157215) ((-1176 . -1175) T) ((-1164 . -107) 157199) ((-1192 . -1129) T) ((-1191 . -1129) T) ((-526 . -1055) 157183) ((-1185 . -1129) T) ((-1143 . -1129) T) ((-353 . -111) 157112) ((-1021 . -1239) T) ((-127 . -1235) T) ((-929 . -1239) T) ((-1286 . -624) 157094) ((-705 . -295) NIL) ((-725 . -1235) T) ((-1192 . -23) T) ((-1191 . -23) T) ((-1185 . -23) T) ((-1159 . -271) 157078) ((-1159 . -232) 157062) ((-1021 . -567) T) ((-1143 . -23) T) ((-929 . -567) T) ((-1092 . -1117) T) ((-253 . -624) 157044) ((-826 . -237) 156941) ((-810 . -132) T) ((-721 . -624) 156923) ((-325 . -728) 156833) ((-322 . -728) 156762) ((-710 . -624) 156744) ((-710 . -625) 156689) ((-418 . -411) 156673) ((-449 . -1117) T) ((-498 . -25) T) ((-498 . -21) T) ((-1137 . -1117) T) ((-219 . -25) T) ((-219 . -21) T) ((-723 . -422) 156657) ((-725 . -1055) 156626) ((-1285 . -624) 156538) ((-1285 . -625) 156499) ((-1271 . -174) T) ((-1208 . -624) 156481) ((-250 . -34) T) ((-353 . -627) 156411) ((-405 . -627) 156393) ((-941 . -991) T) ((-1221 . -1235) T) ((-673 . -802) 156372) ((-673 . -805) 156351) ((-409 . -406) T) ((-534 . -102) 156329) ((-1052 . -1117) T) ((-418 . -915) 156252) ((-224 . -1012) 156236) ((-515 . -102) T) ((-634 . -624) 156218) ((-45 . -861) NIL) ((-634 . -625) 156195) ((-1052 . -621) 156170) ((-916 . -525) 156103) ((-328 . -237) 156055) ((-353 . -1066) T) ((-118 . -625) NIL) ((-118 . -624) 156037) ((-883 . -1235) T) ((-681 . -428) 156021) ((-681 . -1140) 155966) ((-511 . -152) 155948) ((-353 . -238) T) ((-353 . -248) T) ((-40 . -1073) 155893) ((-883 . -896) 155877) ((-883 . -898) 155802) ((-723 . -1075) T) ((-705 . -1019) NIL) ((-1269 . -47) 155772) ((-1248 . -47) 155749) ((-1158 . -1027) 155720) ((-1137 . -728) 155707) ((-3 . |UnionCategory|) T) ((-1122 . -624) 155689) ((-1097 . -148) 155668) ((-1097 . -146) 155619) ((-1021 . -373) T) 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147507) ((-429 . -234) 147452) ((-272 . -387) 147436) ((-252 . -387) 147420) ((-410 . -1117) T) ((-1043 . -102) 147398) ((-349 . -38) 147382) ((-219 . -1009) 147364) ((-118 . -627) 147294) ((-176 . -38) 147226) ((-1269 . -316) 147205) ((-1248 . -316) 147184) ((-669 . -737) T) ((-99 . -624) 147166) ((-488 . -1068) 147131) ((-1185 . -650) 147083) ((-488 . -651) 147048) ((-496 . -25) T) ((-496 . -21) T) ((-1248 . -1039) 147000) ((-1074 . -1235) T) ((-634 . -1066) T) ((-389 . -415) T) ((-401 . -102) T) ((-1122 . -629) 146915) ((-272 . -913) 146861) ((-252 . -913) 146838) ((-118 . -1066) T) ((-827 . -1129) T) ((-1104 . -737) T) ((-634 . -238) 146817) ((-632 . -102) T) ((-793 . -737) T) ((-791 . -737) T) ((-424 . -1129) T) ((-118 . -248) T) ((-40 . -378) NIL) ((-118 . -238) NIL) ((-1240 . -861) T) ((-465 . -737) T) ((-827 . -23) T) ((-742 . -25) T) ((-742 . -21) T) ((-681 . -908) 146738) ((-1094 . -295) 146717) ((-78 . -407) T) ((-78 . -406) T) ((-544 . -778) 146699) ((-705 . -1073) 146649) 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141890) ((-115 . -624) 141872) ((-488 . -38) 141837) ((-1309 . -1306) 141816) ((-1300 . -132) T) ((-1308 . -1075) T) ((-1099 . -102) T) ((-88 . -1235) T) ((-511 . -318) NIL) ((-1017 . -107) 141800) ((-901 . -1117) T) ((-897 . -1117) T) ((-1285 . -662) 141784) ((-1285 . -383) 141768) ((-336 . -1235) T) ((-604 . -861) T) ((-1159 . -1117) T) ((-1159 . -1070) 141708) ((-103 . -525) 141641) ((-942 . -624) 141623) ((-353 . -737) T) ((-30 . -624) 141605) ((-877 . -1117) T) ((-854 . -1075) 141584) ((-40 . -659) 141491) ((-227 . -1239) T) ((-418 . -1075) T) ((-1176 . -152) 141473) ((-1016 . -299) 141424) ((-628 . -1117) T) ((-227 . -567) T) ((-328 . -1266) 141408) ((-328 . -1263) 141378) ((-712 . -657) 141350) ((-1207 . -1211) 141329) ((-1092 . -624) 141311) ((-1207 . -107) 141261) ((-658 . -152) 141245) ((-643 . -152) 141191) ((-117 . -657) 141163) ((-490 . -1211) 141142) ((-498 . -148) T) ((-498 . -146) NIL) ((-1137 . -625) 141057) ((-449 . -624) 141039) ((-219 . -148) T) ((-219 . -146) NIL) 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133385) ((-227 . -132) T) ((-1137 . -111) 133370) ((-171 . -23) T) ((-810 . -148) 133349) ((-810 . -146) 133328) ((-257 . -650) 133234) ((-256 . -650) 133140) ((-328 . -293) 133106) ((-1174 . -525) 133039) ((-488 . -657) 132989) ((-493 . -908) 132856) ((-1150 . -1117) T) ((-227 . -1077) T) ((-826 . -318) 132794) ((-1104 . -913) 132729) ((-793 . -913) 132672) ((-791 . -913) 132656) ((-1307 . -38) 132626) ((-1305 . -38) 132596) ((-1258 . -1129) T) ((-866 . -1129) T) ((-465 . -913) 132573) ((-869 . -1117) T) ((-1258 . -23) T) ((-1137 . -627) 132545) ((-1079 . -132) T) ((-582 . -1129) T) ((-866 . -23) T) ((-634 . -737) T) ((-365 . -935) T) ((-362 . -935) T) ((-298 . -102) T) ((-354 . -935) T) ((-987 . -1100) T) ((-967 . -132) T) ((-827 . -234) 132490) ((-118 . -805) NIL) ((-118 . -802) NIL) ((-118 . -737) T) ((-1063 . -525) 132391) ((-705 . -924) NIL) ((-582 . -23) T) ((-492 . -132) T) ((-429 . -237) 132342) ((-686 . -318) 132280) ((-646 . -772) T) ((-618 . -772) T) ((-1249 . -861) NIL) 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-627) 129761) ((-1130 . -651) 129683) ((-1184 . -102) T) ((-1011 . -102) T) ((-1010 . -21) T) ((-128 . -1027) 129667) ((-122 . -1027) 129651) ((-1010 . -25) T) ((-916 . -120) 129635) ((-1176 . -102) T) ((-1258 . -132) T) ((-1190 . -25) T) ((-353 . -1235) T) ((-1190 . -21) T) ((-866 . -132) T) ((-1142 . -25) T) ((-1142 . -21) T) ((-865 . -25) T) ((-865 . -21) T) ((-793 . -316) 129614) ((-1177 . -318) 129409) ((-1174 . -500) 129393) ((-1167 . -152) 129343) ((-658 . -102) 129321) ((-643 . -102) T) ((-1163 . -624) 129283) ((-582 . -132) T) ((-632 . -859) 129262) ((-1163 . -625) 129223) ((-1041 . -802) T) ((-1041 . -805) T) ((-1041 . -737) T) ((-826 . -915) 129092) ((-723 . -1073) 128915) ((-495 . -318) 128853) ((-464 . -428) 128823) ((-361 . -174) T) ((-298 . -38) 128810) ((-257 . -234) 128701) ((-256 . -234) 128592) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-353 . -1055) 128569) ((-276 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-723 . -111) 128378) ((-364 . -737) T) ((-681 . -271) 128362) ((-681 . -232) 128346) ((-592 . -316) T) ((-529 . -316) T) ((-303 . -525) 128295) ((-108 . -318) NIL) ((-72 . -406) T) ((-1130 . -102) 128047) ((-844 . -422) 128031) ((-1137 . -806) T) ((-1137 . -803) T) ((-712 . -1117) T) ((-589 . -624) 128013) ((-389 . -373) T) ((-171 . -504) 127991) ((-224 . -624) 127923) ((-135 . -1117) T) ((-117 . -1117) T) ((-981 . -1235) T) ((-48 . -737) T) ((-1063 . -500) 127888) ((-142 . -436) 127870) ((-142 . -378) T) ((-1044 . -102) T) ((-523 . -520) 127849) ((-723 . -627) 127605) ((-1192 . -237) 127564) ((-487 . -102) T) ((-474 . -102) T) ((-1191 . -237) 127516) ((-1185 . -237) 127339) ((-1051 . -1129) T) ((-328 . 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-335) 126013) ((-492 . -650) 125961) ((-40 . -1055) 125849) ((-723 . -238) T) ((-712 . -728) 125836) ((-349 . -1117) T) ((-176 . -1117) T) ((-340 . -861) T) ((-429 . -463) 125786) ((-389 . -23) T) ((-369 . -38) 125751) ((-363 . -38) 125716) ((-355 . -38) 125681) ((-80 . -452) T) ((-80 . -406) T) ((-227 . -25) T) ((-227 . -21) T) ((-847 . -1129) T) ((-108 . -38) 125631) ((-838 . -1129) T) ((-785 . -1117) T) ((-117 . -728) 125618) ((-683 . -1055) 125602) ((-623 . -102) T) ((-847 . -23) T) ((-838 . -23) T) ((-1174 . -295) 125554) ((-1130 . -318) 125492) ((-493 . -1068) 125393) ((-1119 . -240) 125377) ((-64 . -407) T) ((-64 . -406) T) ((-1168 . -102) T) ((-110 . -102) T) ((-493 . -651) 125299) ((-40 . -387) 125276) ((-96 . -102) T) ((-664 . -863) 125260) ((-1190 . -234) 125247) ((-1152 . -1100) T) ((-1079 . -21) T) ((-1079 . -25) T) ((-1071 . -1068) 125231) ((-826 . -271) 125200) ((-826 . -232) 125169) ((-967 . -25) T) ((-967 . -21) T) ((-1071 . -651) 125111) ((-632 . -1075) T) ((-1137 . -378) T) ((-1044 . -318) 125049) ((-681 . -657) 125008) ((-492 . -25) T) ((-492 . -21) T) ((-395 . -1068) 124992) ((-901 . -624) 124974) ((-897 . -624) 124956) ((-534 . -525) 124889) ((-257 . -861) 124840) ((-256 . -861) 124791) ((-395 . -651) 124761) ((-882 . -650) 124738) ((-487 . -318) 124676) ((-474 . -318) 124614) ((-361 . -299) T) ((-1174 . -1273) 124598) ((-1159 . -624) 124560) ((-1159 . -625) 124521) ((-1157 . -102) T) ((-1016 . -1073) 124417) ((-40 . -913) 124369) ((-1174 . -615) 124346) ((-1314 . -659) 124333) ((-1080 . -152) 124279) ((-498 . -908) NIL) ((-877 . -501) 124256) ((-1016 . -111) 124138) ((-883 . -1239) T) ((-219 . -908) NIL) ((-349 . -728) 124122) ((-877 . -624) 124084) ((-176 . -728) 124016) ((-883 . -567) T) ((-418 . -295) 123974) ((-245 . -237) 123871) ((-108 . -411) 123853) ((-84 . -394) T) ((-84 . -406) T) ((-712 . -174) T) ((-628 . -624) 123835) ((-99 . -737) T) ((-493 . -102) 123587) ((-99 . -484) T) ((-117 . -174) T) ((-1307 . -657) 123546) ((-1305 . -657) 123505) ((-171 . -650) 123453) ((-1097 . -915) 123324) ((-1071 . -102) T) ((-1016 . -627) 123214) ((-882 . -25) T) ((-826 . -243) 123193) ((-882 . -21) T) ((-829 . -102) T) ((-44 . -657) 123136) ((-1021 . -237) T) ((-425 . -102) T) ((-395 . -102) T) ((-110 . -318) NIL) ((-229 . -102) 123114) ((-128 . -1235) T) ((-122 . -1235) T) ((-108 . -915) NIL) ((-828 . -1068) 123065) ((-828 . -651) 123007) ((-1051 . -132) T) ((-681 . -377) 122991) ((-153 . -657) 122950) ((-646 . -295) 122908) ((-618 . -295) 122866) ((-1314 . -737) T) ((-1016 . -1066) T) ((-1258 . -650) 122814) ((-1121 . -624) 122796) ((-1020 . -624) 122778) ((-575 . -1235) T) ((-506 . -1235) T) ((-526 . -23) T) ((-521 . -23) T) ((-353 . -316) T) ((-519 . -23) T) ((-331 . -132) T) ((-3 . -1117) T) ((-1020 . -625) 122762) ((-1016 . -248) 122741) ((-1016 . -238) 122720) ((-1277 . -146) 122699) ((-1277 . -148) 122678) ((-844 . -1117) T) ((-1270 . -148) 122657) ((-1270 . -146) 122636) ((-1269 . -1239) 122615) ((-1249 . -146) 122522) ((-1249 . -148) 122429) ((-1248 . -1239) 122408) ((-389 . -132) T) ((-227 . -234) 122395) ((-575 . -898) 122377) ((0 . -1117) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1117) T) ((-1271 . -659) 122282) ((-1269 . -567) 122233) ((-725 . -1129) T) ((-1248 . -567) 122184) ((-575 . -1055) 122166) ((-606 . -148) 122145) ((-606 . -146) 122124) ((-506 . -1055) 122067) ((-1152 . -1154) T) ((-87 . -394) T) ((-87 . -406) T) ((-883 . -373) T) ((-847 . -132) T) ((-838 . -132) T) ((-979 . -657) 122011) ((-725 . -23) T) ((-517 . -624) 121977) ((-513 . -624) 121959) ((-826 . -657) 121738) ((-1309 . -1075) T) ((-389 . -1077) T) ((-1043 . -1117) 121716) ((-55 . -1055) 121698) ((-916 . -34) T) ((-493 . -318) 121636) ((-603 . -102) T) ((-1174 . -625) 121597) ((-1174 . -624) 121529) ((-1196 . -1068) 121412) ((-45 . -102) T) ((-828 . -102) T) ((-1196 . -651) 121309) ((-1258 . -25) T) ((-1258 . -21) T) ((-1079 . -234) 121296) ((-866 . -25) T) ((-44 . -377) 121280) ((-866 . -21) T) ((-742 . -463) 121231) ((-1308 . -624) 121213) ((-1297 . -1068) 121183) ((-1071 . -318) 121121) ((-682 . -1100) T) ((-617 . -1100) T) ((-401 . -1117) T) ((-582 . -25) T) ((-582 . -21) T) ((-182 . -1100) T) ((-162 . -1100) T) ((-157 . -1100) T) ((-155 . -1100) T) ((-1297 . -651) 121091) ((-632 . -1117) T) ((-710 . -898) 121073) ((-1285 . -1235) T) ((-229 . -318) 121011) ((-145 . -378) T) ((-1063 . -625) 120953) ((-1063 . -624) 120896) ((-322 . -924) NIL) ((-1243 . -855) T) ((-1130 . -915) 120765) ((-710 . -1055) 120710) ((-722 . -935) T) ((-485 . -1239) 120689) ((-1191 . -463) 120668) ((-1185 . -463) 120647) ((-339 . -102) T) ((-883 . -1129) T) ((-328 . -657) 120529) ((-325 . -659) 120258) ((-322 . -659) 120187) ((-485 . -567) 120138) ((-349 . -525) 120104) ((-561 . -152) 120054) ((-40 . -316) T) ((-854 . -624) 120036) ((-712 . -299) T) ((-883 . -23) T) ((-389 . -504) T) ((-1097 . -271) 120006) ((-1097 . -232) 119976) ((-523 . -102) T) ((-418 . -625) 119783) ((-418 . -624) 119765) 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. -1117) T) ((-391 . -1117) T) ((-1258 . -234) 117552) ((-1234 . -1117) T) ((-82 . -1235) T) ((-1130 . -271) 117521) ((-1079 . -861) T) ((-118 . -913) NIL) ((-793 . -935) 117500) ((-724 . -861) T) ((-542 . -1117) T) ((-511 . -1117) T) ((-365 . -1239) T) ((-362 . -1239) T) ((-354 . -1239) T) ((-272 . -1239) 117479) ((-252 . -1239) 117458) ((-544 . -871) T) ((-1130 . -232) 117427) ((-1176 . -839) T) ((-1159 . -1073) 117411) ((-401 . -772) T) ((-705 . -1235) T) ((-702 . -1055) 117395) ((-365 . -567) T) ((-362 . -567) T) ((-354 . -567) T) ((-272 . -567) 117326) ((-252 . -567) 117257) ((-536 . -1100) T) ((-1159 . -111) 117236) ((-464 . -755) 117206) ((-877 . -1073) 117176) ((-828 . -38) 117118) ((-705 . -896) 117100) ((-705 . -898) 117082) ((-304 . -318) 116886) ((-1174 . -297) 116863) ((-925 . -1239) T) ((-1097 . -657) 116758) ((-1021 . -463) T) ((-681 . -422) 116742) ((-877 . -111) 116707) ((-929 . -463) T) ((-705 . -1055) 116652) ((-925 . -567) T) ((-544 . -624) 116634) ((-592 . -935) T) 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-25) T) ((-838 . -25) T) ((-838 . -21) T) ((-1130 . -657) 114220) ((-1307 . -1075) T) ((-560 . -102) T) ((-1305 . -1075) T) ((-665 . -737) T) ((-1121 . -629) 114123) ((-1020 . -627) 114053) ((-1308 . -1073) 114037) ((-826 . -422) 114006) ((-103 . -120) 113990) ((-130 . -1117) T) ((-52 . -1117) T) ((-941 . -624) 113972) ((-882 . -1009) 113949) ((-834 . -102) T) ((-1308 . -111) 113928) ((-742 . -908) 113903) ((-664 . -38) 113873) ((-582 . -861) T) ((-365 . -1129) T) ((-362 . -1129) T) ((-354 . -1129) T) ((-272 . -1129) T) ((-252 . -1129) T) ((-1167 . -318) 113677) ((-1105 . -234) 113664) ((-634 . -316) 113643) ((-675 . -23) T) ((-535 . -1100) T) ((-320 . -1117) T) ((-493 . -271) 113612) ((-493 . -232) 113581) ((-153 . -1075) T) ((-365 . -23) T) ((-362 . -23) T) ((-354 . -23) T) ((-118 . -316) T) ((-272 . -23) T) ((-252 . -23) T) ((-1020 . -1066) T) ((-723 . -924) 113560) ((-1192 . -908) 113448) ((-1191 . -908) 113329) ((-1185 . -908) 113065) ((-1174 . -627) 113042) ((-1020 . -238) 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-1276) 111546) ((-1192 . -1263) 111523) ((-1191 . -1268) 111484) ((-681 . -1117) T) ((-681 . -1070) 111424) ((-1191 . -1263) 111394) ((-559 . -1117) T) ((-498 . -1169) T) ((-1191 . -1266) 111378) ((-1185 . -1247) 111339) ((-829 . -274) 111323) ((-219 . -1169) T) ((-353 . -935) T) ((-99 . -1235) T) ((-646 . -111) 111302) ((-618 . -111) 111281) ((-1185 . -1263) 111258) ((-854 . -1066) 111237) ((-1185 . -1245) 111221) ((-526 . -25) T) ((-506 . -311) T) ((-522 . -23) T) ((-521 . -25) T) ((-519 . -25) T) ((-518 . -23) T) ((-429 . -1068) 111195) ((-418 . -1066) T) ((-328 . -1075) T) ((-705 . -316) T) ((-429 . -651) 111169) ((-108 . -859) T) ((-723 . -737) T) ((-418 . -248) T) ((-418 . -238) 111148) ((-389 . -234) 111135) ((-498 . -38) 111085) ((-219 . -38) 111035) ((-485 . -504) 111001) ((-1242 . -378) T) ((-1176 . -1161) T) ((-1118 . -102) T) ((-838 . -234) 110974) ((-712 . -624) 110956) ((-712 . -625) 110871) ((-725 . -21) T) ((-725 . -25) T) ((-1152 . -102) T) ((-493 . -657) 110650) 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109633) ((-1190 . -237) T) ((-227 . -148) T) ((-176 . -624) 109615) ((-785 . -624) 109597) ((-129 . -861) T) ((-619 . -240) 109544) ((-486 . -240) 109494) ((-1307 . -728) 109464) ((-48 . -316) T) ((-1305 . -728) 109434) ((-65 . -627) 109363) ((-979 . -1117) T) ((-826 . -1117) 109115) ((-321 . -102) T) ((-916 . -1235) T) ((-48 . -1039) T) ((-1248 . -650) 109023) ((-700 . -102) 109001) ((-44 . -728) 108985) ((-561 . -102) T) ((-303 . -627) 108916) ((-67 . -393) T) ((-498 . -915) NIL) ((-67 . -406) T) ((-219 . -915) NIL) ((-673 . -23) T) ((-828 . -657) 108852) ((-681 . -772) T) ((-1232 . -1117) 108830) ((-361 . -1073) 108775) ((-686 . -1117) 108753) ((-1079 . -148) T) ((-967 . -148) 108732) ((-967 . -146) 108711) ((-810 . -102) T) ((-153 . -728) 108695) ((-492 . -148) 108674) ((-492 . -146) 108653) ((-361 . -111) 108582) ((-1097 . -1075) T) ((-331 . -861) 108561) ((-1277 . -990) 108530) ((-638 . -1117) T) ((-1270 . -990) 108492) ((-522 . -132) T) ((-518 . -132) T) ((-304 . -231) 108442) ((-369 . -1075) T) ((-363 . -1075) T) ((-355 . -1075) T) ((-303 . -1066) 108384) ((-1249 . -990) 108353) ((-389 . -861) T) ((-108 . -1075) T) ((-1016 . -737) T) ((-881 . -935) T) ((-854 . -806) 108332) ((-854 . -803) 108311) ((-429 . -318) 108250) ((-479 . -102) T) ((-606 . -990) 108219) ((-328 . -1117) T) ((-418 . -806) 108198) ((-418 . -803) 108177) ((-511 . -500) 108159) ((-1271 . -1055) 108125) ((-1269 . -21) T) ((-1269 . -25) T) ((-1248 . -21) T) ((-1248 . -25) T) ((-826 . -728) 108067) ((-361 . -627) 107997) ((-710 . -415) T) ((-1298 . -1235) T) ((-1130 . -422) 107966) ((-617 . -102) T) ((-1094 . -1235) T) ((-1020 . -378) NIL) ((-682 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1196 . -657) 107876) ((-748 . -1235) T) ((-742 . -1068) 107719) ((-44 . -772) T) ((-742 . -651) 107568) ((-604 . -102) T) ((-664 . -667) 107552) ((-77 . -407) T) ((-77 . -406) T) ((-142 . -1235) T) ((-882 . -148) T) ((-882 . -146) NIL) ((-1297 . -657) 107497) ((-1277 . -908) 107385) ((-1234 . -93) T) ((-361 . -1066) T) ((-227 . -237) T) ((-70 . -393) T) ((-70 . -406) T) ((-1183 . -102) T) ((-681 . -525) 107318) ((-1270 . -908) 107199) ((-1249 . -908) 106935) ((-700 . -318) 106873) ((-978 . -38) 106770) ((-1198 . -624) 106752) ((-746 . -38) 106722) ((-561 . -318) 106526) ((-1192 . -1068) 106409) ((-325 . -1235) T) ((-361 . -238) T) ((-361 . -248) T) ((-322 . -1235) T) ((-298 . -1117) T) ((-1191 . -1068) 106244) ((-1185 . -1068) 106034) ((-1143 . -1068) 105917) ((-1192 . -651) 105814) ((-1191 . -651) 105655) ((-722 . -1239) T) ((-1185 . -651) 105451) ((-1174 . -662) 105435) ((-1143 . -651) 105332) ((-1229 . -567) 105311) ((-830 . -396) 105295) ((-722 . -567) T) ((-606 . -908) 105206) ((-325 . -896) 105190) ((-325 . -898) 105115) ((-137 . -1235) T) ((-322 . -896) 105076) ((-322 . -898) NIL) ((-810 . -318) 105041) ((-328 . -728) 104882) ((-397 . -396) 104866) ((-333 . -332) 104843) ((-496 . -102) T) ((-485 . -25) T) ((-485 . -21) T) ((-429 . -38) 104817) ((-325 . -1055) 104480) ((-227 . -1220) T) ((-227 . -1223) T) ((-3 . -624) 104462) ((-322 . -1055) 104392) ((-883 . -234) 104337) ((-2 . -1117) T) ((-2 . |RecordCategory|) T) ((-1130 . -1075) 104315) ((-844 . -624) 104297) ((-1079 . -237) T) ((-591 . -935) T) ((-575 . -831) T) ((-575 . -935) T) ((-506 . -935) T) ((-137 . -1055) 104281) ((-227 . -95) T) ((-171 . -148) 104260) ((-75 . -452) T) ((0 . -624) 104242) ((-75 . -406) T) ((-171 . -146) 104193) ((-227 . -35) T) ((-49 . -624) 104175) ((-488 . -1075) T) ((-498 . -271) 104157) ((-498 . -232) 104139) ((-495 . -985) 104123) ((-219 . -271) 104105) ((-219 . -232) 104087) ((-81 . -452) T) ((-81 . -406) T) ((-1163 . -34) T) ((-742 . -102) T) ((-664 . -657) 104046) ((-1043 . -624) 104013) ((-511 . -295) 103963) ((-325 . -387) 103932) ((-322 . -387) 103893) ((-322 . -348) 103854) ((-1102 . -624) 103836) ((-827 . -964) 103783) ((-673 . -132) T) ((-1258 . -146) 103762) ((-1258 . -148) 103741) ((-1192 . -102) T) 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-1239) 101466) ((-62 . -1235) T) ((-488 . -624) 101418) ((-488 . -625) 101340) ((-793 . -567) 101251) ((-791 . -567) 101182) ((-742 . -318) 101169) ((-712 . -627) 101141) ((-493 . -422) 101110) ((-634 . -935) 101089) ((-465 . -1239) 101068) ((-686 . -525) 101001) ((-675 . -25) T) ((-409 . -624) 100983) ((-675 . -21) T) ((-465 . -567) 100914) ((-429 . -915) 100837) ((-365 . -25) T) ((-365 . -21) T) ((-362 . -25) T) ((-118 . -935) T) ((-118 . -831) NIL) ((-362 . -21) T) ((-354 . -25) T) ((-354 . -21) T) ((-272 . -25) T) ((-272 . -21) T) ((-252 . -25) T) ((-252 . -21) T) ((-171 . -237) 100768) ((-83 . -394) T) ((-83 . -406) T) ((-135 . -627) 100750) ((-117 . -627) 100722) ((-1021 . -651) 100672) ((-958 . -997) 100656) ((-929 . -651) 100608) ((-929 . -1068) 100560) ((-925 . -21) T) ((-925 . -25) T) ((-883 . -861) 100511) ((-877 . -659) 100471) ((-722 . -1129) T) ((-722 . -23) T) ((-712 . -1066) T) ((-712 . -238) T) ((-298 . -174) T) ((-665 . -1235) T) ((-320 . -93) T) ((-658 . -1117) 100449) ((-643 . -621) 100424) ((-643 . -1117) T) ((-592 . -1239) T) ((-592 . -567) T) ((-529 . -1239) T) ((-529 . -567) T) ((-498 . -657) 100374) ((-485 . -234) 100320) ((-438 . -1068) 100304) ((-438 . -651) 100288) ((-369 . -728) 100240) ((-363 . -728) 100192) ((-349 . -1073) 100176) ((-355 . -728) 100128) ((-349 . -111) 100107) ((-176 . -1073) 100039) ((-219 . -657) 99989) ((-176 . -111) 99900) ((-108 . -728) 99850) ((-282 . -1117) T) ((-281 . -1117) T) ((-280 . -1117) T) ((-279 . -1117) T) ((-278 . -1117) T) ((-277 . -1117) T) ((-276 . -1117) T) ((-214 . -1117) T) ((-213 . -1117) T) ((-171 . -1223) 99828) ((-171 . -1220) 99806) ((-211 . -1117) T) ((-210 . -1117) T) ((-117 . -1066) T) ((-209 . -1117) T) ((-208 . -1117) T) ((-205 . -1117) T) ((-204 . -1117) T) ((-203 . -1117) T) ((-202 . -1117) T) ((-201 . -1117) T) ((-200 . -1117) T) ((-199 . -1117) T) ((-198 . -1117) T) ((-197 . -1117) T) ((-196 . -1117) T) ((-195 . -1117) T) ((-245 . -102) 99558) ((-171 . -35) 99536) ((-171 . -95) 99514) ((-665 . -1055) 99410) ((-493 . -1075) 99388) ((-1130 . -1117) 99140) ((-1159 . -34) T) ((-681 . -500) 99124) ((-73 . -1235) T) ((-105 . -624) 99106) ((-1309 . -624) 99088) ((-391 . -624) 99070) ((-349 . -627) 99022) ((-176 . -627) 98939) ((-1234 . -501) 98920) ((-742 . -38) 98769) ((-582 . -1223) T) ((-582 . -1220) T) ((-542 . -624) 98751) ((-531 . -318) 98689) ((-511 . -624) 98671) ((-511 . -625) 98653) ((-1234 . -624) 98619) ((-1185 . -1169) NIL) ((-1044 . -1088) 98588) ((-1044 . -1117) T) ((-1021 . -102) T) ((-988 . -102) T) ((-929 . -102) T) ((-905 . -1055) 98565) ((-1159 . -737) T) ((-1020 . -659) 98472) ((-487 . -1117) T) ((-474 . -1117) T) ((-597 . -23) T) ((-582 . -35) T) ((-582 . -95) T) ((-438 . -102) T) ((-1080 . -231) 98418) ((-1192 . -38) 98315) ((-877 . -737) T) ((-705 . -935) T) ((-522 . -25) T) ((-518 . -21) T) ((-518 . -25) T) ((-1191 . -38) 98156) ((-349 . -1066) T) ((-1185 . -38) 97952) ((-1097 . -174) T) ((-176 . -1066) T) ((-1143 . -38) 97849) ((-723 . -47) 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-23) T) ((-492 . -463) 96921) ((-472 . -23) T) ((-391 . -392) 96900) ((-365 . -234) 96873) ((-362 . -234) 96846) ((-354 . -234) 96819) ((-465 . -23) T) ((-272 . -234) 96764) ((-257 . -908) 96631) ((-256 . -908) 96498) ((-96 . -1117) T) ((-723 . -1235) T) ((-681 . -295) 96475) ((-495 . -525) 96408) ((-1277 . -1068) 96291) ((-1277 . -651) 96188) ((-1270 . -651) 96029) ((-1270 . -1068) 95864) ((-1249 . -651) 95660) ((-298 . -299) T) ((-1249 . -1068) 95450) ((-1099 . -624) 95432) ((-1099 . -625) 95413) ((-418 . -924) 95392) ((-1229 . -132) T) ((-50 . -1129) T) ((-1185 . -411) 95344) ((-1041 . -935) T) ((-1020 . -737) T) ((-854 . -659) 95317) ((-723 . -898) NIL) ((-607 . -1068) 95277) ((-592 . -1129) T) ((-529 . -1129) T) ((-606 . -1068) 95160) ((-1174 . -34) T) ((-1021 . -318) NIL) ((-826 . -500) 95144) ((-607 . -651) 95117) ((-364 . -935) T) ((-606 . -651) 95014) ((-925 . -234) 95001) ((-418 . -659) 94917) ((-50 . -23) T) ((-722 . -132) T) ((-723 . -1055) 94797) ((-592 . -23) T) ((-108 . 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93507) ((-664 . -422) 93491) ((-1249 . -102) T) ((-1176 . -525) NIL) ((-673 . -25) T) ((-632 . -1073) 93475) ((-673 . -21) T) ((-978 . -657) 93385) ((-746 . -657) 93330) ((-726 . -657) 93302) ((-401 . -111) 93281) ((-224 . -260) 93265) ((-1071 . -1070) 93205) ((-1071 . -1117) T) ((-1021 . -1169) T) ((-829 . -1117) T) ((-464 . -657) 93120) ((-646 . -659) 93104) ((-353 . -1239) T) ((-632 . -111) 93083) ((-618 . -659) 93067) ((-607 . -102) T) ((-320 . -501) 93048) ((-597 . -132) T) ((-606 . -102) T) ((-425 . -1117) T) ((-395 . -1117) T) ((-320 . -624) 93014) ((-229 . -1117) 92992) ((-658 . -525) 92925) ((-643 . -525) 92769) ((-844 . -1066) 92748) ((-655 . -152) 92732) ((-353 . -567) T) ((-723 . -913) 92675) ((-561 . -231) 92625) ((-1277 . -293) 92591) ((-1270 . -293) 92557) ((-1097 . -299) 92508) ((-498 . -859) T) ((-225 . -1129) T) ((-1249 . -293) 92474) ((-1229 . -504) 92440) ((-1021 . -38) 92390) ((-219 . -859) T) ((-429 . -657) 92349) ((-929 . -38) 92301) ((-854 . -805) 92280) ((-854 . -802) 92259) ((-854 . -737) 92238) ((-369 . -299) T) ((-363 . -299) T) ((-355 . -299) T) ((-171 . -463) 92169) ((-438 . -38) 92153) ((-225 . -23) T) ((-108 . -299) T) ((-418 . -805) 92132) ((-418 . -802) 92111) ((-418 . -737) T) ((-511 . -297) 92086) ((-488 . -1073) 92051) ((-669 . -132) T) ((-632 . -627) 92020) ((-1130 . -525) 91953) ((-346 . -132) T) ((-171 . -413) 91932) ((-493 . -728) 91874) ((-826 . -295) 91851) ((-488 . -111) 91807) ((-664 . -1075) T) ((-1190 . -908) 91710) ((-1142 . -908) 91692) ((-827 . -1068) 91535) ((-1296 . -1100) T) ((-1258 . -463) 91466) ((-827 . -651) 91315) ((-1295 . -1100) T) ((-1104 . -132) T) ((-1071 . -728) 91257) ((-1044 . -525) 91190) ((-793 . -132) T) ((-791 . -132) T) ((-582 . -463) T) ((-632 . -1066) T) ((-603 . -1117) T) ((-544 . -175) T) ((-472 . -132) T) ((-465 . -132) T) ((-389 . -237) T) ((-1016 . -1235) T) ((-45 . -1117) T) ((-395 . -728) 91160) ((-828 . -1117) T) ((-487 . -525) 91093) ((-474 . -525) 91026) ((-1310 . -627) 91008) ((-464 . -377) 90978) ((-45 . -621) 90957) ((-410 . -1235) T) ((-325 . -311) T) ((-838 . -237) 90936) ((-488 . -627) 90886) ((-1249 . -318) 90771) ((-681 . -624) 90733) ((-59 . -861) 90712) ((-1021 . -411) 90694) ((-559 . -624) 90676) ((-810 . -657) 90635) ((-826 . -615) 90612) ((-527 . -861) 90591) ((-507 . -861) 90570) ((-1016 . -1055) 90466) ((-40 . -1239) T) ((-245 . -915) 90335) ((-50 . -132) T) ((-592 . -132) T) ((-529 . -132) T) ((-303 . -659) 90195) ((-353 . -338) 90172) ((-353 . -373) T) ((-331 . -332) 90149) ((-328 . -295) 90107) ((-40 . -567) T) ((-389 . -1220) T) ((-389 . -1223) T) ((-1052 . -1211) 90082) ((-1207 . -240) 90032) ((-1185 . -232) 89984) ((-1185 . -271) 89936) ((-339 . -1117) T) ((-389 . -95) T) ((-389 . -35) T) ((-1052 . -107) 89882) ((-488 . -1066) T) ((-1309 . -1073) 89866) ((-490 . -240) 89816) ((-1177 . -500) 89750) ((-1300 . -1068) 89734) ((-391 . -1073) 89718) ((-1300 . -651) 89688) ((-488 . -248) T) ((-827 . -102) T) ((-725 . -148) 89667) ((-725 . -146) 89646) 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83686) ((-712 . -659) 83658) ((-560 . -855) T) ((-219 . -1117) T) ((-325 . -935) 83637) ((-322 . -935) T) ((-322 . -831) NIL) ((-401 . -731) T) ((-881 . -23) T) ((-117 . -659) 83624) ((-485 . -146) 83603) ((-429 . -422) 83587) ((-485 . -148) 83566) ((-110 . -500) 83548) ((-320 . -627) 83529) ((-2 . -624) 83511) ((-188 . -102) T) ((-1176 . -19) 83493) ((-1176 . -615) 83468) ((-669 . -21) T) ((-669 . -25) T) ((-604 . -1161) T) ((-1130 . -295) 83445) ((-346 . -25) T) ((-346 . -21) T) ((-245 . -657) 83224) ((-506 . -373) T) ((-1307 . -1073) 83208) ((-1305 . -1073) 83192) ((-1300 . -38) 83162) ((-1269 . -1220) 83128) ((-1258 . -908) 83031) ((-1190 . -1068) 82854) ((-1159 . -1235) T) ((-1142 . -1068) 82697) ((-865 . -1068) 82681) ((-643 . -615) 82656) ((-1269 . -1223) 82622) ((-1269 . -95) 82588) ((-1269 . -237) 82540) ((-1190 . -651) 82369) ((-1142 . -651) 82218) ((-865 . -651) 82188) ((-1252 . -102) 82166) ((-1249 . -232) 82118) ((-560 . -1117) T) ((-1104 . -25) T) ((-1104 . -21) T) ((-542 . -803) T) ((-542 . -806) T) ((-118 . -1239) T) ((-978 . -1075) T) ((-634 . -567) T) ((-793 . -25) T) ((-793 . -21) T) ((-791 . -21) T) ((-791 . -25) T) ((-746 . -1075) T) ((-726 . -1075) T) ((-681 . -1073) 82102) ((-528 . -1100) T) ((-472 . -25) T) ((-118 . -567) T) ((-472 . -21) T) ((-465 . -25) T) ((-465 . -21) T) ((-1249 . -271) 82054) ((-1168 . -93) T) ((-1159 . -1055) 81950) ((-828 . -299) 81929) ((-1248 . -1220) 81895) ((-834 . -1117) T) ((-981 . -984) T) ((-681 . -111) 81874) ((-628 . -1235) T) ((-304 . -525) 81666) ((-1248 . -1223) 81632) ((-1248 . -237) 81491) ((-1243 . -378) T) ((-257 . -318) 81429) ((-256 . -318) 81367) ((-1240 . -855) T) ((-1177 . -625) NIL) ((-1177 . -624) 81349) ((-1159 . -387) 81333) ((-1137 . -831) T) ((-1137 . -935) T) ((-96 . -93) T) ((-1130 . -615) 81310) ((-1097 . -625) 81294) ((-1097 . -624) 81276) ((-1021 . -657) 81226) ((-929 . -657) 81163) ((-826 . -297) 81140) ((-495 . -624) 81072) ((-619 . -152) 81019) ((-498 . -728) 80969) ((-429 . -1075) T) 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. -111) 25114) ((-361 . -1239) T) ((-1277 . -1073) 24997) ((-1130 . -387) 24966) ((-1270 . -1073) 24801) ((-1249 . -1073) 24591) ((-1270 . -111) 24412) ((-1249 . -111) 24181) ((-1229 . -318) 24168) ((-1020 . -132) T) ((-925 . -657) 24118) ((-375 . -624) 24100) ((-361 . -567) T) ((-298 . -316) T) ((-607 . -1073) 24060) ((-606 . -1073) 23943) ((-592 . -1068) 23908) ((-529 . -1068) 23853) ((-371 . -1117) T) ((-331 . -1117) T) ((-257 . -624) 23814) ((-256 . -624) 23775) ((-592 . -651) 23740) ((-529 . -651) 23685) ((-705 . -420) 23652) ((-646 . -23) T) ((-618 . -23) T) ((-40 . -908) 23559) ((-669 . -102) T) ((-607 . -111) 23512) ((-606 . -111) 23381) ((-389 . -1117) T) ((-346 . -102) T) ((-171 . -299) 23292) ((-1248 . -859) 23245) ((-725 . -1075) T) ((-1164 . -525) 23178) ((-1208 . -846) 23162) ((-1130 . -913) 23094) ((-847 . -1117) T) ((-838 . -1117) T) ((-836 . -1117) T) ((-97 . -102) T) ((-145 . -861) T) ((-623 . -896) 23078) ((-110 . -1235) T) ((-1104 . -102) T) ((-1080 . -34) T) ((-793 . -102) T) ((-791 . -102) T) ((-1277 . -627) 22960) ((-1270 . -627) 22703) ((-472 . -102) T) ((-465 . -102) T) ((-1249 . -627) 22498) ((-245 . -806) 22477) ((-245 . -803) 22456) ((-660 . -102) T) ((-607 . -627) 22414) ((-606 . -627) 22296) ((-1258 . -299) 22207) ((-675 . -645) 22191) ((-188 . -624) 22173) ((-655 . -295) 22125) ((-1051 . -728) 22109) ((-582 . -299) T) ((-978 . -659) 22034) ((-1308 . -132) T) ((-746 . -659) 21994) ((-726 . -659) 21981) ((-283 . -102) T) ((-464 . -659) 21911) ((-50 . -102) T) ((-592 . -102) T) ((-529 . -102) T) ((-1277 . -1066) T) ((-1270 . -1066) T) ((-1249 . -1066) T) ((-518 . -657) 21893) ((-331 . -728) 21875) ((-1277 . -238) 21834) ((-1270 . -248) 21813) ((-1270 . -238) 21765) ((-1249 . -238) 21652) ((-1249 . -248) 21631) ((-1229 . -38) 21528) ((-607 . -1066) T) ((-606 . -1066) T) ((-1021 . -806) T) ((-1021 . -803) T) ((-988 . -806) T) ((-988 . -803) T) ((-883 . -1075) T) ((-109 . -624) 21510) ((-705 . -463) T) ((-389 . -728) 21475) ((-429 . -659) 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-318) 20212) ((-1090 . -1117) T) ((-229 . -1235) T) ((-1083 . -1117) T) ((-1053 . -1117) T) ((-1036 . -1117) T) ((-793 . -318) 20199) ((-791 . -318) 20186) ((-1190 . -624) 20168) ((-827 . -111) 19997) ((-1142 . -624) 19979) ((-637 . -1117) T) ((-588 . -175) T) ((-540 . -175) T) ((-465 . -318) 19966) ((-494 . -1117) T) ((-1142 . -625) 19714) ((-1051 . -174) T) ((-958 . -297) 19691) ((-220 . -1117) T) ((-865 . -624) 19673) ((-619 . -525) 19456) ((-81 . -627) 19397) ((-829 . -1055) 19381) ((-486 . -525) 19173) ((-978 . -737) T) ((-746 . -737) T) ((-726 . -737) T) ((-361 . -1129) T) ((-1197 . -624) 19155) ((-225 . -102) T) ((-493 . -387) 19124) ((-526 . -1117) T) ((-521 . -1117) T) ((-519 . -1117) T) ((-810 . -659) 19098) ((-1041 . -463) T) ((-973 . -525) 19031) ((-361 . -23) T) ((-646 . -132) T) ((-618 . -132) T) ((-364 . -463) T) ((-245 . -378) 19010) ((-389 . -174) T) ((-1269 . -1075) T) ((-1248 . -1075) T) ((-227 . -1019) T) ((-827 . -627) 18747) ((-710 . -398) T) ((-429 . -737) T) 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-629) 16058) ((-588 . -587) T) ((-588 . -538) T) ((-540 . -538) T) ((-118 . -908) NIL) ((-1185 . -924) NIL) ((-1079 . -625) 15973) ((-1079 . -624) 15955) ((-967 . -624) 15937) ((-724 . -501) 15887) ((-353 . -102) T) ((-257 . -1073) 15808) ((-256 . -1073) 15729) ((-405 . -102) T) ((-31 . -1117) T) ((-967 . -625) 15590) ((-724 . -624) 15525) ((-1298 . -1228) 15494) ((-492 . -624) 15476) ((-492 . -625) 15337) ((-272 . -422) 15321) ((-252 . -422) 15305) ((-322 . -237) NIL) ((-257 . -111) 15221) ((-256 . -111) 15137) ((-1192 . -659) 15062) ((-1191 . -659) 14959) ((-1185 . -659) 14811) ((-1143 . -659) 14736) ((-361 . -132) T) ((-82 . -452) T) ((-82 . -406) T) ((-1020 . -25) T) ((-1020 . -21) T) ((-884 . -1117) 14687) ((-40 . -1068) 14632) ((-883 . -728) 14584) ((-40 . -651) 14529) ((-389 . -299) T) ((-171 . -1019) 14480) ((-1104 . -915) 14379) ((-705 . -398) T) ((-1016 . -1014) 14363) ((-712 . -1129) T) ((-705 . -167) 14345) ((-793 . -915) 14252) ((-791 . -915) 14236) ((-1269 . -1117) T) 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\ No newline at end of file
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. -1237) T) ((-1019 . -625) 190642) ((-706 . -272) 190624) ((-706 . -232) 190606) ((-726 . -111) 190571) ((-656 . -34) T) ((-250 . -501) 190555) ((-1316 . -1171) T) ((-1311 . -21) T) ((-1311 . -25) T) ((-1309 . -132) T) ((-1121 . -1117) 190539) ((-173 . -1119) T) ((-1307 . -132) T) ((-1300 . -102) T) ((-1283 . -625) 190505) ((-1279 . -1237) T) ((-1272 . -1237) T) ((-969 . -926) 190484) ((-1272 . -1057) 190419) ((-1251 . -1237) T) ((-1251 . -899) NIL) ((-527 . -628) 190403) ((-1251 . -897) 190355) ((-1251 . -1057) 190321) ((-1231 . -526) 190288) ((-493 . -926) 190267) ((-1209 . -626) NIL) ((-1209 . -625) 190249) ((-1106 . -729) 190098) ((-1081 . -660) 190070) ((-969 . -660) 189959) ((-609 . -502) 189940) ((-597 . -502) 189921) ((-794 . -729) 189750) ((-609 . -625) 189716) ((-597 . -625) 189682) ((-548 . -625) 189664) ((-548 . -626) 189645) ((-792 . -729) 189494) ((-1096 . -102) T) ((-392 . -25) T) ((-635 . -658) 189466) ((-392 . -21) T) ((-493 . -660) 189355) ((-473 . -729) 189326) ((-466 . -729) 189175) ((-1006 . -102) T) ((-1161 . -1142) 189120) ((-1065 . -1230) 189049) ((-918 . -319) 188987) ((-749 . -102) T) ((-118 . -658) 188917) ((-617 . -628) 188899) ((-888 . -93) T) ((-726 . -628) 188853) ((-543 . -25) T) ((-693 . -93) T) ((-688 . -93) T) ((-676 . -625) 188835) ((-657 . -502) 188816) ((-142 . -102) T) ((-44 . -132) T) ((-657 . -625) 188769) ((-607 . -1237) T) ((-354 . -1077) T) ((-299 . -1131) T) ((-490 . -93) T) ((-419 . -237) 188720) ((-366 . -625) 188702) ((-363 . -625) 188684) ((-355 . -625) 188666) ((-273 . -626) 188414) ((-273 . -625) 188396) ((-253 . -625) 188378) ((-253 . -626) 188239) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1160 . -625) 188221) ((-1139 . -652) 188208) ((-1139 . -1070) 188195) ((-831 . -738) T) ((-831 . -869) T) ((-614 . -298) 188172) ((-593 . -729) 188137) ((-491 . -626) NIL) ((-491 . -625) 188119) ((-530 . -729) 188064) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-927 . -625) 188046) ((-927 . -626) 188028) ((-398 . -738) T) ((-884 . -1075) 187980) ((-884 . -111) 187918) ((-726 . -1068) T) ((-724 . -1263) 187902) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 187834) ((-390 . -807) T) ((-225 . -1119) T) ((-169 . -1237) T) ((-390 . -804) T) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -626) 187795) ((-59 . -625) 187707) ((-227 . -738) T) ((-528 . -626) 187668) ((-528 . -625) 187580) ((-509 . -625) 187512) ((-508 . -626) 187473) ((-508 . -625) 187385) ((-1099 . -374) 187336) ((-40 . -423) 187313) ((-77 . -1237) T) ((-883 . -926) NIL) ((-370 . -339) 187297) ((-370 . -374) T) ((-364 . -339) 187281) ((-364 . -374) T) ((-356 . -339) 187265) ((-356 . -374) T) ((-326 . -294) 187244) ((-108 . -374) T) ((-70 . -1237) T) ((-1251 . -349) 187196) ((-883 . -660) 187141) ((-1251 . -388) 187093) ((-981 . -132) 186948) ((-827 . -132) 186819) ((-975 . -663) 186803) ((-1106 . -174) 186714) ((-975 . -384) 186698) ((-1081 . -806) T) ((-1081 . -803) T) ((-884 . -628) 186596) ((-794 . -174) 186487) ((-792 . -174) 186398) ((-828 . -47) 186360) ((-1081 . -738) T) ((-337 . -501) 186344) ((-969 . -738) T) ((-1300 . -319) 186282) ((-1279 . -915) 186195) ((-466 . -174) 186106) ((-250 . -296) 186058) ((-1272 . -915) 185964) ((-1271 . -1075) 185799) ((-1251 . -915) 185632) ((-493 . -738) T) ((-1250 . -1075) 185440) ((-1231 . -300) 185419) ((-1206 . -1237) T) ((-1203 . -379) T) ((-1202 . -379) T) ((-1165 . -152) 185403) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 185370) ((-1022 . -421) 185342) ((-944 . -972) T) ((-749 . -319) 185280) ((-75 . -1237) T) ((-676 . -393) 185252) ((-171 . -926) 185205) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185187) ((-1018 . -909) 185108) ((-129 . -663) 185090) ((-50 . -632) 185074) ((-706 . -658) 185009) ((-607 . -915) 184922) ((-450 . -102) T) ((-129 . -384) 184904) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 184883) ((-81 . -1237) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 184865) ((-171 . -660) 184739) ((-519 . -625) 184721) ((-362 . -148) 184703) ((-362 . -146) T) ((-370 . -1131) T) ((-364 . -1131) T) ((-356 . -1131) T) ((-1023 . -317) T) ((-931 . -317) T) ((-884 . -248) T) ((-108 . -1131) T) ((-884 . -238) 184682) ((-1271 . -111) 184503) ((-1250 . -111) 184292) ((-250 . -1275) 184276) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184263) ((-323 . -319) 184204) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184185) ((-108 . -23) T) ((-666 . -1070) 184169) ((-250 . -616) 184146) ((-343 . -1119) T) ((-666 . -652) 184116) ((-1273 . -38) 184008) ((-1260 . -926) 183987) ((-112 . -1119) T) ((-828 . -1237) T) ((-1054 . -102) T) ((-1260 . -660) 183876) ((-883 . -806) NIL) ((-867 . -660) 183850) ((-883 . -803) NIL) ((-828 . -899) NIL) ((-883 . -738) T) ((-1106 . -526) 183723) ((-794 . -526) 183670) ((-792 . -526) 183622) ((-583 . -660) 183609) ((-828 . -1057) 183437) ((-466 . -526) 183380) ((-400 . -401) T) ((-1271 . -628) 183193) ((-1250 . -628) 182941) ((-60 . -1237) T) ((-633 . -862) 182920) ((-512 . -673) T) ((-1165 . -995) 182889) ((-1043 . -658) 182826) ((-1022 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1075) 182661) ((-512 . -113) T) ((-354 . -1119) T) ((-323 . -1171) NIL) ((-299 . -132) T) ((-406 . -1119) T) ((-882 . -1077) T) ((-706 . -381) 182628) ((-365 . -658) 182558) ((-225 . -632) 182535) ((-337 . -296) 182487) ((-486 . -111) 182308) ((-1271 . -1068) T) ((-1250 . -1068) T) ((-828 . -388) 182292) ((-171 . -738) T) ((-666 . -102) T) ((-1271 . -248) 182271) ((-1271 . -238) 182223) ((-1250 . -238) 182128) ((-1250 . -248) 182107) ((-1022 . -414) NIL) ((-682 . -651) 182055) ((-326 . -38) 181965) ((-323 . -38) 181894) ((-69 . -625) 181876) ((-329 . -505) 181842) ((-48 . -658) 181792) ((-1209 . -298) 181771) ((-1245 . -862) T) ((-1132 . -1131) 181749) ((-83 . -1237) T) ((-61 . -625) 181731) ((-491 . -298) 181710) ((-1302 . -1057) 181687) ((-1184 . -1119) T) ((-1132 . -23) 181539) ((-828 . -915) 181475) ((-1260 . -738) T) ((-1121 . -1237) T) ((-486 . -628) 181301) ((-362 . -237) T) ((-1106 . -300) 181232) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181143) ((-337 . -19) 181127) ((-59 . -298) 181104) ((-792 . -300) 181035) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181012) ((-337 . -616) 180989) ((-508 . -298) 180966) ((-466 . -300) 180897) ((-1054 . -319) 180748) ((-888 . -502) 180729) ((-888 . -625) 180695) ((-693 . -502) 180676) ((-583 . -738) T) ((-688 . -502) 180657) ((-693 . -625) 180607) ((-688 . -625) 180573) ((-674 . -625) 180555) ((-490 . -502) 180536) ((-490 . -625) 180502) ((-250 . -626) 180463) ((-250 . -502) 180440) ((-139 . -502) 180421) ((-138 . -502) 180402) ((-134 . -502) 180383) ((-250 . -625) 180275) ((-215 . -102) T) ((-139 . -625) 180241) ((-138 . -625) 180207) ((-134 . -625) 180173) ((-1166 . -34) T) ((-960 . -1237) T) ((-354 . -729) 180118) ((-682 . -25) T) ((-682 . -21) T) ((-1196 . -628) 180099) ((-486 . -1068) T) ((-647 . -429) 180064) ((-619 . -429) 180029) ((-1139 . -1171) T) ((-724 . -1070) 179852) ((-593 . -300) T) ((-530 . -300) T) ((-1272 . -317) 179831) ((-486 . -238) 179783) ((-486 . -248) 179762) ((-1251 . -317) 179741) ((-724 . -652) 179570) ((-1251 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 179549) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 179528) ((-656 . -1029) 179512) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 179496) ((-323 . -412) 179457) ((-364 . -132) T) ((-356 . -132) T) ((-1201 . -1119) T) ((-1139 . -38) 179444) ((-1113 . -625) 179411) ((-108 . -132) T) ((-971 . -1119) T) ((-938 . -1119) T) ((-783 . -1119) T) ((-684 . -1119) T) ((-713 . -148) T) ((-117 . -148) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-1307 . -21) T) ((-1307 . -25) T) ((-676 . -1075) 179395) ((-543 . -862) T) ((-512 . -862) T) ((-366 . -1075) 179347) ((-363 . -1075) 179299) ((-355 . -1075) 179251) ((-258 . -1237) T) ((-257 . -1237) T) ((-273 . -1075) 179094) ((-253 . -1075) 178937) ((-676 . -111) 178916) ((-829 . -1241) 178895) ((-559 . -856) T) ((-326 . -917) 178861) ((-366 . -111) 178799) ((-363 . -111) 178737) ((-355 . -111) 178675) ((-273 . -111) 178504) ((-253 . -111) 178333) ((-323 . -917) NIL) ((-635 . -423) 178317) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178223) ((-829 . -568) 178202) ((-258 . -1057) 178029) ((-257 . -1057) 177856) ((-127 . -120) 177840) ((-927 . -1075) 177805) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 177786) ((-597 . -628) 177767) ((-548 . -630) 177670) ((-354 . -174) T) ((-88 . -625) 177652) ((-153 . -21) T) ((-153 . -25) T) ((-927 . -111) 177608) ((-40 . -729) 177553) ((-882 . -1119) T) ((-676 . -628) 177530) ((-657 . -628) 177511) ((-366 . -628) 177448) ((-363 . -628) 177385) ((-559 . -1119) T) ((-355 . -628) 177322) ((-337 . -626) 177283) ((-337 . -625) 177195) ((-273 . -628) 176948) ((-253 . -628) 176733) ((-1250 . -804) 176686) ((-1250 . -807) 176639) ((-258 . -388) 176608) ((-257 . -388) 176577) ((-666 . -38) 176547) ((-620 . -34) T) ((-494 . -1131) 176525) ((-487 . -34) T) ((-1132 . -132) 176396) ((-981 . -25) 176207) ((-927 . -628) 176157) ((-886 . -625) 176139) ((-981 . -21) 176094) ((-827 . -25) 175927) ((-827 . -21) 175838) ((-1243 . -379) T) ((-635 . -1077) T) ((-1198 . -568) 175817) ((-1192 . -47) 175794) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 175646) ((-355 . -1068) T) ((-273 . -1068) T) ((-253 . -1068) T) ((-1144 . -47) 175618) ((-118 . -1077) T) ((-1053 . -660) 175592) ((-975 . -34) T) ((-366 . -238) 175571) ((-366 . -248) T) ((-363 . -238) 175550) ((-363 . -248) T) ((-355 . -238) 175529) ((-355 . -248) T) ((-273 . -336) 175501) ((-253 . -336) 175458) ((-273 . -238) 175437) ((-1176 . -152) 175421) ((-258 . -915) 175353) ((-257 . -915) 175285) ((-1161 . -909) 175206) ((-1101 . -862) T) ((-426 . -1131) T) ((-1073 . -23) T) ((-1043 . -860) T) ((-927 . -1068) T) ((-332 . -660) 175188) ((-713 . -237) T) ((-682 . -234) 175133) ((-1231 . -1021) 175099) ((-1193 . -937) 175078) ((-1187 . -937) 175057) ((-1187 . -832) NIL) ((-1018 . -1070) 174953) ((-984 . -1237) T) ((-927 . -248) T) ((-829 . -374) 174932) ((-396 . -23) T) ((-128 . -1119) 174910) ((-122 . -1119) 174888) ((-927 . -238) T) ((-129 . -34) T) ((-390 . -660) 174853) ((-1018 . -652) 174801) ((-882 . -729) 174788) ((-1316 . -658) 174760) ((-1065 . -152) 174725) ((-1012 . -1237) T) ((-40 . -174) T) ((-706 . -423) 174707) ((-724 . -319) 174694) ((-848 . -660) 174654) ((-839 . -660) 174628) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 174607) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-250 . -298) 174584) ((-1192 . -1237) T) ((-1144 . -1237) T) ((-323 . -272) 174545) ((-323 . -232) 174506) ((-1192 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174365) ((-130 . -862) T) ((-1192 . -1057) 174245) ((-1144 . -1057) 174128) ((-185 . -625) 174110) ((-866 . -1057) 174006) ((-794 . -296) 173933) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 173862) ((-614 . -663) 173846) ((-1022 . -909) 173753) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 173731) ((-706 . -1077) T) ((-614 . -384) 173715) ((-362 . -464) T) ((-354 . -300) T) ((-1288 . -1119) T) ((-254 . -1119) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1119) T) ((-711 . -1119) T) ((-372 . -485) T) ((-1231 . -625) 173697) ((-1192 . -388) 173681) ((-1144 . -388) 173665) ((-1043 . -423) 173627) ((-142 . -231) 173609) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 173591) ((-724 . -38) 173420) ((-1287 . -1285) 173404) ((-362 . -414) T) ((-1287 . -1119) 173354) ((-1210 . -1119) T) ((-592 . -729) 173341) ((-576 . -729) 173328) ((-507 . -729) 173293) ((-1273 . -658) 173183) ((-326 . -641) 173162) ((-848 . -738) T) ((-839 . -738) T) ((-656 . -1237) T) ((-1099 . -651) 173110) ((-1192 . -915) 173053) ((-1144 . -915) 173037) ((-827 . -234) 172928) ((-674 . -1075) 172912) ((-108 . -651) 172894) ((-494 . -132) 172765) ((-1198 . -1131) T) ((-969 . -47) 172734) ((-635 . -1119) T) ((-674 . -111) 172713) ((-503 . -625) 172679) ((-337 . -298) 172656) ((-493 . -47) 172613) ((-1198 . -23) T) ((-118 . -1119) T) ((-103 . -102) 172591) ((-1299 . -1131) T) ((-560 . -862) T) ((-227 . -1237) T) ((-1073 . -132) T) ((-1043 . -1077) T) ((-1299 . -23) T) ((-831 . -1057) 172575) ((-1217 . -625) 172557) ((-1022 . -736) 172529) ((-1139 . -840) T) ((-711 . -729) 172494) ((-598 . -625) 172476) ((-398 . -1057) 172460) ((-365 . -1077) T) ((-396 . -132) T) ((-334 . -1057) 172444) ((-1124 . -1119) T) ((-1099 . -21) T) ((-1099 . -25) T) ((-227 . -899) 172426) ((-1023 . -937) T) ((-91 . -34) T) ((-1023 . -832) T) ((-931 . -937) T) ((-1018 . -319) 172391) ((-888 . -628) 172372) ((-499 . -1241) T) ((-726 . -660) 172332) ((-693 . -628) 172313) ((-688 . -628) 172294) ((-219 . -1241) T) ((-419 . -909) 172215) ((-227 . -1057) 172175) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 172156) ((-370 . -25) T) ((-326 . -658) 171811) ((-323 . -658) 171725) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 171671) ((-250 . -628) 171648) ((-139 . -628) 171629) ((-138 . -628) 171610) ((-134 . -628) 171591) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1077) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1081 . -1237) T) ((-969 . -1237) T) ((-670 . -625) 171573) ((-493 . -1237) T) ((-749 . -748) 171557) ((-347 . -625) 171539) ((-68 . -394) T) ((-68 . -407) T) ((-1121 . -107) 171523) ((-1081 . -899) 171505) ((-969 . -899) 171430) ((-665 . -1131) T) ((-635 . -729) 171417) ((-493 . -899) NIL) ((-1165 . -102) T) ((-1113 . -630) 171401) ((-1081 . -1057) 171383) ((-97 . -625) 171365) ((-489 . -148) T) ((-969 . -1057) 171245) ((-118 . -729) 171190) ((-724 . -917) 171097) ((-665 . -23) T) ((-493 . -1057) 170973) ((-1106 . -626) NIL) ((-1106 . -625) 170955) ((-794 . -626) NIL) ((-794 . -625) 170916) ((-792 . -626) 170550) ((-792 . -625) 170464) ((-1132 . -651) 170370) ((-473 . -625) 170352) ((-466 . -625) 170334) ((-466 . -626) 170195) ((-1054 . -231) 170141) ((-884 . -926) 170120) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170102) ((-590 . -102) T) ((-366 . -1306) 170086) ((-363 . -1306) 170070) ((-355 . -1306) 170054) ((-128 . -526) 169987) ((-122 . -526) 169920) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 169858) ((-224 . -102) 169836) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 169752) ((-65 . -395) T) ((-284 . -625) 169734) ((-65 . -407) T) ((-969 . -388) 169718) ((-882 . -300) T) ((-50 . -625) 169700) ((-1018 . -38) 169648) ((-1139 . -658) 169620) ((-593 . -625) 169602) ((-493 . -388) 169586) ((-593 . -626) 169568) ((-530 . -625) 169550) ((-927 . -1306) 169537) ((-883 . -1237) T) ((-713 . -464) T) ((-507 . -526) 169503) ((-499 . -374) T) ((-366 . -379) 169482) ((-363 . -379) 169461) ((-355 . -379) 169440) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1310 . -1301) 169424) ((-883 . -897) 169401) ((-883 . -899) NIL) ((-981 . -862) 169300) ((-827 . -862) 169251) ((-1244 . -102) T) ((-666 . -668) 169235) ((-1223 . -34) T) ((-173 . -625) 169217) ((-1132 . -25) 169050) ((-1132 . -21) 168961) ((-883 . -1057) 168938) ((-969 . -915) 168919) ((-1260 . -47) 168896) ((-927 . -379) T) ((-59 . -663) 168880) ((-528 . -663) 168864) ((-493 . -915) 168841) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -663) 168825) ((-59 . -384) 168809) ((-635 . -174) T) ((-528 . -384) 168793) ((-508 . -384) 168777) ((-839 . -720) 168761) ((-1192 . -317) 168740) ((-1198 . -132) T) ((-1161 . -1070) 168724) ((-118 . -174) T) ((-1161 . -652) 168656) ((-1165 . -319) 168594) ((-171 . -1237) T) ((-1299 . -132) T) ((-878 . -1070) 168564) ((-647 . -756) 168548) ((-619 . -756) 168532) ((-1272 . -937) 168511) ((-1251 . -937) 168490) ((-1251 . -832) NIL) ((-878 . -652) 168460) ((-706 . -729) 168410) ((-1250 . -926) 168363) ((-1043 . -1119) T) ((-883 . -388) 168340) ((-883 . -349) 168317) ((-922 . -1131) T) ((-171 . -897) 168301) ((-171 . -899) 168226) ((-1287 . -526) 168159) ((-1271 . -660) 168056) ((-1099 . -234) 167929) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 167825) ((-304 . -909) 167782) ((-329 . -862) T) ((-1250 . -660) 167590) ((-884 . -806) 167569) ((-884 . -803) 167548) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 167521) ((-364 . -234) 167494) ((-356 . -234) 167467) ((-225 . -625) 167449) ((-176 . -464) T) ((-224 . -319) 167387) ((-86 . -453) T) ((-86 . -407) T) ((-108 . -234) 167374) ((-219 . -23) T) ((-1311 . -1304) 167353) ((-689 . -1057) 167337) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-137 . -482) 167292) ((-1260 . -1237) T) ((-666 . -658) 167251) ((-48 . -1119) T) ((-724 . -272) 167235) ((-724 . -232) 167219) ((-883 . -915) NIL) ((-1260 . -899) NIL) ((-902 . -102) T) ((-898 . -102) T) ((-400 . -1119) T) ((-171 . -388) 167203) ((-171 . -349) 167187) ((-1260 . -1057) 167067) ((-867 . -1057) 166963) ((-1161 . -102) T) ((-1018 . -917) 166886) ((-674 . -804) 166865) ((-665 . -132) T) ((-674 . -807) 166844) ((-118 . -526) 166752) ((-583 . -1057) 166734) ((-304 . -1294) 166704) ((-878 . -102) T) ((-980 . -568) 166683) ((-1231 . -1075) 166566) ((-1022 . -1070) 166511) ((-494 . -651) 166417) ((-921 . -1119) T) ((-1043 . -729) 166354) ((-723 . -1075) 166319) ((-1022 . -652) 166264) ((-629 . -102) T) ((-614 . -34) T) ((-1166 . -1237) T) ((-1231 . -111) 166133) ((-486 . -660) 166030) ((-365 . -729) 165975) ((-171 . -915) 165934) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 165890) ((-1316 . -1077) T) ((-1260 . -388) 165874) ((-430 . -1241) 165852) ((-1137 . -625) 165834) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1250 . -803) 165787) ((-1250 . -806) 165740) ((-1271 . -738) T) ((-1250 . -738) T) ((-48 . -729) 165705) ((-227 . -1041) T) ((-1273 . -423) 165671) ((-362 . -1294) 165648) ((-1260 . -915) 165591) ((-730 . -738) T) ((-343 . -625) 165573) ((-1231 . -628) 165455) ((-1132 . -234) 165346) ((-112 . -625) 165328) ((-112 . -626) 165310) ((-730 . -485) T) ((-723 . -628) 165260) ((-1310 . -1070) 165244) ((-494 . -25) 165077) ((-128 . -501) 165061) ((-122 . -501) 165045) ((-494 . -21) 164956) ((-1310 . -652) 164926) ((-635 . -300) T) ((-598 . -1075) 164901) ((-449 . -1119) T) ((-1081 . -317) T) ((-118 . -300) T) ((-1123 . -102) T) ((-1022 . -102) T) ((-598 . -111) 164869) ((-1161 . -319) 164807) ((-1231 . -1068) T) ((-1081 . -1041) T) ((-66 . -1237) T) ((-1073 . -25) T) ((-1073 . -21) T) ((-723 . -1068) T) ((-396 . -21) T) ((-396 . -25) T) ((-706 . -526) NIL) ((-1043 . -174) T) ((-723 . -248) T) ((-1081 . -557) T) ((-724 . -658) 164717) ((-518 . -102) T) ((-514 . -102) T) ((-365 . -174) T) ((-354 . -625) 164699) ((-419 . -1070) 164651) ((-406 . -625) 164633) ((-1139 . -860) T) ((-486 . -738) T) ((-905 . -1057) 164601) ((-419 . -652) 164553) ((-108 . -862) T) ((-670 . -1075) 164537) ((-499 . -132) T) ((-1273 . -1077) T) ((-219 . -132) T) ((-1176 . -102) 164515) ((-99 . -1119) T) ((-250 . -678) 164499) ((-250 . -663) 164483) ((-670 . -111) 164462) ((-598 . -628) 164446) ((-326 . -423) 164430) ((-250 . -384) 164414) ((-1179 . -240) 164361) ((-1018 . -272) 164345) ((-1018 . -232) 164329) ((-74 . -1237) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1310 . -102) T) ((-1217 . -628) 164311) ((-1107 . -1237) T) ((-1106 . -1075) 164154) ((-1095 . -1237) T) ((-273 . -926) 164133) ((-253 . -926) 164112) ((-794 . -1075) 163935) ((-792 . -1075) 163778) ((-620 . -1237) T) ((-1184 . -625) 163760) ((-1106 . -111) 163589) ((-1065 . -102) T) ((-487 . -1237) T) ((-473 . -1075) 163560) ((-466 . -1075) 163403) ((-676 . -660) 163387) ((-883 . -317) T) ((-794 . -111) 163196) ((-792 . -111) 163025) ((-366 . -660) 162977) ((-363 . -660) 162929) ((-355 . -660) 162881) ((-273 . -660) 162770) ((-253 . -660) 162659) ((-1178 . -862) T) ((-1107 . -1057) 162643) ((-473 . -111) 162604) ((-466 . -111) 162433) ((-1095 . -1057) 162410) ((-1019 . -34) T) ((-983 . -625) 162392) ((-975 . -1237) T) ((-127 . -1029) 162376) ((-980 . -1131) T) ((-883 . -1041) NIL) ((-747 . -1131) T) ((-727 . -1131) T) ((-670 . -628) 162294) ((-1287 . -501) 162278) ((-1161 . -38) 162238) ((-980 . -23) T) ((-927 . -660) 162203) ((-877 . -1119) T) ((-855 . -102) T) ((-829 . -21) T) ((-647 . -1070) 162187) ((-619 . -1070) 162171) ((-829 . -25) T) ((-747 . -23) T) ((-727 . -23) T) ((-647 . -652) 162155) ((-110 . -673) T) ((-619 . -652) 162139) ((-593 . -1075) 162104) ((-530 . -1075) 162049) ((-229 . -57) 162007) ((-465 . -23) T) ((-419 . -102) T) ((-270 . -102) T) ((-110 . -113) T) ((-706 . -300) T) ((-878 . -38) 161977) ((-593 . -111) 161933) ((-530 . -111) 161862) ((-1106 . -628) 161598) ((-430 . -1131) T) ((-326 . -1077) 161488) ((-323 . -1077) T) ((-129 . -1237) T) ((-794 . -628) 161236) ((-792 . -628) 161002) ((-670 . -1068) T) ((-1316 . -1119) T) ((-466 . -628) 160787) ((-171 . -317) 160718) ((-430 . -23) T) ((-40 . -625) 160700) ((-40 . -626) 160684) ((-108 . -1011) 160666) ((-117 . -881) 160650) ((-661 . -628) 160634) ((-48 . -526) 160600) ((-1223 . -1029) 160584) ((-1201 . -625) 160551) ((-1209 . -34) T) ((-971 . -625) 160517) ((-938 . -625) 160499) ((-1132 . -862) 160450) ((-783 . -625) 160432) ((-684 . -625) 160414) ((-1176 . -319) 160352) ((-491 . -34) T) ((-1111 . -1237) T) ((-489 . -464) T) ((-1160 . -34) T) ((-1106 . -1068) T) ((-50 . -628) 160321) ((-794 . -1068) T) ((-792 . -1068) T) ((-659 . -240) 160305) ((-644 . -240) 160251) ((-593 . -628) 160201) ((-530 . -628) 160131) ((-494 . -234) 160022) ((-1260 . -317) 160001) ((-1106 . -336) 159962) ((-466 . -1068) T) ((-1198 . -21) T) ((-1106 . -238) 159941) ((-794 . -336) 159918) ((-794 . -238) T) ((-792 . -336) 159890) ((-743 . -1241) 159869) ((-337 . -663) 159853) ((-1198 . -25) T) ((-59 . -34) T) ((-531 . -34) T) ((-528 . -34) T) ((-466 . -336) 159832) ((-337 . -384) 159816) ((-509 . -34) T) ((-508 . -34) T) ((-1022 . -1171) NIL) ((-743 . -568) 159747) ((-647 . -102) T) ((-619 . -102) T) ((-366 . -738) T) ((-363 . -738) T) ((-355 . -738) T) ((-273 . -738) T) ((-253 . -738) T) ((-390 . -1237) T) ((-1065 . -319) 159655) ((-1299 . -21) T) ((-918 . -1119) 159633) ((-830 . -234) 159620) ((-50 . -1068) T) ((-1299 . -25) T) ((-1194 . -568) 159599) ((-1193 . -1241) 159578) ((-1193 . -568) 159529) ((-1187 . -1241) 159508) ((-1187 . -568) 159459) ((-593 . -1068) T) ((-530 . -1068) T) ((-1043 . -300) T) ((-372 . -1057) 159443) ((-332 . -1057) 159427) ((-1022 . -38) 159372) ((-390 . -899) 159354) ((-1018 . -658) 159277) ((-848 . -1237) T) ((-839 . -1237) 159256) ((-811 . -1131) T) ((-927 . -738) T) ((-593 . -248) T) ((-593 . -238) T) ((-530 . -238) T) ((-530 . -248) T) ((-1145 . -568) 159235) ((-365 . -300) T) ((-659 . -707) 159219) ((-390 . -1057) 159179) ((-304 . -1070) 159100) ((-350 . -909) 159079) ((-1139 . -1077) T) ((-103 . -126) 159063) ((-304 . -652) 159005) ((-811 . -23) T) ((-1309 . -1304) 158981) ((-1307 . -1304) 158960) ((-1287 . -296) 158912) ((-419 . -319) 158877) ((-1273 . -1119) T) ((-1161 . -917) 158800) ((-882 . -625) 158782) ((-848 . -1057) 158751) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 158733) ((-507 . -1021) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -862) T) ((-666 . -423) 158717) ((-682 . -237) 158668) ((-225 . -628) 158630) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1310 . -38) 158600) ((-118 . -296) 158551) ((-1287 . -19) 158535) ((-1287 . -616) 158512) ((-1300 . -1119) T) ((-362 . -1070) 158457) ((-1096 . -1119) T) ((-1006 . -1119) T) ((-980 . -132) T) ((-829 . -234) 158444) ((-749 . -1119) T) ((-362 . -652) 158389) ((-747 . -132) T) ((-727 . -132) T) ((-523 . -805) T) ((-523 . -806) T) ((-465 . -132) T) ((-419 . -1171) 158367) ((-225 . -1068) T) ((-304 . -102) 158149) ((-142 . -1119) T) ((-711 . -1021) T) ((-1124 . -296) 158105) ((-91 . -1237) T) ((-128 . -625) 158037) ((-122 . -625) 157969) ((-1316 . -174) T) ((-1193 . -374) 157948) ((-1187 . -374) 157927) ((-326 . -1119) T) ((-430 . -132) T) ((-323 . -1119) T) ((-419 . -38) 157879) ((-1152 . -102) T) ((-1273 . -729) 157771) ((-666 . -1077) T) ((-1154 . -1282) T) ((-329 . -146) 157750) ((-329 . -148) 157729) ((-140 . -1119) T) ((-137 . -1119) T) ((-115 . -1119) T) ((-870 . -102) T) ((-592 . -625) 157711) ((-576 . -626) 157610) ((-576 . -625) 157592) ((-507 . -625) 157574) ((-507 . -626) 157519) ((-497 . -23) T) ((-494 . -862) 157470) ((-499 . -651) 157452) ((-982 . -625) 157434) ((-1022 . -917) 157343) ((-219 . -651) 157325) ((-227 . -416) T) ((-674 . -660) 157309) ((-55 . -625) 157291) ((-1192 . -937) 157270) ((-743 . -1131) T) ((-362 . -102) T) ((-1236 . -1102) T) ((-1139 . -856) T) ((-830 . -862) T) ((-743 . -23) T) ((-354 . -1075) 157215) ((-1178 . -1177) T) ((-1166 . -107) 157199) ((-1194 . -1131) T) ((-1193 . -1131) T) ((-527 . -1057) 157183) ((-1187 . -1131) T) ((-1145 . -1131) T) ((-354 . -111) 157112) ((-1023 . -1241) T) ((-127 . -1237) T) ((-931 . -1241) T) ((-1288 . -625) 157094) ((-706 . -296) NIL) ((-726 . -1237) T) ((-1194 . -23) T) ((-1193 . -23) T) ((-1187 . -23) T) ((-1161 . -272) 157078) ((-1161 . -232) 157062) ((-1023 . -568) T) ((-1145 . -23) T) ((-931 . -568) T) ((-1094 . -1119) T) ((-254 . -625) 157044) ((-827 . -237) 156941) ((-811 . -132) T) ((-722 . -625) 156923) ((-326 . -729) 156833) ((-323 . -729) 156762) ((-711 . -625) 156744) ((-711 . -626) 156689) ((-419 . -412) 156673) ((-450 . -1119) T) ((-499 . -25) T) ((-499 . -21) T) ((-1139 . -1119) T) ((-219 . -25) T) ((-219 . -21) T) ((-724 . -423) 156657) ((-726 . -1057) 156626) ((-1287 . -625) 156538) ((-1287 . -626) 156499) ((-1273 . -174) T) ((-1210 . -625) 156481) ((-250 . -34) T) ((-354 . -628) 156411) ((-406 . -628) 156393) ((-943 . -993) T) ((-1223 . -1237) T) ((-674 . -803) 156372) ((-674 . -806) 156351) ((-410 . -407) T) ((-535 . -102) 156329) ((-1054 . -1119) T) ((-419 . -917) 156252) ((-224 . -1014) 156236) ((-516 . -102) T) ((-635 . -625) 156218) ((-45 . -862) NIL) ((-635 . -626) 156195) ((-1054 . -622) 156170) ((-918 . -526) 156103) ((-329 . -237) 156055) ((-354 . -1068) T) ((-118 . -626) NIL) ((-118 . -625) 156037) ((-884 . -1237) T) ((-682 . -429) 156021) ((-682 . -1142) 155966) ((-512 . -152) 155948) ((-354 . -238) T) ((-354 . -248) T) ((-40 . -1075) 155893) ((-884 . -897) 155877) ((-884 . -899) 155802) ((-724 . -1077) T) ((-706 . -1021) NIL) ((-1271 . -47) 155772) ((-1250 . -47) 155749) ((-1160 . -1029) 155720) ((-1139 . -729) 155707) ((-3 . |UnionCategory|) T) ((-1124 . -625) 155689) ((-1099 . -148) 155668) ((-1099 . -146) 155619) ((-1023 . -374) T) ((-983 . -628) 155603) ((-227 . -937) T) ((-40 . -111) 155532) ((-884 . -1057) 155396) ((-1022 . -232) 155373) ((-1022 . -272) 155350) ((-713 . -1070) 155337) ((-931 . -374) T) ((-713 . -652) 155324) ((-329 . -1225) 155290) ((-390 . -317) T) ((-329 . -1222) 155256) ((-326 . -174) 155235) ((-323 . -174) T) ((-593 . -1306) 155222) ((-530 . -1306) 155199) ((-370 . -148) 155178) ((-117 . -1070) 155165) ((-370 . -146) 155116) ((-364 . -148) 155095) ((-364 . -146) 155046) ((-356 . -148) 155025) ((-620 . -1213) 155001) ((-117 . -652) 154988) ((-356 . -146) 154939) ((-329 . -35) 154905) ((-487 . -1213) 154884) ((0 . |EnumerationCategory|) T) ((-329 . -95) 154850) ((-390 . -1041) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -240) 154800) ((-666 . -1119) T) ((-620 . -107) 154747) ((-497 . -132) T) ((-487 . -107) 154697) ((-245 . -1131) 154675) ((-884 . -388) 154659) ((-884 . -349) 154643) ((-245 . -23) 154495) ((-40 . -628) 154425) ((-1081 . -937) T) ((-1081 . -832) T) ((-593 . -379) T) 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-1237) T) ((-608 . -568) 153524) ((-439 . -1131) T) ((-350 . -1070) 153508) ((-215 . -1119) T) ((-176 . -1070) 153440) ((-486 . -47) 153410) ((-40 . -238) 153382) ((-40 . -248) T) ((-135 . -102) T) ((-117 . -102) T) ((-607 . -568) 153361) ((-350 . -652) 153345) ((-706 . -626) 153253) ((-326 . -526) 153219) ((-176 . -652) 153151) ((-323 . -526) 153043) ((-499 . -234) 153030) ((-1271 . -1057) 153014) ((-1250 . -1057) 152800) ((-1018 . -423) 152784) ((-219 . -234) 152771) ((-439 . -23) T) ((-1139 . -174) T) ((-1273 . -300) T) ((-666 . -729) 152741) ((-145 . -1119) T) ((-48 . -1021) T) ((-419 . -272) 152725) ((-419 . -232) 152709) ((-305 . -240) 152659) ((-883 . -937) T) ((-883 . -832) NIL) ((-882 . -628) 152631) ((-876 . -862) T) ((-1250 . -349) 152601) ((-1250 . -388) 152571) ((-1099 . -237) 152450) ((-224 . -1140) 152434) ((-304 . -917) 152393) ((-1287 . -298) 152370) ((-370 . -237) 152349) ((-364 . -237) 152328) ((-486 . -1237) T) ((-356 . -237) 152307) ((-108 . -237) T) ((-1231 . -660) 152232) ((-1022 . -658) 152162) ((-980 . -21) T) ((-980 . -25) T) ((-747 . -21) T) ((-747 . -25) T) ((-727 . -21) T) ((-727 . -25) T) ((-723 . -660) 152127) ((-465 . -21) T) ((-465 . -25) T) ((-350 . -102) T) ((-176 . -102) T) ((-1018 . -1077) T) ((-882 . -1068) T) ((-786 . -102) T) ((-1272 . -374) 152106) ((-1271 . -915) 152012) ((-1251 . -374) 151991) ((-1250 . -915) 151842) ((-1043 . -625) 151824) ((-419 . -840) 151777) ((-1194 . -505) 151743) ((-171 . -937) 151674) ((-1193 . -505) 151640) ((-1187 . -505) 151606) ((-724 . -1119) T) ((-1145 . -505) 151572) ((-592 . -1075) 151559) ((-576 . -1075) 151546) ((-507 . -1075) 151511) ((-326 . -300) 151490) ((-323 . -300) T) ((-365 . -625) 151472) ((-430 . -25) T) ((-430 . -21) T) ((-99 . -296) 151451) ((-592 . -111) 151436) ((-576 . -111) 151421) ((-507 . -111) 151377) ((-1196 . -899) 151344) ((-918 . -501) 151328) ((-48 . -625) 151310) ((-48 . -626) 151255) ((-245 . -132) 151126) ((-1310 . -658) 151085) ((-1260 . -937) 151064) ((-828 . -1241) 151043) ((-400 . -502) 151024) ((-1054 . -526) 150868) ((-400 . -625) 150834) ((-828 . -568) 150765) ((-598 . -660) 150740) ((-273 . -47) 150712) ((-253 . -47) 150669) ((-543 . -521) 150646) ((-592 . -628) 150618) ((-576 . -628) 150590) ((-507 . -628) 150523) ((-1093 . -1237) T) ((-1019 . -1237) T) ((-1279 . -23) T) ((-1279 . -1131) T) ((-1272 . -1131) T) ((-711 . -1075) 150488) ((-1272 . -23) T) ((-1251 . -1131) T) ((-1251 . -23) T) ((-1231 . -738) T) ((-1139 . -300) T) ((-1022 . -381) 150460) ((-112 . -379) T) ((-486 . -915) 150366) ((-1132 . -237) 150263) ((-921 . -625) 150245) ((-55 . -628) 150227) ((-91 . -107) 150211) ((-1023 . -132) T) ((-922 . -862) 150162) ((-713 . -1171) T) ((-711 . -111) 150118) ((-855 . -658) 150035) ((-608 . -1131) T) ((-607 . -1131) T) ((-724 . -729) 149864) ((-723 . -738) T) ((-990 . -132) T) ((-931 . -132) T) ((-499 . -862) T) ((-811 . -25) T) ((-811 . -21) T) ((-592 . -1068) T) ((-219 . -862) T) ((-419 . -658) 149801) ((-576 . -1068) T) ((-548 . -1237) T) ((-507 . -1068) T) ((-608 . -23) T) ((-354 . -1306) 149778) ((-329 . -464) 149757) ((-350 . -319) 149744) ((-607 . -23) T) ((-439 . -132) T) ((-670 . -660) 149718) ((-250 . -1029) 149702) ((-884 . -317) T) ((-1311 . -1301) 149686) ((-783 . -804) T) ((-783 . -807) T) ((-713 . -38) 149673) ((-576 . -238) T) ((-507 . -248) T) ((-507 . -238) T) ((-1169 . -240) 149623) ((-1106 . -926) 149602) ((-117 . -38) 149589) ((-211 . -812) T) ((-210 . -812) T) ((-209 . -812) T) ((-208 . -812) T) ((-884 . -1041) 149567) ((-1300 . -501) 149551) ((-794 . -926) 149530) ((-792 . -926) 149509) ((-1209 . -1237) T) ((-366 . -1237) 149488) ((-363 . -1237) 149467) ((-355 . -1237) 149446) ((-273 . -1237) T) ((-253 . -1237) T) ((-466 . -926) 149425) ((-749 . -501) 149409) ((-1106 . -660) 149298) ((-711 . -628) 149233) ((-794 . -660) 149122) ((-635 . -1075) 149109) ((-491 . -1237) T) ((-354 . -379) T) ((-142 . -501) 149091) ((-792 . -660) 148980) ((-1160 . -1237) T) ((-561 . -862) T) ((-473 . -660) 148951) ((-273 . -899) 148810) ((-253 . -899) NIL) ((-118 . -1075) 148755) ((-466 . -660) 148644) ((-676 . -1057) 148621) ((-635 . -111) 148606) ((-402 . -1070) 148590) ((-366 . -1057) 148574) ((-363 . -1057) 148558) ((-355 . -1057) 148542) ((-273 . -1057) 148386) ((-253 . -1057) 148262) ((-927 . -1237) T) ((-118 . -111) 148191) ((-59 . -1237) T) ((-402 . -652) 148175) ((-633 . -1070) 148159) ((-531 . -1237) T) ((-528 . -1237) T) ((-509 . -1237) T) ((-508 . -1237) T) ((-449 . -625) 148141) ((-446 . -625) 148123) ((-633 . -652) 148107) ((-3 . -102) T) ((-1046 . -1230) 148076) ((-845 . -102) T) ((-701 . -57) 148034) ((-711 . -1068) T) ((-647 . -658) 148003) ((-619 . -658) 147972) ((-50 . -660) 147946) ((-299 . -464) T) ((-488 . -1230) 147915) ((0 . -102) T) ((-593 . -660) 147880) ((-530 . -660) 147825) ((-49 . -102) T) ((-927 . -1057) 147812) ((-711 . -248) T) ((-1099 . -421) 147791) ((-743 . -651) 147739) ((-1018 . -1119) T) ((-724 . -174) 147630) ((-635 . -628) 147525) ((-499 . -1011) 147507) ((-430 . -234) 147452) ((-273 . -388) 147436) ((-253 . -388) 147420) ((-411 . -1119) T) ((-1045 . -102) 147398) ((-350 . -38) 147382) ((-219 . -1011) 147364) ((-118 . -628) 147294) ((-176 . -38) 147226) ((-1271 . -317) 147205) ((-1250 . -317) 147184) ((-670 . -738) T) ((-99 . -625) 147166) ((-489 . -1070) 147131) ((-1187 . -651) 147083) ((-489 . -652) 147048) ((-497 . -25) T) ((-497 . -21) T) ((-1250 . -1041) 147000) ((-1076 . -1237) T) ((-635 . -1068) T) ((-390 . -416) T) ((-402 . -102) T) ((-1124 . -630) 146915) ((-273 . -915) 146861) ((-253 . -915) 146838) ((-118 . -1068) T) ((-828 . -1131) T) ((-1106 . -738) T) ((-635 . -238) 146817) ((-633 . -102) T) ((-794 . -738) T) ((-792 . -738) T) ((-425 . -1131) T) ((-118 . -248) T) ((-40 . -379) NIL) ((-118 . -238) NIL) ((-1242 . -862) T) ((-466 . -738) T) ((-828 . -23) T) ((-743 . -25) T) ((-743 . -21) T) ((-682 . -909) 146738) ((-1096 . -296) 146717) ((-78 . -408) T) ((-78 . -407) T) ((-545 . -779) 146699) ((-706 . -1075) 146649) 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143114) ((-1300 . -625) 143076) ((-633 . -38) 143060) ((-1300 . -626) 143021) ((-1194 . -234) 142974) ((-1096 . -625) 142956) ((-1043 . -248) T) ((-365 . -1068) T) ((-827 . -1294) 142926) ((-258 . -23) T) ((-257 . -23) T) ((-1006 . -625) 142908) ((-1193 . -234) 142854) ((-1187 . -234) 142671) ((-749 . -626) 142632) ((-749 . -625) 142614) ((-1179 . -152) 142561) ((-811 . -862) 142540) ((-1023 . -25) T) ((-1018 . -526) 142452) ((-365 . -238) T) ((-365 . -248) T) ((-400 . -628) 142433) ((-927 . -317) T) ((-142 . -625) 142415) ((-142 . -626) 142374) ((-329 . -909) 142278) ((-1023 . -21) T) ((-990 . -25) T) ((-931 . -21) T) ((-931 . -25) T) ((-439 . -21) T) ((-439 . -25) T) ((-855 . -423) 142262) ((-48 . -1068) T) ((-1309 . -1301) 142246) ((-1307 . -1301) 142230) ((-1054 . -616) 142205) ((-326 . -626) 142066) ((-326 . -625) 142048) ((-323 . -626) NIL) ((-323 . -625) 142030) ((-48 . -248) T) ((-48 . -238) T) ((-666 . -296) 141991) ((-562 . -240) 141941) ((-140 . -625) 141908) ((-137 . -625) 141890) ((-115 . -625) 141872) ((-489 . -38) 141837) ((-1311 . -1308) 141816) ((-1302 . -132) T) ((-1310 . -1077) T) ((-1101 . -102) T) ((-88 . -1237) T) ((-512 . -319) NIL) ((-1019 . -107) 141800) ((-902 . -1119) T) ((-898 . -1119) T) ((-1287 . -663) 141784) ((-1287 . -384) 141768) ((-337 . -1237) T) ((-605 . -862) T) ((-1161 . -1119) T) ((-1161 . -1072) 141708) ((-103 . -526) 141641) ((-944 . -625) 141623) ((-354 . -738) T) ((-30 . -625) 141605) ((-878 . -1119) T) ((-855 . -1077) 141584) ((-40 . -660) 141491) ((-227 . -1241) T) ((-419 . -1077) T) ((-1178 . -152) 141473) ((-1018 . -300) 141424) ((-629 . -1119) T) ((-227 . -568) T) ((-329 . -1268) 141408) ((-329 . -1265) 141378) ((-713 . -658) 141350) ((-1209 . -1213) 141329) ((-1094 . -625) 141311) ((-1209 . -107) 141261) ((-659 . -152) 141245) ((-644 . -152) 141191) ((-117 . -658) 141163) ((-491 . -1213) 141142) ((-499 . -148) T) ((-499 . -146) NIL) ((-1139 . -626) 141057) ((-450 . -625) 141039) ((-219 . -148) T) ((-219 . -146) NIL) 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-234) 137070) ((-845 . -658) 136987) ((-486 . -937) 136966) ((-329 . -1070) 136801) ((-326 . -1075) 136711) ((-323 . -1075) 136640) ((-1018 . -296) 136598) ((-419 . -729) 136550) ((-329 . -652) 136391) ((-607 . -234) 136344) ((-713 . -860) T) ((-1273 . -1068) T) ((-326 . -111) 136240) ((-323 . -111) 136153) ((-981 . -102) T) ((-827 . -102) 135905) ((-724 . -626) NIL) ((-724 . -625) 135887) ((-1273 . -336) 135831) ((-670 . -1057) 135727) ((-1106 . -1237) T) ((-1054 . -298) 135702) ((-592 . -738) T) ((-576 . -806) T) ((-171 . -374) 135653) ((-576 . -803) T) ((-576 . -738) T) ((-507 . -738) T) ((-794 . -1237) T) ((-792 . -1237) T) ((-1165 . -501) 135637) ((-466 . -1237) T) ((-1106 . -899) NIL) ((-883 . -1131) T) ((-118 . -926) NIL) ((-1309 . -1308) 135613) ((-1307 . -1308) 135592) ((-794 . -899) NIL) ((-792 . -899) 135451) ((-1302 . -25) T) ((-1302 . -21) T) ((-1234 . -102) 135429) ((-1125 . -407) T) ((-635 . -660) 135416) ((-466 . -899) NIL) ((-687 . -102) 135394) ((-1106 . -1057) 135221) ((-883 . -23) T) ((-794 . -1057) 135080) ((-792 . -1057) 134937) ((-118 . -660) 134882) ((-466 . -1057) 134758) ((-326 . -628) 134322) ((-323 . -628) 134205) ((-402 . -658) 134174) ((-661 . -1057) 134158) ((-639 . -102) T) ((-593 . -1237) T) ((-530 . -1237) T) ((-224 . -501) 134142) ((-1287 . -34) T) ((-633 . -658) 134101) ((-299 . -1070) 134088) ((-137 . -628) 134072) ((-299 . -652) 134059) ((-647 . -729) 134043) ((-619 . -729) 134027) ((-682 . -38) 133987) ((-329 . -102) T) ((-85 . -625) 133969) ((-50 . -1057) 133953) ((-1139 . -1075) 133940) ((-1106 . -388) 133924) ((-794 . -388) 133908) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-593 . -1057) 133895) ((-530 . -1057) 133872) ((-60 . -57) 133834) ((-334 . -132) T) ((-326 . -1068) 133724) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 133708) ((-45 . -152) 133658) ((-1023 . -1011) 133640) ((-466 . -388) 133624) ((-419 . -174) T) ((-326 . -248) 133603) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133385) ((-227 . -132) T) ((-1139 . -111) 133370) ((-171 . -23) T) ((-811 . -148) 133349) ((-811 . -146) 133328) ((-258 . -651) 133234) ((-257 . -651) 133140) ((-329 . -294) 133106) ((-1176 . -526) 133039) ((-489 . -658) 132989) ((-494 . -909) 132856) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 132794) ((-1106 . -915) 132729) ((-794 . -915) 132672) ((-792 . -915) 132656) ((-1309 . -38) 132626) ((-1307 . -38) 132596) ((-1260 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 132573) ((-870 . -1119) T) ((-1260 . -23) T) ((-1139 . -628) 132545) ((-1081 . -132) T) ((-583 . -1131) T) ((-867 . -23) T) ((-635 . -738) T) ((-366 . -937) T) ((-363 . -937) T) ((-299 . -102) T) ((-355 . -937) T) ((-989 . -1102) T) ((-969 . -132) T) ((-828 . -234) 132490) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132391) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132342) ((-687 . -319) 132280) ((-647 . -773) T) ((-619 . -773) T) ((-1251 . -862) NIL) 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. -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-724 . -111) 128378) ((-365 . -738) T) ((-682 . -272) 128362) ((-682 . -232) 128346) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 128295) ((-108 . -319) NIL) ((-72 . -407) T) ((-1132 . -102) 128047) ((-845 . -423) 128031) ((-1139 . -807) T) ((-1139 . -804) T) ((-713 . -1119) T) ((-590 . -625) 128013) ((-390 . -374) T) ((-171 . -505) 127991) ((-224 . -625) 127923) ((-135 . -1119) T) ((-117 . -1119) T) ((-983 . -1237) T) ((-48 . -738) T) ((-1065 . -501) 127888) ((-142 . -437) 127870) ((-142 . -379) T) ((-1046 . -102) T) ((-524 . -521) 127849) ((-724 . -628) 127605) ((-1194 . -237) 127564) ((-488 . -102) T) ((-475 . -102) T) ((-1193 . -237) 127516) ((-1187 . -237) 127339) ((-1053 . -1131) T) ((-329 . 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-336) 126013) ((-493 . -651) 125961) ((-40 . -1057) 125849) ((-724 . -238) T) ((-713 . -729) 125836) ((-350 . -1119) T) ((-176 . -1119) T) ((-341 . -862) T) ((-430 . -464) 125786) ((-390 . -23) T) ((-370 . -38) 125751) ((-364 . -38) 125716) ((-356 . -38) 125681) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1131) T) ((-108 . -38) 125631) ((-839 . -1131) T) ((-786 . -1119) T) ((-117 . -729) 125618) ((-684 . -1057) 125602) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1176 . -296) 125554) ((-1132 . -319) 125492) ((-494 . -1070) 125393) ((-1121 . -240) 125377) ((-64 . -408) T) ((-64 . -407) T) ((-1170 . -102) T) ((-110 . -102) T) ((-494 . -652) 125299) ((-40 . -388) 125276) ((-96 . -102) T) ((-665 . -864) 125260) ((-1192 . -234) 125247) ((-1154 . -1102) T) ((-1081 . -21) T) ((-1081 . -25) T) ((-1073 . -1070) 125231) ((-827 . -272) 125200) ((-827 . -232) 125169) ((-969 . -25) T) ((-969 . -21) T) ((-1073 . -652) 125111) ((-633 . -1077) T) ((-1139 . -379) T) ((-1046 . -319) 125049) ((-682 . -658) 125008) ((-493 . -25) T) ((-493 . -21) T) ((-396 . -1070) 124992) ((-902 . -625) 124974) ((-898 . -625) 124956) ((-535 . -526) 124889) ((-258 . -862) 124840) ((-257 . -862) 124791) ((-396 . -652) 124761) ((-883 . -651) 124738) ((-488 . -319) 124676) ((-475 . -319) 124614) ((-362 . -300) T) ((-1176 . -1275) 124598) ((-1161 . -625) 124560) ((-1161 . -626) 124521) ((-1159 . -102) T) ((-1018 . -1075) 124417) ((-40 . -915) 124369) ((-1176 . -616) 124346) ((-1316 . -660) 124333) ((-1082 . -152) 124279) ((-499 . -909) NIL) ((-878 . -502) 124256) ((-1018 . -111) 124138) ((-884 . -1241) T) ((-219 . -909) NIL) ((-350 . -729) 124122) ((-878 . -625) 124084) ((-176 . -729) 124016) ((-884 . -568) T) ((-419 . -296) 123974) ((-245 . -237) 123871) ((-108 . -412) 123853) ((-84 . -395) T) ((-84 . -407) T) ((-713 . -174) T) ((-629 . -625) 123835) ((-99 . -738) T) ((-494 . -102) 123587) ((-99 . -485) T) ((-117 . -174) T) ((-1309 . -658) 123546) ((-1307 . -658) 123505) ((-171 . -651) 123453) ((-1099 . -917) 123324) ((-1073 . -102) T) ((-1018 . -628) 123214) ((-883 . -25) T) ((-827 . -243) 123193) ((-883 . -21) T) ((-830 . -102) T) ((-44 . -658) 123136) ((-1023 . -237) T) ((-426 . -102) T) ((-396 . -102) T) ((-110 . -319) NIL) ((-229 . -102) 123114) ((-128 . -1237) T) ((-122 . -1237) T) ((-108 . -917) NIL) ((-829 . -1070) 123065) ((-829 . -652) 123007) ((-1053 . -132) T) ((-682 . -378) 122991) ((-153 . -658) 122950) ((-647 . -296) 122908) ((-619 . -296) 122866) ((-1316 . -738) T) ((-1018 . -1068) T) ((-1260 . -651) 122814) ((-1123 . -625) 122796) ((-1022 . -625) 122778) ((-576 . -1237) T) ((-507 . -1237) T) ((-527 . -23) T) ((-522 . -23) T) ((-354 . -317) T) ((-520 . -23) T) ((-332 . -132) T) ((-3 . -1119) T) ((-1022 . -626) 122762) ((-1018 . -248) 122741) ((-1018 . -238) 122720) ((-1279 . -146) 122699) ((-1279 . -148) 122678) ((-845 . -1119) T) ((-1272 . -148) 122657) ((-1272 . -146) 122636) ((-1271 . -1241) 122615) ((-1251 . -146) 122522) ((-1251 . -148) 122429) ((-1250 . -1241) 122408) ((-390 . -132) T) ((-227 . -234) 122395) ((-576 . -899) 122377) ((0 . -1119) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1119) T) ((-1273 . -660) 122282) ((-1271 . -568) 122233) ((-726 . -1131) T) ((-1250 . -568) 122184) ((-576 . -1057) 122166) ((-607 . -148) 122145) ((-607 . -146) 122124) ((-507 . -1057) 122067) ((-1154 . -1156) T) ((-87 . -395) T) ((-87 . -407) T) ((-884 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-981 . -658) 122011) ((-726 . -23) T) ((-518 . -625) 121977) ((-514 . -625) 121959) ((-827 . -658) 121738) ((-1311 . -1077) T) ((-390 . -1079) T) ((-1045 . -1119) 121716) ((-55 . -1057) 121698) ((-918 . -34) T) ((-494 . -319) 121636) ((-604 . -102) T) ((-1176 . -626) 121597) ((-1176 . -625) 121529) ((-1198 . -1070) 121412) ((-45 . -102) T) ((-829 . -102) T) ((-1198 . -652) 121309) ((-1260 . -25) T) ((-1260 . -21) T) ((-1081 . -234) 121296) ((-867 . -25) T) ((-44 . -378) 121280) ((-867 . -21) 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. -1119) T) ((-392 . -1119) T) ((-1260 . -234) 117552) ((-1236 . -1119) T) ((-82 . -1237) T) ((-1132 . -272) 117521) ((-1081 . -862) T) ((-118 . -915) NIL) ((-794 . -937) 117500) ((-725 . -862) T) ((-543 . -1119) T) ((-512 . -1119) T) ((-366 . -1241) T) ((-363 . -1241) T) ((-355 . -1241) T) ((-273 . -1241) 117479) ((-253 . -1241) 117458) ((-545 . -872) T) ((-1132 . -232) 117427) ((-1178 . -840) T) ((-1161 . -1075) 117411) ((-402 . -773) T) ((-706 . -1237) T) ((-703 . -1057) 117395) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117326) ((-253 . -568) 117257) ((-537 . -1102) T) ((-1161 . -111) 117236) ((-465 . -756) 117206) ((-878 . -1075) 117176) ((-829 . -38) 117118) ((-706 . -897) 117100) ((-706 . -899) 117082) ((-305 . -319) 116886) ((-1176 . -298) 116863) ((-927 . -1241) T) ((-1099 . -658) 116758) ((-1023 . -464) T) ((-682 . -423) 116742) ((-878 . -111) 116707) ((-931 . -464) T) ((-706 . -1057) 116652) ((-927 . -568) T) ((-545 . -625) 116634) ((-593 . -937) T) 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-25) T) ((-839 . -25) T) ((-839 . -21) T) ((-1132 . -658) 114220) ((-1309 . -1077) T) ((-561 . -102) T) ((-1307 . -1077) T) ((-666 . -738) T) ((-1123 . -630) 114123) ((-1022 . -628) 114053) ((-1310 . -1075) 114037) ((-827 . -423) 114006) ((-103 . -120) 113990) ((-130 . -1119) T) ((-52 . -1119) T) ((-943 . -625) 113972) ((-883 . -1011) 113949) ((-835 . -102) T) ((-1310 . -111) 113928) ((-743 . -909) 113903) ((-665 . -38) 113873) ((-583 . -862) T) ((-366 . -1131) T) ((-363 . -1131) T) ((-355 . -1131) T) ((-273 . -1131) T) ((-253 . -1131) T) ((-1169 . -319) 113677) ((-1107 . -234) 113664) ((-635 . -317) 113643) ((-676 . -23) T) ((-536 . -1102) T) ((-321 . -1119) T) ((-494 . -272) 113612) ((-494 . -232) 113581) ((-153 . -1077) T) ((-366 . -23) T) ((-363 . -23) T) ((-355 . -23) T) ((-118 . -317) T) ((-273 . -23) T) ((-253 . -23) T) ((-1022 . -1068) T) ((-724 . -926) 113560) ((-1194 . -909) 113448) ((-1193 . -909) 113329) ((-1187 . -909) 113065) ((-1176 . -628) 113042) ((-1022 . -238) 113014) ((-1022 . -248) T) ((-1145 . -909) 112996) ((-118 . -1041) NIL) ((-927 . -1131) T) ((-1272 . -464) 112975) ((-1251 . -464) 112954) ((-535 . -625) 112886) ((-724 . -660) 112775) ((-419 . -1075) 112727) ((-516 . -625) 112709) ((-927 . -23) T) ((-499 . -319) NIL) ((-1310 . -628) 112665) ((-486 . -132) T) ((-219 . -319) NIL) ((-419 . -111) 112603) ((-827 . -1077) 112581) ((-749 . -1117) 112565) ((-1271 . -505) 112531) ((-1250 . -505) 112497) ((-560 . -856) T) ((-142 . -1117) 112479) ((-489 . -300) T) ((-1310 . -1068) T) ((-258 . -237) 112376) ((-257 . -237) 112273) ((-1242 . -102) T) ((-1082 . -102) T) ((-855 . -628) 112141) ((-512 . -526) NIL) ((-494 . -243) 112120) ((-419 . -628) 112018) ((-980 . -1070) 111901) ((-747 . -1070) 111871) ((-980 . -652) 111768) ((-1192 . -146) 111747) ((-747 . -652) 111717) ((-465 . -1070) 111687) ((-1192 . -148) 111666) ((-1144 . -148) 111645) ((-1144 . -146) 111624) ((-647 . -1075) 111608) ((-619 . -1075) 111592) ((-465 . -652) 111562) ((-1194 . 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-658) 107497) ((-1279 . -909) 107385) ((-1236 . -93) T) ((-362 . -1068) T) ((-227 . -237) T) ((-70 . -394) T) ((-70 . -407) T) ((-1185 . -102) T) ((-682 . -526) 107318) ((-1272 . -909) 107199) ((-1251 . -909) 106935) ((-701 . -319) 106873) ((-980 . -38) 106770) ((-1200 . -625) 106752) ((-747 . -38) 106722) ((-562 . -319) 106526) ((-1194 . -1070) 106409) ((-326 . -1237) T) ((-362 . -238) T) ((-362 . -248) T) ((-323 . -1237) T) ((-299 . -1119) T) ((-1193 . -1070) 106244) ((-1187 . -1070) 106034) ((-1145 . -1070) 105917) ((-1194 . -652) 105814) ((-1193 . -652) 105655) ((-723 . -1241) T) ((-1187 . -652) 105451) ((-1176 . -663) 105435) ((-1145 . -652) 105332) ((-1231 . -568) 105311) ((-831 . -397) 105295) ((-723 . -568) T) ((-607 . -909) 105206) ((-326 . -897) 105190) ((-326 . -899) 105115) ((-137 . -1237) T) ((-323 . -897) 105076) ((-323 . -899) NIL) ((-811 . -319) 105041) ((-329 . -729) 104882) ((-398 . -397) 104866) ((-334 . -333) 104843) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 104817) ((-326 . -1057) 104480) ((-227 . -1222) T) ((-227 . -1225) T) ((-3 . -625) 104462) ((-323 . -1057) 104392) ((-884 . -234) 104337) ((-2 . -1119) T) ((-2 . |RecordCategory|) T) ((-1132 . -1077) 104315) ((-845 . -625) 104297) ((-1081 . -237) T) ((-592 . -937) T) ((-576 . -832) T) ((-576 . -937) T) ((-507 . -937) T) ((-137 . -1057) 104281) ((-227 . -95) T) ((-171 . -148) 104260) ((-75 . -453) T) ((0 . -625) 104242) ((-75 . -407) T) ((-171 . -146) 104193) ((-227 . -35) T) ((-49 . -625) 104175) ((-489 . -1077) T) ((-499 . -272) 104157) ((-499 . -232) 104139) ((-496 . -987) 104123) ((-219 . -272) 104105) ((-219 . -232) 104087) ((-81 . -453) T) ((-81 . -407) T) ((-1165 . -34) T) ((-743 . -102) T) ((-665 . -658) 104046) ((-1045 . -625) 104013) ((-512 . -296) 103963) ((-326 . -388) 103932) ((-323 . -388) 103893) ((-323 . -349) 103854) ((-1104 . -625) 103836) ((-828 . -966) 103783) ((-674 . -132) T) ((-1260 . -146) 103762) ((-1260 . -148) 103741) ((-1194 . -102) T) 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-1241) 101466) ((-62 . -1237) T) ((-489 . -625) 101418) ((-489 . -626) 101340) ((-794 . -568) 101251) ((-792 . -568) 101182) ((-743 . -319) 101169) ((-713 . -628) 101141) ((-494 . -423) 101110) ((-635 . -937) 101089) ((-466 . -1241) 101068) ((-687 . -526) 101001) ((-676 . -25) T) ((-410 . -625) 100983) ((-676 . -21) T) ((-466 . -568) 100914) ((-430 . -917) 100837) ((-366 . -25) T) ((-366 . -21) T) ((-363 . -25) T) ((-118 . -937) T) ((-118 . -832) NIL) ((-363 . -21) T) ((-355 . -25) T) ((-355 . -21) T) ((-273 . -25) T) ((-273 . -21) T) ((-253 . -25) T) ((-253 . -21) T) ((-171 . -237) 100768) ((-83 . -395) T) ((-83 . -407) T) ((-135 . -628) 100750) ((-117 . -628) 100722) ((-1023 . -652) 100672) ((-960 . -999) 100656) ((-931 . -652) 100608) ((-931 . -1070) 100560) ((-927 . -21) T) ((-927 . -25) T) ((-884 . -862) 100511) ((-878 . -660) 100471) ((-723 . -1131) T) ((-723 . -23) T) ((-713 . -1068) T) ((-713 . -238) T) ((-299 . -174) T) ((-666 . -1237) T) ((-321 . -93) T) ((-659 . -1119) 100449) ((-644 . -622) 100424) ((-644 . -1119) T) ((-593 . -1241) T) ((-593 . -568) T) ((-530 . -1241) T) ((-530 . -568) T) ((-499 . -658) 100374) ((-486 . -234) 100320) ((-439 . -1070) 100304) ((-439 . -652) 100288) ((-370 . -729) 100240) ((-364 . -729) 100192) ((-350 . -1075) 100176) ((-356 . -729) 100128) ((-350 . -111) 100107) ((-176 . -1075) 100039) ((-219 . -658) 99989) ((-176 . -111) 99900) ((-108 . -729) 99850) ((-283 . -1119) T) ((-282 . -1119) T) ((-281 . -1119) T) ((-280 . -1119) T) ((-279 . -1119) T) ((-278 . -1119) T) ((-277 . -1119) T) ((-214 . -1119) T) ((-213 . -1119) T) ((-171 . -1225) 99828) ((-171 . -1222) 99806) ((-211 . -1119) T) ((-210 . -1119) T) ((-117 . -1068) T) ((-209 . -1119) T) ((-208 . -1119) T) ((-205 . -1119) T) ((-204 . -1119) T) ((-203 . -1119) T) ((-202 . -1119) T) ((-201 . -1119) T) ((-200 . -1119) T) ((-199 . -1119) T) ((-198 . -1119) T) ((-197 . -1119) T) ((-196 . -1119) T) ((-195 . -1119) T) ((-245 . -102) 99558) ((-171 . -35) 99536) ((-171 . -95) 99514) ((-666 . -1057) 99410) ((-494 . -1077) 99388) ((-1132 . -1119) 99140) ((-1161 . -34) T) ((-682 . -501) 99124) ((-73 . -1237) T) ((-105 . -625) 99106) ((-1311 . -625) 99088) ((-392 . -625) 99070) ((-350 . -628) 99022) ((-176 . -628) 98939) ((-1236 . -502) 98920) ((-743 . -38) 98769) ((-583 . -1225) T) ((-583 . -1222) T) ((-543 . -625) 98751) ((-532 . -319) 98689) ((-512 . -625) 98671) ((-512 . -626) 98653) ((-1236 . -625) 98619) ((-1187 . -1171) NIL) ((-1046 . -1090) 98588) ((-1046 . -1119) T) ((-1023 . -102) T) ((-990 . -102) T) ((-931 . -102) T) ((-906 . -1057) 98565) ((-1161 . -738) T) ((-1022 . -660) 98472) ((-488 . -1119) T) ((-475 . -1119) T) ((-598 . -23) T) ((-583 . -35) T) ((-583 . -95) T) ((-439 . -102) T) ((-1082 . -231) 98418) ((-1194 . -38) 98315) ((-878 . -738) T) ((-706 . -937) T) ((-523 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1193 . -38) 98156) ((-350 . -1068) T) ((-1187 . -38) 97952) ((-1099 . -174) T) ((-176 . -1068) T) ((-1145 . -38) 97849) ((-724 . -47) 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-23) T) ((-493 . -464) 96921) ((-473 . -23) T) ((-392 . -393) 96900) ((-366 . -234) 96873) ((-363 . -234) 96846) ((-355 . -234) 96819) ((-466 . -23) T) ((-273 . -234) 96764) ((-258 . -909) 96631) ((-257 . -909) 96498) ((-96 . -1119) T) ((-724 . -1237) T) ((-682 . -296) 96475) ((-496 . -526) 96408) ((-1279 . -1070) 96291) ((-1279 . -652) 96188) ((-1272 . -652) 96029) ((-1272 . -1070) 95864) ((-1251 . -652) 95660) ((-299 . -300) T) ((-1251 . -1070) 95450) ((-1101 . -625) 95432) ((-1101 . -626) 95413) ((-419 . -926) 95392) ((-1231 . -132) T) ((-50 . -1131) T) ((-1187 . -412) 95344) ((-1043 . -937) T) ((-1022 . -738) T) ((-855 . -660) 95317) ((-724 . -899) NIL) ((-608 . -1070) 95277) ((-593 . -1131) T) ((-530 . -1131) T) ((-607 . -1070) 95160) ((-1176 . -34) T) ((-1023 . -319) NIL) ((-827 . -501) 95144) ((-608 . -652) 95117) ((-365 . -937) T) ((-607 . -652) 95014) ((-927 . -234) 95001) ((-419 . -660) 94917) ((-50 . -23) T) ((-723 . -132) T) ((-724 . -1057) 94797) ((-593 . -23) T) ((-108 . 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93507) ((-665 . -423) 93491) ((-1251 . -102) T) ((-1178 . -526) NIL) ((-674 . -25) T) ((-633 . -1075) 93475) ((-674 . -21) T) ((-980 . -658) 93385) ((-747 . -658) 93330) ((-727 . -658) 93302) ((-402 . -111) 93281) ((-224 . -261) 93265) ((-1073 . -1072) 93205) ((-1073 . -1119) T) ((-1023 . -1171) T) ((-830 . -1119) T) ((-465 . -658) 93120) ((-647 . -660) 93104) ((-354 . -1241) T) ((-633 . -111) 93083) ((-619 . -660) 93067) ((-608 . -102) T) ((-321 . -502) 93048) ((-598 . -132) T) ((-607 . -102) T) ((-426 . -1119) T) ((-396 . -1119) T) ((-321 . -625) 93014) ((-229 . -1119) 92992) ((-659 . -526) 92925) ((-644 . -526) 92769) ((-845 . -1068) 92748) ((-656 . -152) 92732) ((-354 . -568) T) ((-724 . -915) 92675) ((-562 . -231) 92625) ((-1279 . -294) 92591) ((-1272 . -294) 92557) ((-1099 . -300) 92508) ((-499 . -860) T) ((-225 . -1131) T) ((-1251 . -294) 92474) ((-1231 . -505) 92440) ((-1023 . -38) 92390) ((-219 . -860) T) ((-430 . -658) 92349) ((-931 . -38) 92301) ((-855 . -806) 92280) ((-855 . -803) 92259) ((-855 . -738) 92238) ((-370 . -300) T) ((-364 . -300) T) ((-356 . -300) T) ((-171 . -464) 92169) ((-439 . -38) 92153) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92132) ((-419 . -803) 92111) ((-419 . -738) T) ((-512 . -298) 92086) ((-489 . -1075) 92051) ((-670 . -132) T) ((-633 . -628) 92020) ((-1132 . -526) 91953) ((-347 . -132) T) ((-171 . -414) 91932) ((-494 . -729) 91874) ((-827 . -296) 91851) ((-489 . -111) 91807) ((-665 . -1077) T) ((-1192 . -909) 91710) ((-1144 . -909) 91692) ((-828 . -1070) 91535) ((-1298 . -1102) T) ((-1260 . -464) 91466) ((-828 . -652) 91315) ((-1297 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91257) ((-1046 . -526) 91190) ((-794 . -132) T) ((-792 . -132) T) ((-583 . -464) T) ((-633 . -1068) T) ((-604 . -1119) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1018 . -1237) T) ((-45 . -1119) T) ((-396 . -729) 91160) ((-829 . -1119) T) ((-488 . -526) 91093) ((-475 . -526) 91026) ((-1312 . -628) 91008) ((-465 . -378) 90978) ((-45 . -622) 90957) ((-411 . -1237) T) ((-326 . -312) T) ((-839 . -237) 90936) ((-489 . -628) 90886) ((-1251 . -319) 90771) ((-682 . -625) 90733) ((-59 . -862) 90712) ((-1023 . -412) 90694) ((-560 . -625) 90676) ((-811 . -658) 90635) ((-827 . -616) 90612) ((-528 . -862) 90591) ((-508 . -862) 90570) ((-1018 . -1057) 90466) ((-40 . -1241) T) ((-245 . -917) 90335) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90195) ((-354 . -339) 90172) ((-354 . -374) T) ((-332 . -333) 90149) ((-329 . -296) 90107) ((-40 . -568) T) ((-390 . -1222) T) ((-390 . -1225) T) ((-1054 . -1213) 90082) ((-1209 . -240) 90032) ((-1187 . -232) 89984) ((-1187 . -272) 89936) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 89882) ((-489 . -1068) T) ((-1311 . -1075) 89866) ((-491 . -240) 89816) ((-1179 . -501) 89750) ((-1302 . -1070) 89734) ((-392 . -1075) 89718) ((-1302 . -652) 89688) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 89667) ((-726 . -146) 89646) 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83686) ((-713 . -660) 83658) ((-561 . -856) T) ((-219 . -1119) T) ((-326 . -937) 83637) ((-323 . -937) T) ((-323 . -832) NIL) ((-402 . -732) T) ((-882 . -23) T) ((-117 . -660) 83624) ((-486 . -146) 83603) ((-430 . -423) 83587) ((-486 . -148) 83566) ((-110 . -501) 83548) ((-321 . -628) 83529) ((-2 . -625) 83511) ((-188 . -102) T) ((-1178 . -19) 83493) ((-1178 . -616) 83468) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1163) T) ((-1132 . -296) 83445) ((-347 . -25) T) ((-347 . -21) T) ((-245 . -658) 83224) ((-507 . -374) T) ((-1309 . -1075) 83208) ((-1307 . -1075) 83192) ((-1302 . -38) 83162) ((-1271 . -1222) 83128) ((-1260 . -909) 83031) ((-1192 . -1070) 82854) ((-1161 . -1237) T) ((-1144 . -1070) 82697) ((-866 . -1070) 82681) ((-644 . -616) 82656) ((-1271 . -1225) 82622) ((-1271 . -95) 82588) ((-1271 . -237) 82540) ((-1192 . -652) 82369) ((-1144 . -652) 82218) ((-866 . -652) 82188) ((-1254 . -102) 82166) ((-1251 . -232) 82118) ((-561 . -1119) T) ((-1106 . -25) T) ((-1106 . -21) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1241) T) ((-980 . -1077) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1077) T) ((-727 . -1077) T) ((-682 . -1075) 82102) ((-529 . -1102) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1251 . -272) 82054) ((-1170 . -93) T) ((-1161 . -1057) 81950) ((-829 . -300) 81929) ((-1250 . -1222) 81895) ((-835 . -1119) T) ((-983 . -986) T) ((-682 . -111) 81874) ((-629 . -1237) T) ((-305 . -526) 81666) ((-1250 . -1225) 81632) ((-1250 . -237) 81491) ((-1245 . -379) T) ((-258 . -319) 81429) ((-257 . -319) 81367) ((-1242 . -856) T) ((-1179 . -626) NIL) ((-1179 . -625) 81349) ((-1161 . -388) 81333) ((-1139 . -832) T) ((-1139 . -937) T) ((-96 . -93) T) ((-1132 . -616) 81310) ((-1099 . -626) 81294) ((-1099 . -625) 81276) ((-1023 . -658) 81226) ((-931 . -658) 81163) ((-827 . -298) 81140) ((-496 . -625) 81072) ((-620 . -152) 81019) ((-499 . -729) 80969) ((-430 . -1077) T) 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((-334 . -102) T) ((-220 . -1102) T) ((-980 . -1119) T) ((-153 . -1068) T) ((-743 . -423) 76496) ((-118 . -23) T) ((-1022 . -915) 76448) ((-747 . -1119) T) ((-727 . -1119) T) ((-1279 . -658) 76358) ((-465 . -1119) T) ((-419 . -1237) T) ((-326 . -442) 76342) ((-604 . -93) T) ((-1272 . -658) 76224) ((-1046 . -626) 76185) ((-1043 . -1241) T) ((-227 . -102) T) ((-1046 . -625) 76147) ((-828 . -272) 76131) ((-828 . -232) 76115) ((-827 . -628) 75913) ((-1251 . -658) 75750) ((-1043 . -568) T) ((-845 . -660) 75723) ((-365 . -1241) T) ((-488 . -625) 75685) ((-488 . -626) 75646) ((-475 . -626) 75607) ((-475 . -625) 75569) ((-608 . -658) 75528) ((-419 . -897) 75512) ((-329 . -1075) 75347) ((-419 . -899) 75272) ((-607 . -658) 75182) ((-855 . -1057) 75078) ((-499 . -526) NIL) ((-494 . -616) 75055) ((-593 . -234) 75042) ((-365 . -568) T) ((-530 . -234) 75029) ((-219 . -526) NIL) ((-884 . -464) T) ((-430 . -1119) T) ((-419 . -1057) 74893) ((-329 . -111) 74714) ((-706 . -374) T) ((-227 . -294) T) 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. -102) T) ((-656 . -292) 71832) ((-711 . -1079) T) ((-1298 . -102) T) ((-1297 . -102) T) ((-489 . -660) 71797) ((-480 . -1119) T) ((-45 . -616) 71722) ((-1178 . -298) 71697) ((-299 . -628) 71669) ((-40 . -651) 71608) ((-1260 . -1070) 71431) ((-867 . -1070) 71415) ((-48 . -374) T) ((-1125 . -625) 71397) ((-1260 . -652) 71226) ((-867 . -652) 71196) ((-644 . -298) 71171) ((-828 . -658) 71081) ((-583 . -1070) 71068) ((-494 . -625) 70761) ((-245 . -423) 70730) ((-969 . -319) 70717) ((-583 . -652) 70704) ((-65 . -1237) T) ((-1192 . -917) 70611) ((-1185 . -1119) T) ((-1082 . -526) 70455) ((-683 . -1119) T) ((-635 . -132) T) ((-493 . -319) 70442) ((-618 . -1119) T) ((-558 . -102) T) ((-118 . -132) T) ((-299 . -1068) T) ((-182 . -1119) T) ((-162 . -1119) T) ((-157 . -1119) T) ((-155 . -1119) T) ((-465 . -773) T) ((-31 . -1102) T) ((-980 . -174) 70393) ((-1144 . -917) 70377) ((-989 . -93) T) ((-1132 . -298) 70354) ((-1099 . -1075) 70264) ((-633 . -806) 70243) ((-605 . -1119) T) ((-633 . -803) 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T) ((-519 . -1119) T) ((-128 . -319) 4423) ((-122 . -319) 4361) ((-608 . -660) 4335) ((-607 . -660) 4260) ((-593 . -658) 4210) ((-227 . -1068) T) ((-530 . -658) 4140) ((-390 . -1021) T) ((-227 . -248) T) ((-227 . -238) T) ((-1081 . -628) 4112) ((-1081 . -630) 4093) ((-975 . -626) 4054) ((-975 . -625) 3966) ((-969 . -628) 3755) ((-882 . -38) 3742) ((-725 . -628) 3692) ((-1271 . -300) 3643) ((-1250 . -300) 3594) ((-493 . -628) 3379) ((-1139 . -464) T) ((-514 . -862) T) ((-326 . -1158) 3358) ((-1018 . -148) 3337) ((-1018 . -146) 3316) ((-507 . -319) 3303) ((-305 . -1213) 3282) ((-1204 . -625) 3264) ((-1203 . -625) 3246) ((-1202 . -625) 3228) ((-883 . -1075) 3173) ((-489 . -1131) T) ((-140 . -847) 3155) ((-115 . -847) 3136) ((-635 . -102) T) ((-1223 . -501) 3120) ((-258 . -379) 3099) ((-257 . -379) 3078) ((-1081 . -1068) T) ((-305 . -107) 3028) ((-131 . -625) 3010) ((-129 . -626) NIL) ((-129 . -625) 2954) ((-118 . -102) T) ((-969 . -1068) T) ((-883 . -111) 2883) ((-489 . -23) T) ((-465 . -1237) T) ((-493 . -1068) T) ((-1081 . -238) T) ((-969 . -336) 2852) ((-40 . -917) 2761) ((-493 . -336) 2718) ((-366 . -174) T) ((-363 . -174) T) ((-355 . -174) T) ((-273 . -174) 2629) ((-253 . -174) 2540) ((-980 . -1057) 2436) ((-529 . -502) 2417) ((-747 . -1057) 2388) ((-529 . -625) 2354) ((-430 . -1237) T) ((-1124 . -102) T) ((-1111 . -625) 2313) ((-1053 . -625) 2295) ((-706 . -1070) 2245) ((-1300 . -152) 2229) ((-1298 . -628) 2210) ((-1297 . -628) 2191) ((-1292 . -625) 2173) ((-1279 . -738) T) ((-706 . -652) 2123) ((-1272 . -738) T) ((-1251 . -803) NIL) ((-1251 . -806) NIL) ((-171 . -1075) 2033) ((-927 . -174) T) ((-883 . -628) 1963) ((-1251 . -738) T) ((-1022 . -353) 1937) ((-225 . -658) 1889) ((-1019 . -526) 1822) ((-855 . -862) 1801) ((-576 . -1171) T) ((-486 . -300) 1752) ((-608 . -738) T) ((-372 . -625) 1734) ((-332 . -625) 1716) ((-430 . -1057) 1612) ((-607 . -738) T) ((-419 . -862) 1563) ((-171 . -111) 1459) ((-845 . -132) 1411) ((-749 . -152) 1395) ((-1287 . -319) 1333) 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\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 699e5263..bf9bc7a8 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3485856131)            
-(4463 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3485863920)            
+(4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -74,9 +74,9 @@
  |DirectProductCategory&| |DirectProductCategory|
  |DirectProductFunctions2| |DirectProduct| |DisplayPackage|
  |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList|
- |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial|
- |Domain| |DomainConstructor| |DomainTemplate|
- |DirectProductMatrixModule| |DirectProductModule|
+ |DiscreteLogarithmPackage| |DifferentialModuleExtension|
+ |DistributedMultivariatePolynomial| |Domain| |DomainConstructor|
+ |DomainTemplate| |DirectProductMatrixModule| |DirectProductModule|
  |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory|
  |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions|
  |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex|
@@ -333,9 +333,9 @@
  |PartialDifferentialDomain&| |PartialDifferentialDomain|
  |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition|
  |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem|
- |PartialDifferentialRing| |PartialDifferentialSpace&|
- |PartialDifferentialSpace| |PendantTree| |Permanent|
- |PermutationCategory| |PermutationGroup| |Permutation|
+ |PartialDifferentialModule| |PartialDifferentialRing|
+ |PartialDifferentialSpace&| |PartialDifferentialSpace| |PendantTree|
+ |Permanent| |PermutationCategory| |PermutationGroup| |Permutation|
  |PolynomialFactorizationByRecursion|
  |PolynomialFactorizationByRecursionUnivariate|
  |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit|
@@ -488,670 +488,665 @@
  |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram|
  |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
  |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |generic?| |child| |semiResultantEuclidean2|
- |member?| |getGoodPrime| |matrixConcat3D| |generateIrredPoly|
- |factorSquareFree| |head| |ran| |in?| |set| |elliptic| |ListOfTerms|
- |mdeg| |d01fcf| |mapGen| |numberOfComposites| |cothIfCan| |totalfract|
- |queue| |c06gsf| |returnType!| |listLoops|
- |factorSquareFreePolynomial| |doublyTransitive?| |getProperties| |xn|
- |rightQuotient| |isAnd| |binding| |composites|
- |combineFeatureCompatibility| |modularGcd|
- |removeRedundantFactorsInPols| |areEquivalent?| |mindegTerm|
- |ramified?| |sec2cos| |rootSimp| |mkcomm| |leftMinimalPolynomial|
- |startTableInvSet!| |semiResultantEuclideannaif| |rename!| |identity|
- |lists| |factors| |character?| |generalizedEigenvector|
- |lfextendedint| |squareTop| |zag| |genericLeftNorm| |prologue|
- |extension| |trueEqual| |zeroSetSplitIntoTriangularSystems|
- |brillhartIrreducible?| |irCtor| |d03faf| |signature| |nextPrime|
- |lookupFunction| |f01qdf| |realZeros| |iicosh| |rur| |argument|
- |supRittWu?| |selectAndPolynomials| |pdf2ef| |lambert|
- |chainSubResultants| |empty| |OMread| |rationalPoints| |UP2ifCan|
- |f01rcf| |search| |connectTo| |zeroSquareMatrix| |expr|
- |uncouplingMatrices| |numberOfMonomials| |maxint| |presub| |ode1|
- |tryFunctionalDecomposition| |characteristicSerie|
- |indiceSubResultant| |extendedSubResultantGcd| |pointData| |paren|
- |removeDuplicates!| |f02aaf| |mapUnivariateIfCan| |outputList|
- |univcase| |minPoints| |dmpToHdmp| |showClipRegion| |cyclic| |maxrow|
- |createNormalPrimitivePoly| |printingInfo?| |iCompose| |wreath| |show|
- |maxdeg| |exprHasWeightCosWXorSinWX| |univariatePolynomials|
- |cycleEntry| |tubePoints| |noValueMode| |loopPoints| |interReduce|
- |closed| |nonQsign| |printStatement| |zeroDimensional?| |mathieu23|
- |variable| |removeRoughlyRedundantFactorsInPol| |drawComplex|
- |modulus| |isTimes| |computeInt| |s18aff| |trace| |meshPar2Var| |cdr|
- |var1Steps| |iterators| |calcRanges| |rightRegularRepresentation|
- |leftTrace| |var2StepsDefault| |companionBlocks| |bivariate?| |e01daf|
- |viewport2D| |normFactors| |wordInStrongGenerators| |datalist|
- |radicalSimplify| |imagj| |matrixGcd| |systemCommand|
- |balancedBinaryTree| |e02bcf| |makeVariable| |setColumn!| |char|
- |functionIsContinuousAtEndPoints| |checkPrecision| |subst| |hconcat|
- |minColIndex| |internalLastSubResultant| |stronglyReduce| |subscript|
- |eisensteinIrreducible?| |OMgetBVar| |RittWuCompare| |bitior|
- |generalPosition| |purelyAlgebraic?| |lifting1| |mirror|
- |PollardSmallFactor| |slash| |beauzamyBound| |clikeUniv| |OMreadStr|
- |insertRoot!| |genericRightTraceForm| |attributeData|
- |rightExactQuotient| |lexGroebner| |sizeMultiplication| |precision|
- |normal| |f01maf| |list?| |s18dcf| |contract| |support| |LiePoly|
- |sturmVariationsOf| |leftAlternative?| |cond| |conditionP| |isPlus|
- |concat| |Frobenius| |consnewpol| |bat| |currentScope|
- |unrankImproperPartitions0| |rootKerSimp| |iiasin| |sech| |iiacsch|
- |regime| |se2rfi| |alphanumeric| |bracket| |df2st| |viewWriteDefault|
- |oneDimensionalArray| |leftMult| |csch| |operation| |prem|
- |coth2trigh| |compound?| |element?| |bothWays| |objects| |float|
- |find| |elaboration| |subscriptedVariables| |screenResolution3D|
- |asinh| |gcdcofactprim| |dimensions| |addPointLast| |base|
- |useEisensteinCriterion?| |totalLex| |ridHack1| |cubic| |setnext!|
- |acosh| |socf2socdf| |lfintegrate| |simplify| |generalSqFr| |kind|
- |vconcat| |subresultantSequence| |putProperty| |fortranReal| |arg1|
- |tableau| |f01mcf| |leftDivide| |pseudoDivide| |atanh|
- |sylvesterMatrix| |getMatch| |shallowExpand| |f01ref| |nthExpon| |op|
- |getGraph| |equality| |jacobi| |internalInfRittWu?| |arg2| |expIfCan|
- |f02aef| |acoth| |blankSeparate| |permutationRepresentation|
- |argscript| |exportedOperators| |HermiteIntegrate| |autoReduced?|
- |LiePolyIfCan| |writeInt8!| |FormatArabic| |asech| |e04naf| |numer|
- |writeBytes!| |pop!| |addmod| |palgint0| |roughSubIdeal?| |conditions|
- |setTopPredicate| |mainCoefficients| |sts2stst| |dimension|
- |variables| |cRationalPower| |denom| |topFortranOutputStack| |besselY|
- |d01aqf| |listBranches| |match| |coth2tanh| |options| |commaSeparate|
- |multiple| |null?| |genericLeftDiscriminant| |overset?|
- |identityMatrix| |rational| |bubbleSort!| |rootOfIrreduciblePoly|
- |allRootsOf| |e04dgf| |applyQuote| |asinIfCan|
- |irreducibleRepresentation| |tanIfCan| |factorials| |pi| |tree|
- |edf2efi| |submod| |approximants| |s17dhf| |fortranDoubleComplex|
- |superHeight| |c06fqf| |infinity| |ipow| |resultantReduit| |union|
- |numberOfHues| |showIntensityFunctions| |any| |froot| |setleaves!|
- |string| |ldf2vmf| |fill!| |indices| |bigEndian| |changeName|
- |newTypeLists| |splitDenominator| |exponent| |rk4a| |ruleset|
- |dioSolve| |rectangularMatrix| |s18acf| |brillhartTrials|
- |subResultantGcd| |stiffnessAndStabilityFactor| |elRow1!| |heap|
- |primextendedint| |isOp| |tanNa| |kernel| |partialDenominators|
- |previous| |leadingIdeal| |gethi| |pile| |recur| |s19acf|
- |bombieriNorm| |qqq| |mainMonomials| |stoseInvertibleSetreg| |list|
- |complexNumeric| |multMonom| |numberOfComponents| |pastel| |sinh2csch|
- |conjug| |factorByRecursion| |suchThat| |putGraph| |hostByteOrder|
- |open?| |elseBranch| |compdegd| |draw| |unravel| |nextsousResultant2|
- |npcoef| |adjoint| |trace2PowMod| |specialTrigs| |OMgetEndBind|
- |cartesian| |modifyPointData| |subtractIfCan|
- |numberOfIrreduciblePoly| |sumOfKthPowerDivisors| |d01ajf| |adaptive?|
- |sech2cosh| |oddintegers| |top!| |f01brf| |localAbs| |asimpson|
- |monomials| |euclideanSize| |negative?| |selectsecond| |changeBase|
- |charthRoot| |iflist2Result| |simpleBounds?| |realElementary|
- |LagrangeInterpolation| |inverse| |write!| |rightNorm| |headAst|
- |opeval| |pquo| |rquo| |duplicates?| |position!| |expint|
- |nextIrreduciblePoly| |prinb| |makeObject| |dihedral| |pdf2df|
- |ScanFloatIgnoreSpacesIfCan| |reduction| |cyclicGroup| |lazyEvaluate|
- |nary?| |monicDivide| |OMmakeConn| |center| |multiplyExponents|
- |degree| |coef| |s17dcf| |roughUnitIdeal?| |innerSolve|
- |primitiveElement| |roughBase?| |stack|
- |setLegalFortranSourceExtensions| |pointPlot| |primlimintfrac|
- |csubst| |indicialEquationAtInfinity| |label| |OMputEndAttr|
- |toseInvertibleSet| |mkPrim| |vectorise| |basisOfRightAnnihilator|
- |endSubProgram| |setprevious!| |cycleSplit!| |normalizedDivide|
- |e01sbf| |name| |iroot| |getProperty| |d01alf| |quadratic|
- |mainCharacterization| |mkIntegral| |messagePrint| |iterationVar|
- |badValues| |oddInfiniteProduct| |body| |mainVariable?|
- |axesColorDefault| |meshPar1Var| |Is| |schwerpunkt| |rangeIsFinite|
- |nextsubResultant2| |typeForm| |rotate| |singularitiesOf| |e02aef|
- |findConstructor| |index?| |baseRDE| |interpret|
- |selectOptimizationRoutines| |f04maf| |patternMatch| |virtualDegree|
- |padicallyExpand| |binaryTree| |rightPower| |c06ekf| |hspace| |iiacsc|
- |getlo| |iitanh| |distance| |getSyntaxFormsFromFile| |getMeasure|
- |alternating| |qinterval| |bitLength| |hasSolution?| |musserTrials|
- |completeEchelonBasis| |belong?| |removeIrreducibleRedundantFactors|
- |rightZero| |solveLinearPolynomialEquationByRecursion|
- |createNormalPoly| |complexEigenvectors| |curveColorPalette|
- |OMputAtp| |cardinality| |fmecg| |c02agf| |iicsc| |normalise| |point|
- |completeHensel| |length| |lazyPseudoRemainder| |changeMeasure|
- |readUInt32!| |extendedIntegrate| |bfEntry|
- |rewriteSetByReducingWithParticularGenerators|
- |createPrimitiveElement| |option| |constantKernel| |scripts|
- |internalSubPolSet?| |cyclicEqual?| |s17aff| |aQuartic| |notelem|
- |recoverAfterFail| |internalDecompose| |OMgetAttr| SEGMENT |irVar|
- |iisqrt2| |eulerPhi| |leftExtendedGcd| |OMgetEndApp|
- |lineColorDefault| |port| |innerint| |setPoly| |modularGcdPrimitive|
- |satisfy?| |variable?| |intersect| |series| |adaptive3D?| |sechIfCan|
- |explimitedint| |aromberg| |sequence| |boundOfCauchy| |ParCondList|
- |viewPosDefault| |perfectSquare?| |charClass| |divisors|
- |OMsupportsSymbol?| |primitivePart!| |expandTrigProducts| |t|
- |internalIntegrate| |scalarMatrix| |perfectSqrt| |ptFunc| |nodes|
- |lookup| |permutations| |resetNew| |redPol| |tube| |reopen!|
- |alternatingGroup| |simpson| |leaf?| |e02agf| |setButtonValue|
- |sorted?| |rightUnits| |setErrorBound| |createNormalElement|
- |primintfldpoly| |s17aef| |d02gaf| |f07adf| |bernoulli| |min| |delay|
- |integralLastSubResultant| |back| |limitPlus| |alphanumeric?|
- |cyclePartition| |inverseLaplace| |PDESolve| |polar| |s18def|
- |tanhIfCan| |swapColumns!| |f02adf| |nilFactor| |solveLinear|
- |coerceListOfPairs| |fractionPart| |select!| |addBadValue|
- |mainKernel| |createThreeSpace| |evaluateInverse| |mergeFactors|
- |square?| |startTable!| |diagonal?| |rightFactorIfCan| |unknown|
- |apply| |tubePlot| |reduceLODE| |mapExponents| |eyeDistance|
- |divideIfCan!| |cAtan| |makeViewport2D| |measure2Result|
- |internalZeroSetSplit| |getIdentifier| |aLinear| |first| |groebner|
- |coefChoose| |rowEchLocal| |f04asf| |mapMatrixIfCan| |leftFactor|
- |palgextint| |isPower| |xor| |imag| |euler| |localUnquote|
- |separateFactors| |rest| |generalizedContinuumHypothesisAssumed|
- |ReduceOrder| |certainlySubVariety?| |ode2| |range| |directProduct|
- |antisymmetricTensors| |case| |incrementKthElement| |Hausdorff|
- |randomR| |noKaratsuba| |binomThmExpt| |OMputSymbol| |unitNormal|
- |extend| |headReduce| |leftUnit| GF2FG |Zero| |lowerCase!| |e02bdf|
- |initiallyReduced?| |ramifiedAtInfinity?| |leadingExponent| |keys|
- |comp| |true| |setProperty| |atanhIfCan| |tryFunctionalDecomposition?|
- |void| |sayLength| |shiftRoots| |fillPascalTriangle| |One| |top|
- |iiacoth| |setMaxPoints| |f04atf| |coordinate| |clipWithRanges| |cap|
- |rightFactorCandidate| |continue| |s15adf| |binary| |empty?| |sin?|
- |mainContent| |inverseIntegralMatrixAtInfinity| |showTheIFTable|
- |hclf| |Gamma| |goodnessOfFit| |sort| |plusInfinity| |setStatus|
- |fortranComplex| |leftLcm| |iibinom| |factorial| |elem?|
- |complexElementary| |prolateSpheroidal| |iisech| |idealSimplify|
- |minusInfinity| |solveid| |palgintegrate| |schema| |ignore?| |hessian|
- |lieAdmissible?| |f02awf| |zero?| |var2Steps| |genericRightNorm|
- |roman| |tubeRadius| |iomode| |id| |tanSum| |selectfirst|
- |invertible?| |central?| |stopTableGcd!| |infRittWu?|
- |reciprocalPolynomial| |host| |sortConstraints| |BasicMethod|
- |splitConstant| |ratpart| |OMgetEndAttr| |elt| |quotientByP| |lo|
- |s17agf| |atoms| |ddFact| |exptMod| |changeVar| |random| |fixedPoints|
- |f02ajf| |OMserve| |inR?| |collectUnder| |next| |listexp|
- |symmetricDifference| |spherical| |halfExtendedResultant1| |rspace|
- |check| |stoseInvertible?reg| |fintegrate| |endOfFile?| |setrest!|
- |hcrf| |weierstrass| |nextPrimitiveNormalPoly| |polyRicDE|
- |modifyPoint| |badNum| |quickSort| |totolex| |basis| |OMgetObject|
- |leastPower| |rubiksGroup| |sparsityIF| |complexSolve|
- |stoseInvertible?| |principalIdeal| |physicalLength| |trim|
- |doubleRank| |compiledFunction| |OMgetFloat| |nthRoot|
- |integralAtInfinity?| |extensionDegree| |genericLeftTrace| |debug3D|
- |iipow| |charpol| |ord| |hitherPlane| |complexNumericIfCan|
- |karatsubaOnce| |commutative?| |rowEch| |rischDE|
- |constantToUnaryFunction| |mainSquareFreePart| |complement|
- |addPoint2| |insert| |youngDiagram| |abelianGroup| |unmakeSUP|
- |someBasis| |randomLC| |subQuasiComponent?| |powers|
- |basisOfLeftAnnihilator| |iiabs| |readUInt8!| |symmetricSquare|
- |leader| |chvar| |lagrange| |push| |intensity| |rightUnit| |quote|
- |rootRadius| |primintegrate| |c06ecf| |critpOrder| |OMgetError|
- |viewWriteAvailable| |iicos| |df2ef| |compBound| |rationalIfCan|
- |f02xef| |stirling2| |normDeriv2| |upDateBranches| |viewDefaults|
- |cAtanh| |OMputEndError| |torsionIfCan| |maxPoints3D| |lowerCase|
- |doubleComplex?| |enterInCache| |setEmpty!| |critM| |monicModulo|
- |subResultantGcdEuclidean| |integers| |iidsum| |parametersOf|
- |partialFraction| |resultantEuclideannaif| |iiatanh| |dark|
- |binaryTournament| |palgRDE0| |subNode?| |addiag| |stFunc2| |vspace|
- |mainVariable| |rational?| |makeViewport3D| |setOrder| |dequeue!|
- |nullary| |s17akf| |inverseIntegralMatrix| |realSolve| |reify|
- |e02bef| |setsubMatrix!| |structuralConstants| |symbolTable|
- |gcdcofact| |e01saf| |seriesSolve| |whileLoop| |pow| |middle|
- |tracePowMod| |f04mcf| |coordinates| |subset?| |checkRur|
- |coefficients| |weight| |status| |relationsIdeal| |orbit| |goodPoint|
- |postfix| |s18aef| |OMencodingSGML| |pushFortranOutputStack|
- |setAttributeButtonStep| |isOpen?| |setUnion| |OMwrite| |normalize|
- |reseed| |cAcosh| |clearTheIFTable| |extractProperty| |constantRight|
- |popFortranOutputStack| |irDef| |lazy?| |width| |cycles| |lazyPquo|
- |iicsch| |super| |cosIfCan| |rCoord| |computeCycleEntry| |tanQ|
- |outputAsFortran| |cyclotomic| |appendPoint| |leftGcd| |s14aaf|
- |irreducibleFactors| |tRange| |positiveSolve| |number?| Y |deref|
- |fortranLogical| |findBinding| |bitCoef| |meshFun2Var| |d02bhf|
- |cyclicParents| |solid| |exponential| |maxIndex| |SturmHabicht|
- |infinityNorm| |binomial| |fortranLiteralLine| |denomLODE|
- |variationOfParameters| |generalInfiniteProduct| |newSubProgram|
- |subResultantsChain| |lepol| |subTriSet?| |reduceBasisAtInfinity|
- |stFunc1| |semiSubResultantGcdEuclidean1| |internalSubQuasiComponent?|
- |flexible?| |geometric| |linearAssociatedExp| |OMputError| |palgLODE0|
- |pseudoQuotient| |clearCache| |fglmIfCan| |radicalEigenvectors|
- |credPol| |dAndcExp| |lift| |table| |partialNumerators|
- |totalDifferential| |cCsch| |hyperelliptic| |sumOfSquares|
- |nativeModuleExtension| |leftOne| |harmonic| |digit|
- |nthFractionalTerm| |reduce| |new| |basisOfMiddleNucleus| |jacobian|
- |updateStatus!| |obj| |imagi| |tableForDiscreteLogarithm|
- |subresultantVector| |rotatex| |quoted?| |normal?| |minordet|
- |wordInGenerators| |exp1| |just| |cache|
- |unprotectedRemoveRedundantFactors| |row| |bat1| |li| |digits|
- |column| |denominator| |sign| |fortranInteger| |setvalue!| |isExpt|
- |revert| |minGbasis| |retractable?| |pole?| |clearTable!|
- |possiblyInfinite?| |lowerBound| |antiCommutator| |multinomial|
- |algSplitSimple| |radicalSolve| |lifting| |quasiAlgebraicSet| |edf2ef|
- |idealiser| |cPower| |setClosed| |factor| |ocf2ocdf| |hexDigit?|
- |triangularSystems| |testModulus| |fixedDivisor| |unparse|
- |OMopenFile| |iisec| |minPol| |degreePartition| |numberOfNormalPoly|
- |positive?| |algebraicCoefficients?| |triangulate|
- |rewriteIdealWithQuasiMonicGenerators| |iiatan| |createPrimitivePoly|
- |makeResult| |removeRedundantFactors| |sinhIfCan|
- |rightRankPolynomial| |plus!| |rk4| |vector| |genericLeftTraceForm|
- |hostPlatform| |fractionFreeGauss!| |remove!|
- |generalizedContinuumHypothesisAssumed?| |diagonalMatrix| |e02gaf|
- |primitivePart| |OMclose| |userOrdered?| |differentiate| |symbolIfCan|
- |OMputEndAtp| |OMgetString| |lazyIrreducibleFactors| |overlap|
- |resize| |divisor| |predicate| |eq?| |wronskianMatrix| |qfactor| |box|
- |eigenvector| |Vectorise| |pureLex| |unvectorise| |prinshINFO|
- |internalAugment| |resultantEuclidean| |getButtonValue| |usingTable?|
- |stoseInternalLastSubResultant| |magnitude| |ellipticCylindrical|
- |safeCeiling| |clearFortranOutputStack| |size| |useSingleFactorBound|
- |btwFact| |left| ** |monomial| |infiniteProduct| |besselK| |dom|
- |test| |read!| |logical?| |lazyVariations| |coerceImages|
- |semiIndiceSubResultantEuclidean| |byte| |differentialVariables|
- |integralCoordinates| |innerSolve1| |extendedResultant| |right|
- |multivariate| |lquo| |split| |factorAndSplit|
- |nextNormalPrimitivePoly| |singleFactorBound| |imaginary| |string?|
- |paraboloidal| |polyred| |unknownEndian| |makeop| |leadingIndex|
- |retractIfCan| |cycle| |e02daf| |iicot| |build|
- |getMultiplicationMatrix| |getVariableOrder| |outputMeasure| |s15aef|
- |whatInfinity| |algebraicOf| |close| |linear| |unitCanonical|
- |primeFrobenius| |irForm| |root?| |getMultiplicationTable| |wrregime|
- |complexIntegrate| |setelt!| |completeEval| |insertMatch| |tan2cot|
- |sqrt| |closedCurve| |resetAttributeButtons| |readLine!|
- |semiResultantEuclidean1| |removeRoughlyRedundantFactorsInContents|
- |showFortranOutputStack| |physicalLength!| |e01sff| |leaves| |hasoln|
- |display| |polynomial| |high| |real| |title| |ravel| |curveColor|
- |eigenvalues| |separate| |OMsend| |untab| |prefix| |units|
- |lazyResidueClass| |insertionSort!| |numberOfImproperPartitions|
- |rationalFunction| |inputBinaryFile| |basisOfRightNucleus|
- |completeHermite| |GospersMethod| |points| |reshape| |rdregime| |mix|
- |printStats!| |elaborate| |pascalTriangle| |parameters| |shape| |dn|
- |iiacot| |node?| |elRow2!| |e04ucf| |leftZero| |int| |power|
- |numberOfChildren| |cAsec| |cos2sec| |copies| |e| |cCoth| |coord|
- |e02ahf| |e01bgf| |squareMatrix| |node| |capacity| |singular?|
- |ODESolve| |rightDiscriminant| |laurentIfCan| |pushdterm| |c06fuf|
- |s13aaf| |ScanFloatIgnoreSpaces| |f07aef| |create3Space|
- |basisOfNucleus| |ksec| |rewriteIdealWithHeadRemainder| |input|
- |OMgetBind| |pointColorDefault| |map| |shellSort|
- |purelyAlgebraicLeadingMonomial?| |inHallBasis?| |unitsColorDefault|
- |numberOfCycles| |brace| |kernels| |dequeue| |code| |d02bbf|
- |acschIfCan| |euclideanNormalForm| |library| |constantIfCan| |conical|
- |mapCoef| |removeCoshSq| |perfectNthRoot| |gramschmidt| |vertConcat|
- |update| |eq| |operator| |showSummary| |minIndex| |isEquiv| |fortran|
- |swap| |saturate| |leadingTerm| |sturmSequence| |logGamma|
- |radicalEigenvalues| |integralMatrix| |shallowCopy| |getDatabase|
- |fractRagits| |iter| |e04jaf| |optimize| |strongGenerators| |fi2df|
- |rowEchelonLocal| |replaceKthElement| |OMcloseConn|
- |balancedFactorisation| |nthExponent| |exprex|
- |standardBasisOfCyclicSubmodule| |countable?| |orbits| |option?|
- |prevPrime| |stoseLastSubResultant| |extractSplittingLeaf|
- |partialQuotients| |rotatey| |LyndonWordsList| |child?| |assert|
- |digamma| |wholeRadix| |chiSquare| |pointColor| |viewport3D|
- |numerators| |curve| |generalizedEigenvectors| |convert| |zeroVector|
- |gradient| |setAdaptive| |copyInto!| |midpoints| |discreteLog| |critT|
- |subspace| |showAttributes| |argumentListOf| |LyndonCoordinates|
- |level| |outputGeneral| |rename| |algint| |OMreadFile| |position|
- |symFunc| |f04qaf| |tubeRadiusDefault| |genericRightDiscriminant|
- |interpretString| |arrayStack| |mappingMode| |fortranLiteral|
- |monomialIntPoly| |shanksDiscLogAlgorithm| |redPo| |lexTriangular|
- |tanh2coth| |makeMulti| |copy!| |bit?| |makingStats?| |lyndon?|
- |quatern| |scopes| |lfunc| |branchPoint?| |kovacic| |s19adf| |measure|
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- |headRemainder| |integerBound| |OMsetEncoding| |nextPrimitivePoly|
- |cSech| |interactiveEnv| |toseLastSubResultant| |OMlistSymbols|
- |reset| |decrease| |readUInt16!| |safetyMargin| |bright| |operations|
- |leftRemainder| |rightGcd| |gcdPrimitive| |makeTerm| |failed?|
- |complexEigenvalues| F |leftQuotient| |writeLine!|
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- |simpsono| |setelt| |save| |constant?| |setfirst!|
- |localIntegralBasis| |s13adf| |acoshIfCan| |iisin| |dual|
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- |stopTable!| |leviCivitaSymbol| |outputFloating| |semicolonSeparate|
- |round| |sn| |setFormula!| |ranges| |reduced?| |laurentRep|
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- |and| |monicCompleteDecompose| |FormatRoman| |numFunEvals3D|
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- |quasiComponent| |e02akf| |stoseInvertibleSetsqfreg| |superscript|
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- |integer?| |algintegrate| |sinIfCan| |normal01| |startTableGcd!|
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- |newLine| |useNagFunctions| |raisePolynomial| |halfExtendedResultant2|
- |e02adf| |isQuotient| |sncndn| |optpair| |extractIfCan|
- |functionIsOscillatory| |representationType| |sqfree| |lprop| |cTan|
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- |decompose| |moebius| |rootPower| |semiLastSubResultantEuclidean|
- |monomRDE| |fortranTypeOf| |dec| |moreAlgebraic?| |cAcsch|
- |gcdPolynomial| |removeZero| |pdct| |concat!| |tubePointsDefault|
- |removeRedundantFactorsInContents| |setOfMinN| |setMinPoints3D|
- |numberOfOperations| |gcdprim| |power!| |d02cjf| |qPot| |multisect|
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- |isMult| |colorFunction| |nthCoef| |dualSignature| |f04arf|
- |linearAssociatedLog| |univariate?| |norm| |df2fi| |lflimitedint|
- |makeCos| |henselFact| |genericLeftMinimalPolynomial|
- |semiDiscriminantEuclidean| |factorsOfCyclicGroupSize| |d02raf|
- |clipSurface| |leftTraceMatrix| |cCos| |quadraticNorm| |s20adf|
- |expenseOfEvaluation| |regularRepresentation| |minPoints3D| |nthr|
- |euclideanGroebner| |mapdiv| |RemainderList| |fullDisplay| |s21bcf|
- |mathieu22| |triangular?| |mat| |rischDEsys| |debug| |An| |failed|
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- |arity| |getOrder| |substring?| D |equiv| |diophantineSystem|
- |product| |degreeSubResultantEuclidean| |imagJ| |graphState| |f02axf|
- |scan| |makeYoungTableau| |hermiteH| |clearDenominator| |yellow|
- |extractBottom!| |df2mf| |padecf| |coleman| |suffix?| |clipBoolean|
- |exponential1| |stosePrepareSubResAlgo| |truncate| |unitNormalize|
- |setleft!| |numericalIntegration| |contours| |axes| |llprop|
- |repeatUntilLoop| |nil| |associator| |cosSinInfo| |tail| |log|
- |univariate| |prefix?| |prepareSubResAlgo| |real?| |laguerreL|
- |Lazard| |readable?| |transform| |LazardQuotient| |f02fjf| |init|
- |increase| |polygon| |leftRegularRepresentation| |isList| |besselJ|
- |minrank| |macroExpand| |rangePascalTriangle| |medialSet| |cyclic?|
- |radicalOfLeftTraceForm| |sumSquares| |plotPolar| |varList|
- |OMputEndBind| |generic| |nextColeman| |currentCategoryFrame|
- |cyclotomicFactorization| |critMonD1| |approximate| |complexLimit|
- |OMgetVariable| |reverseLex| |toseSquareFreePart| |neglist|
- |sizePascalTriangle| |constantOpIfCan| |complex| |probablyZeroDim?|
- |max| |yCoord| |ScanRoman| |padicFraction| |processTemplate|
- |totalDegree| |positiveRemainder| |computeCycleLength| |primeFactor|
- |expenseOfEvaluationIF| |rotatez| |monicLeftDivide|
- |removeConstantTerm| |conjugate| |infieldint| |print| |iilog| |solve|
- |stoseInvertible?sqfreg| |properties| |extendedEuclidean| |c05nbf|
- |toroidal| |infix?| |romberg| |resolve| |e04ycf| |invmultisect|
- |translate| |powerSum| |invertibleElseSplit?| |lieAlgebra?| |mask|
- |squareFreeLexTriangular| |declare| |OMgetSymbol| |laguerre| |pack!|
- |more?| |scaleRoots| |firstUncouplingMatrix| |crest| |fprindINFO|
- |acothIfCan| |coshIfCan| |quoByVar| |numberOfDivisors| |Beta|
- |groebnerFactorize| |weights| |asecIfCan| |factor1| |cotIfCan|
- |supDimElseRittWu?| |leftCharacteristicPolynomial| |OMputEndApp|
- |prime?| |cylindrical| |palglimint0| |bitTruth| |green|
- |selectMultiDimensionalRoutines| |integralBasisAtInfinity| |updatF|
- |optional?| GE |vark| |numericIfCan| |solid?| |light|
- |createLowComplexityNormalBasis| |OMputEndBVar| |complete|
- |scanOneDimSubspaces| GT |getOperator| |airyAi| |karatsuba| |edf2df|
- |goto| |fractRadix| |randnum| |s21baf| |say| |OMputVariable|
- |components| LE |sequences| |cycleRagits| |delta| |moduloP|
- |alternative?| |hdmpToDmp| |binarySearchTree| |readInt8!| LT
- |sizeLess?| |conditionsForIdempotents| |numberOfFactors| |deepExpand|
- |signatureAst| |e01bff| |fortranCharacter| |frobenius|
- |setIntersection| |internal?| |plus| |f04adf| |upperCase?| |ef2edf|
- |s17dlf| |writeByte!| |resetVariableOrder| |parabolic| |d01amf|
- |outputAsScript| |OMconnOutDevice| |children| |normalized?|
- |genericRightMinimalPolynomial| |powmod| |shift|
- |integralMatrixAtInfinity| |prefixRagits| |csch2sinh| |recolor|
- |extendIfCan| |OMgetApp| |remove| |ParCond| |eigenMatrix|
- |setImagSteps| |redpps| |rightTraceMatrix|
- |halfExtendedSubResultantGcd1| |pushucoef| |cosh2sech|
- |listYoungTableaus| |mapDown!| |over| |leftPower| |OMUnknownCD?|
- |times| |monicRightFactorIfCan| |insertTop!|
- |unrankImproperPartitions1| |mesh| |showAll?| |last|
- |rationalApproximation| |morphism| |parseString| |partitions|
- |lastSubResultantElseSplit| |generator| |aQuadratic| |iisqrt3|
- |logpart| |mantissa| |algebraicDecompose| |collectQuasiMonic|
- |symmetricTensors| |assoc| |genericRightTrace| |s17adf|
- |factorGroebnerBasis| |stFuncN| |iiasinh| |useEisensteinCriterion|
- |transcendentalDecompose| |lfinfieldint| |numberOfFractionalTerms|
- |cyclicEntries| |antiCommutative?| |eof?| UTS2UP |quasiRegular|
- |OMreceive| |e02zaf| BY |fixPredicate| |symmetric?| |before?|
- |condition| |ratDsolve| |part?| |d02ejf| |s19abf| |rightScalarTimes!|
- |monom| |fortranCompilerName| |callForm?| |linSolve| |content|
- |OMgetEndAtp| |printHeader| |rowEchelon| |deepestTail| |ode|
- |UpTriBddDenomInv| |omError| |symbol?| |mightHaveRoots| |Nul|
- |acscIfCan| |s17acf| |removeZeroes| |monicRightDivide|
- |leadingBasisTerm| |OMputBVar| |largest| |OMencodingXML| |erf|
- |makeCrit| |mainVariables| |getExplanations| |c06gqf| |output|
- |common| |showScalarValues| |patternMatchTimes| |pointLists| |mapmult|
- |leftRankPolynomial| |weakBiRank| |denominators| |curry| |Lazard2|
- |e04fdf| |permutation| |printCode| |makeSin| |cAcsc| |constant|
- |generalizedInverse| |integral| |irreducibleFactor|
- |inputOutputBinaryFile| |constructor| |split!| |sh| |finiteBasis|
- |linearDependence| |leftExactQuotient| |dilog| |powerAssociative?|
- |relativeApprox| NOT |create| |extractClosed| |tablePow| |incr|
- |presuper| |groebner?| |mvar| |point?| |sin| |function| |ricDsolve|
- |initializeGroupForWordProblem| OR |interval| |extendedint| |key?|
- |hi| |nor| |binaryFunction| |isAbsolutelyIrreducible?| |move| |cos|
- |extract!| |stiffnessAndStabilityOfODEIF| |d01bbf| AND |rightTrim|
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- |separant| |tan| |d01apf| |infinite?| |logIfCan| |outputAsTex|
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- |simplifyExp| |reindex| |cot| |distFact| |derivationCoordinates|
- |addMatchRestricted| |chiSquare1| |linearPart| |componentUpperBound|
- |realRoots| |hue| |setStatus!| |sec| |groebgen| |cot2trig| |entry?|
- |permutationGroup| |splitNodeOf!| |perfectNthPower?| |KrullNumber|
- |monicDecomposeIfCan| |evenInfiniteProduct| |csc| |symbol| |shufflein|
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- |d03edf| |wholePart| |setDifference| |asin| |expression| |moebiusMu|
- |csc2sin| |normalizeAtInfinity| |traceMatrix| |repeating| |tab1|
- |setPosition| |twoFactor| |f01rdf| |acos| |functorData| |integer|
- |nil?| |destruct| |directSum| |showTheSymbolTable| |derivative|
- |rightMult| |f01qef| |legendreP| |biRank| |splitLinear| |atan|
- |removeRoughlyRedundantFactorsInPols| |showArrayValues| |setright!|
- |viewZoomDefault| |setref| |solveLinearlyOverQ|
- |coercePreimagesImages| |findCycle| |anfactor|
- |stripCommentsAndBlanks| |acot| |s19aaf| |abs| |f2st| |hasPredicate?|
- |cAcos| |extractTop!| |readLineIfCan!| |expandLog| |rightRemainder|
- |asec| |jordanAdmissible?| |changeWeightLevel| * |normalizeIfCan|
- |subHeight| |minus!| |lhs| |createMultiplicationTable| |lex|
- |triangSolve| |kroneckerDelta| |acsc| |rightAlternative?|
- |complexRoots| |lcm| |dflist| |karatsubaDivide|
- |fortranCarriageReturn| |rhs| |nand| |approxSqrt| |f02agf| |cSinh|
- |sinh| |lazyPseudoQuotient| |low| |represents| |mulmod| |one?|
- |generate| |diff| |laplacian| |lighting| |plenaryPower| |principal?|
- |cosh| |createIrreduciblePoly| |idealiserMatrix| |anticoord| |append|
- |hash| = |currentEnv| |clearTheFTable| |returns| |tValues| |isImplies|
- |pattern| |floor| |tanh| |count| |gcd| |symbolTableOf|
- |complexNormalize| |cAcot| |commutativeEquality| |incrementBy|
- |normInvertible?| |associates?| |groebSolve| |initTable!|
- |showTheFTable| |nonLinearPart| |coth| |e02ajf| |false| |lp|
- |atrapezoidal| < |removeSuperfluousQuasiComponents| |decomposeFunc|
- |expand| |category| |rationalPoint?| |getZechTable| |pmintegrate|
- |ptree| |sin2csc| |solve1| |flatten| |rightRecip| |inGroundField?|
- |OMParseError?| > |root| |filterWhile| |domain| |intPatternMatch|
- |conjugates| |diagonal| |loadNativeModule| |poisson|
- |oblateSpheroidal| |pushup| |sub| <= |parent| |generators|
- |filterUntil| |package| |iiasech| |asinhIfCan| |interpolate| |message|
- |tanh2trigh| |minimalPolynomial| |unit?| |overbar| >= |externalList|
- |matrixDimensions| |select| |cycleLength| |separateDegrees|
- |defineProperty| |OMgetEndError| |polCase| |prod| |algebraicSort|
- |hdmpToP| |exactQuotient!| |packageCall| |double| |drawStyle| |space|
- |delete!| |polarCoordinates| |parts| |exponents|
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- |squareFreePolynomial| |arbitrary| |complex?| |OMopenString|
- |viewDeltaYDefault| |figureUnits| |c06fpf| |characteristicSet|
- |dominantTerm| |zeroSetSplit| + |makeprod| |setAdaptive3D|
- |palginfieldint| |mappingAst| |summation| |parents| |s21bbf| |rarrow|
- |linearlyDependentOverZ?| |qualifier| |univariatePolynomialsGcds| -
- |controlPanel| |determinant| |inspect| |blue| |solveRetract|
- |createMultiplicationMatrix| |maximumExponent| |getBadValues|
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- |prindINFO| |reflect| |birth| |tanintegrate|
- |solveLinearPolynomialEquation| |makeRecord| |collect| |difference|
- |univariateSolve| |createRandomElement| |twist| |s17dgf|
- |lastSubResultantEuclidean| |outerProduct| |setCondition!|
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- |declare!| |fibonacci| |initiallyReduce| |assign| |removeDuplicates|
- |selectFiniteRoutines| |startPolynomial| |selectOrPolynomials|
- |roughBasicSet| |operators| |zeroDimPrimary?|
- |resultantReduitEuclidean| |selectODEIVPRoutines|
- |intermediateResultsIF| |computeBasis| |outputArgs| |lllip|
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- |minPoly| |imagE| |factorSquareFreeByRecursion| |headReduced?| |rules|
- |discriminantEuclidean| |algebraicVariables| |composite| |palgLODE|
- |nullary?| |rdHack1| |e02ddf| |halfExtendedSubResultantGcd2|
- |showAllElements| |nextNormalPoly| |basisOfLeftNucleus| |setEpilogue!|
- |iitan| |definingInequation| |step| |taylorIfCan| |makeUnit|
- |finiteBound| |prepareDecompose| |errorInfo| |cAsinh| |inconsistent?|
- |stirling1| |swap!| |linGenPos| |airyBi| |backOldPos| |zeroDim?|
- |any?| |constantOperator| |stoseSquareFreePart| |returnTypeOf|
- |tan2trig| |unitVector| |segment| |diagonalProduct| |quotedOperators|
- |topPredicate| |leastMonomial| |stopMusserTrials| |sumOfDivisors|
- |genericPosition| |palgint| |cyclicCopy| |signAround| |f04faf|
- |htrigs| |outlineRender| |zeroDimPrime?| |transcendenceDegree|
- |expextendedint| |block| |OMconnInDevice| |ip4Address| |bindings|
- |c05adf| |s13acf| |parametric?| |iiacosh| |commutator| |OMputString|
- |atom?| |writeUInt8!| |scripted?| |pushuconst| |alphabetic?|
- |integral?| |iExquo| |primlimitedint| |recip| |normalDenom|
- |pushNewContour| |putProperties| |leadingSupport| |merge|
- |associatedEquations| |key| |cAsin| |resultant| |multiple?|
- |setScreenResolution| |errorKind| |leftDiscriminant| |closeComponent|
- |color| |clip| |connect| |maxColIndex| |value| |upperBound|
- |divisorCascade| |drawToScale| |linears| |filename| |exists?|
- |factorList| |bits| |closedCurve?| |exprToXXP| |HenselLift|
- |taylorQuoByVar| |optional| |polyRDE| |supersub| |imagK|
- |approxNthRoot| |mathieu12| |times!| |rightLcm| |lazyGintegrate|
- |duplicates| |formula| |parse| |d01asf| |car| |minset| |nextSublist|
- |prime| |squareFreePrim| |initials| |explicitlyFinite?| |stop|
- |substitute| |nextLatticePermutation| |component| |insert!|
- |setProperties| |s14abf| |evenlambert| |mr| |arguments|
- |resetBadValues| |front| |var1StepsDefault| |leftRank| |seed|
- |readIfCan!| |bumptab| |fortranDouble| |disjunction| |relerror|
- |getConstant| |intChoose| |rischNormalize| |limitedint|
- |chineseRemainder| |imagk| |iifact| |infLex?| |d01gbf| |nrows|
- |result| |subPolSet?| |shiftRight| |c05pbf| |ceiling| |accuracyIF|
- |d01anf| |stoseIntegralLastSubResultant| |members|
- |SturmHabichtCoefficients| |odd?| |ncols| |groebnerIdeal| |OMputBind|
- |universe| |rk4qc| |symmetricProduct| |sPol| |subNodeOf?|
- |patternVariable| |latex| |bsolve| |e04mbf| |setMaxPoints3D|
- |shrinkable| |mapSolve| |tower| |explicitlyEmpty?| |preprocess|
- |symmetricPower| |minRowIndex| |routines| |e04gcf| |colorDef| |iiacos|
- |divideIfCan| |c06frf| |squareFree| |rootProduct| |scale| |freeOf?|
- |rootsOf| |bezoutMatrix| |totalGroebner| |indiceSubResultantEuclidean|
- |compactFraction| |taylor| |comment| |conjunction| |OMputApp|
- |setPredicates| |thenBranch| |hexDigit| |zeroMatrix| |knownInfBasis|
- |mainMonomial| |numerator| |laurent| |semiResultantReduitEuclidean|
- |elementary| |qroot| LODO2FUN |toScale| |e02dff| |choosemon|
- |property| |expt| |puiseux| |basisOfCommutingElements|
- |continuedFraction| |quasiMonicPolynomials| |makeFR| |matrix| |index|
- |rroot| |mainValue| |reducedQPowers| |diagonals| |deleteRoutine!|
- |pointColorPalette| |monomRDEsys| RF2UTS |jokerMode| |midpoint|
- |cyclotomicDecomposition| |elements| |semiDegreeSubResultantEuclidean|
- |uniform01| |inv| |aCubic| |lambda| |critMTonD1| |highCommonTerms|
- |primextintfrac| |dmpToP| |leftNorm| |exprHasLogarithmicWeights|
- |elliptic?| |s20acf| |att2Result| |float?| |setRealSteps| |ground?|
- |f01bsf| |exprToGenUPS| |partition| |jacobiIdentity?| |pair|
- |doubleResultant| |ground| |prinpolINFO| |showRegion| |iiGamma|
- |primaryDecomp| |fixedPoint| |rightExtendedGcd| |unaryFunction|
- |mesh?| |addPoint| |squareFreeFactors| |directory|
- |identitySquareMatrix| |decreasePrecision| |increasePrecision|
- |OMencodingUnknown| |mainPrimitivePart| |leadingMonomial|
- |primPartElseUnitCanonical| |factorset| |hypergeometric0F1|
- |viewThetaDefault| |hasHi| |sum| |basisOfRightNucloid|
- |possiblyNewVariety?| |phiCoord| |reverse| |OMgetType| |pade|
- |leadingCoefficient| |pomopo!| |style| |rightOne| |setClipValue|
- |integrate| |simplifyPower| |listRepresentation| |ideal| |graphs|
- |primitiveMonomials| |leftFactorIfCan| |d01gaf| |makeEq|
- |numericalOptimization| |resultantnaif| |e02bbf| |retract|
- |bipolarCylindrical| |varselect| |basisOfCenter| |flagFactor|
- |lSpaceBasis| |reductum| |addMatch| |pol| |increment| |lowerCase?|
- |makeFloatFunction| |OMputFloat| |OMsupportsCD?| |s17def|
- |roughEqualIdeals?| |divide| |torsion?| |multiEuclidean|
- |trivialIdeal?| |inRadical?| |characteristic| |rank|
- |removeSquaresIfCan| |sincos| |putColorInfo| |const|
- |stopTableInvSet!| |mindeg| |mathieu24| |primPartElseUnitCanonical!|
- |rightDivide| |monomialIntegrate| |f04axf| |bottom!|
- |hasTopPredicate?| |definingPolynomial| |iicoth| |exprToUPS|
- |argumentList!| |OMgetInteger| |nil| |infinite| |arbitraryExponent|
- |approximate| |complex| |shallowMutable| |canonical| |noetherian|
- |central| |partiallyOrderedSet| |arbitraryPrecision|
- |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary|
- |additiveValuation| |unitsKnown| |canonicalUnitNormal|
- |multiplicativeValuation| |finiteAggregate| |shallowlyMutable|
- |commutative|) 
\ No newline at end of file
+ |Record| |Union| |distribute| |thenBranch| |createPrimitivePoly|
+ |nthRootIfCan| |arrayStack| |makeEq| |coercePreimagesImages|
+ |doubleDisc| |leastPower| |mainDefiningPolynomial| |ipow|
+ |commutative?| |set| |perfectSqrt| |hermiteH| |setMaxPoints|
+ |cRationalPower| |SturmHabichtSequence| |internalDecompose|
+ |findConstructor| |d02gbf| |bringDown| |d03edf| |edf2df|
+ |showAllElements| |matrixConcat3D| |setUnion| |physicalLength!|
+ |readUInt32!| |useSingleFactorBound| |addMatchRestricted|
+ |OMUnknownSymbol?| |findBinding| |encodingDirectory| |power|
+ |OMgetEndAtp| |deepCopy| |numberOfDivisors| |squareFreeLexTriangular|
+ |generic| |red| |iiacsc| |hdmpToP| |intChoose| |s17agf| |partition|
+ |scalarTypeOf| |cyclotomicDecomposition| |wrregime| |s18acf| |head|
+ |lists| |extendedResultant| |lazyPseudoDivide| |f01ref| |point?|
+ |unravel| |cyclePartition| |exists?| |compound?| |prinshINFO|
+ |mapSolve| |ffactor| |probablyZeroDim?| |nodeOf?| |quasiRegular?|
+ |checkForZero| |inHallBasis?| |signature| |infieldIntegrate|
+ |LyndonWordsList1| |functionIsContinuousAtEndPoints| |isList| |cAtan|
+ |c06gsf| |OMputFloat| |realSolve| |tableForDiscreteLogarithm|
+ |addPoint| |writeByte!| |torsionIfCan| |antisymmetric?|
+ |genericPosition| |nthRoot| |search| |leftPower| |scripted?|
+ |anticoord| |s17dcf| |listOfMonoms| |expr| |sumOfKthPowerDivisors|
+ |numericalOptimization| |elColumn2!| |viewWriteAvailable| |subCase?|
+ |zeroSetSplitIntoTriangularSystems| |strongGenerators| |mirror|
+ |makeResult| |outputForm| |birth| |topFortranOutputStack| |findCycle|
+ |linearlyDependentOverZ?| |sort!| |cAsech| |outputList| |hexDigit|
+ |antiAssociative?| |ptFunc| |clearDenominator| |setLength!|
+ |leftUnits| |extendedIntegrate| |OMgetAttr| |rubiksGroup|
+ |splitNodeOf!| |bitCoef| |rowEch| |show| |goto| |nextNormalPoly|
+ |mappingMode| |OMwrite| |complexIntegrate| |e01sff| |modTree| |index?|
+ |newReduc| |resultantReduit| |atoms| |numberOfChildren| |f04atf|
+ |variable| |cAcoth| |OMgetSymbol| |Beta| |btwFact| |chiSquare1|
+ |categoryMode| |trace| |wholePart| |rischNormalize| |thetaCoord|
+ |iterators| |printHeader| |increasePrecision| |root| |factorList|
+ |elements| |brillhartTrials| |nextColeman| |OMencodingUnknown|
+ |exteriorDifferential| |getlo| |complementaryBasis| |nthExpon|
+ |datalist| |jacobiIdentity?| |factorsOfCyclicGroupSize|
+ |inverseLaplace| |systemCommand| |iicos| |element?| |ran| |besselJ|
+ |char| |top!| |subst| |checkPrecision| |max| |exactQuotient!| |reify|
+ |ricDsolve| |nextsousResultant2| FG2F |horizConcat| |maxPoints3D|
+ |hconcat| |internalAugment| |bitior| |fortranLinkerArgs| |lquo|
+ |OMputInteger| |OMsupportsCD?| |isMult| |resetVariableOrder|
+ |anfactor| |pushdown| |isobaric?| |palgint| |pushuconst|
+ |makeViewport2D| |clearTheFTable| |roughUnitIdeal?|
+ |subresultantVector| |precision| |normal| |unitsColorDefault| |irVar|
+ |radicalEigenvector| |linearPart| |integralAtInfinity?| |fi2df|
+ |returnType!| |yellow| |integerIfCan| |tanintegrate| |bfEntry| |cond|
+ |groebnerFactorize| |perfectNthPower?| |concat| |enumerate|
+ |PollardSmallFactor| |OMUnknownCD?| |cAsec| |removeRedundantFactors|
+ |s14baf| |mkcomm| |sech| |setelt!| |hasoln| |orthonormalBasis|
+ |subResultantGcd| |voidMode| |zeroMatrix| |basisOfLeftNucleus| |nodes|
+ |printStatement| |rightOne| |csch| |operation| |laguerre|
+ |semiDegreeSubResultantEuclidean| |minrank| |baseRDE| |numberOfHues|
+ |objects| |rischDE| |float| |alphabetic| |fractRadix| |e02def|
+ |firstSubsetGray| |asinh| |bits| |bothWays| |resultantEuclidean|
+ |currentCategoryFrame| |base| |limitedint| |ddFact| |coordinate|
+ |baseRDEsys| |Lazard2| |acosh| |df2ef| |kovacic| |swapRows!|
+ |infiniteProduct| |cyclicCopy| |kind| |cyclotomicFactorization|
+ |selectSumOfSquaresRoutines| |fortranLiteral| |arg1|
+ |initializeGroupForWordProblem| |getGraph| |oddintegers|
+ |setCondition!| |atanh| |pointData| |in?| |bytes| |lowerCase|
+ |OMencodingXML| |certainlySubVariety?| |op| |besselK| |externalList|
+ |factors| |makeSeries| |asechIfCan| |arg2| |rowEchelon| |writeBytes!|
+ |acoth| |complexExpand| |invertibleSet| |ip4Address| |acoshIfCan|
+ |bindings| |makeTerm| |e02bef| |s17def| |doubleResultant| |lifting|
+ |asech| |numer| |semiResultantEuclidean2| |viewpoint| |elliptic|
+ |square?| |returns| |makeCos| |innerSolve| |c06fpf| |npcoef| |s21bcf|
+ |conditions| |stoseInvertible?sqfreg| |variables| |denom|
+ |symmetricGroup| |minColIndex| |setImagSteps|
+ |internalLastSubResultant| |rotatex| |extractBottom!| |Ei| |match|
+ |bat1| |options| |iFTable| |multiple| |predicates| |getVariableOrder|
+ |componentUpperBound| |extensionDegree| |leadingTerm|
+ |genericLeftTrace| |lookup| |sinhIfCan| |colorFunction| |applyQuote|
+ |selectODEIVPRoutines| |leftDiscriminant| |s13adf| |iidprod|
+ |stiffnessAndStabilityFactor| |pi| |tree| |rootsOf| |integralBasis|
+ |solveLinearPolynomialEquation| |cycleEntry| |sturmVariationsOf|
+ |ReduceOrder| |getButtonValue| |infinity| |KrullNumber| |factorials|
+ |union| |bumprow| |equiv| |viewPosDefault| |any| |isAtom| |f07fef|
+ |string| |genericRightTrace| |less?| |computeInt|
+ |rangePascalTriangle| |leftGcd| |monicDecomposeIfCan| |solid?|
+ |headReduced?| |zeroDimensional?| |s17aef| |ruleset| |child?|
+ |lagrange| |signAround| |selectOptimizationRoutines| |s18aff|
+ |perspective| |infRittWu?| |var1StepsDefault| |clipWithRanges| |has?|
+ |legendreP| |rroot| |kernel| |previous| |matrixDimensions| |f04maf|
+ |putProperty| |monomial?| |rootNormalize| |setClipValue| |regime|
+ |startStats!| |nonSingularModel| |axesColorDefault| |list|
+ |complexNumeric| |read!| |closed?| |decimal| |close!|
+ |monomialIntPoly| |e04fdf| |suchThat| |sign| |reduceBasisAtInfinity|
+ |OMputAtp| |ksec| |logIfCan| |draw| |critMonD1| |failed?| |mulmod|
+ |leftExactQuotient| |deepestTail| |pleskenSplit| |paren|
+ |outputMeasure| |moreAlgebraic?| |bottom!| |setIntersection| |c05adf|
+ |startTable!| |varselect| |vspace| |pop!| |extendedEuclidean|
+ |setMinPoints| |getProperty| |symmetricProduct| |makeCrit|
+ |ListOfTerms| |redpps| |cCot| |ScanFloatIgnoreSpacesIfCan|
+ |setProperty| |mathieu22| |closeComponent| |characteristicSet|
+ |normFactors| |laguerreL| |domainTemplate| |hclf| |sturmSequence|
+ |pascalTriangle| |minPol| |dfRange| |quasiAlgebraicSet| |ratDenom|
+ |s17adf| |sparsityIF| |resize| |makeObject| |bezoutMatrix|
+ |perfectSquare?| |stronglyReduce| |diophantineSystem| |curve?|
+ |algint| |intermediateResultsIF| |leftAlternative?| |digamma| |center|
+ |cExp| |returnTypeOf| |coef| |edf2efi| |debug3D| |light|
+ |discriminantEuclidean| |d02ejf| |stack| |biRank| |graphCurves|
+ |nextPrimitiveNormalPoly| |mainValue| |pmintegrate| |label|
+ |dictionary| |graphImage| |leftRank| |showClipRegion| |elliptic?|
+ |d02gaf| |push| |se2rfi| |c06gcf| |cot2tan| |name| |s14aaf|
+ |evenInfiniteProduct| |reciprocalPolynomial| |fortranReal| |conjug|
+ |hermite| |cAcsch| |transcendent?| |meshPar1Var| |nonQsign| |body|
+ |meshPar2Var| |direction| |rootBound| |mapBivariate| |unary?|
+ |associatedSystem| |typeForm| |cardinality| |stFunc1|
+ |rewriteIdealWithHeadRemainder| |outputAsTex| |powerAssociative?|
+ |patternMatch| |cycleLength| |interpret| |one?| |harmonic|
+ |permutation| |c05nbf| |dominantTerm| |extractIndex| |internal?|
+ |logical?| |complexEigenvalues| |OMgetEndObject| |mainVariable| |isOr|
+ |integrate| |s15aef| |mpsode| |sPol| |hasTopPredicate?| |complexLimit|
+ |diagonal?| |basisOfCenter| |tab| |completeSmith| |addmod|
+ |createPrimitiveElement| |color| |d01alf| |wordInStrongGenerators|
+ |logGamma| |s13acf| |charClass| |degreePartition| |sup|
+ |factorGroebnerBasis| |cSin| |point| |length| |conditionP| |divisor|
+ |complexSolve| |rightTraceMatrix| |mdeg|
+ |createLowComplexityNormalBasis| |reduction| |atanhIfCan| |option|
+ |associative?| |computeBasis| |scripts| |wholeRadix| |testDim|
+ |Lazard| |iipow| |numberOfMonomials| |totalGroebner| SEGMENT |shape|
+ |s19abf| |f07adf| |reducedQPowers| |intensity| |mapExpon| |tan2trig|
+ |port| |submod| |subscript| |seed| |product| |OMreadFile|
+ |outputBinaryFile| |series| |inrootof| |alphanumeric| |every?|
+ |sin2csc| |cLog| |irreducibleFactors| |algebraicVariables| |lambert|
+ |s20acf| |goodPoint| |splitLinear| |gcdPolynomial| |polyRicDE| |Is|
+ |t| |f04mbf| |numberOfVariables| |host| |tableau| |factorByRecursion|
+ |printCode| |semiSubResultantGcdEuclidean1| |fmecg| |f04adf| |merge!|
+ |separateDegrees| |shufflein| |lfextlimint| |overlabel| |digit|
+ |subResultantChain| |toroidal| |printTypes| |OMgetBind|
+ |deepestInitial| |cscIfCan| |cdr| |systemSizeIF| |rational?|
+ |normalForm| |simplifyPower| |lfunc| |min| |whatInfinity|
+ |zeroSetSplit| |definingPolynomial| |subNodeOf?| |virtualDegree|
+ |leftQuotient| |diff| |relativeApprox| |f02abf| |character?|
+ |goodnessOfFit| |clip| |constantKernel| |radicalSimplify| |quadratic|
+ |OMgetVariable| |rightFactorIfCan| |flagFactor| |wholeRagits| |f02akf|
+ |palgint0| |isPlus| |chiSquare| |eq?| |dimensionsOf| |unknown| |apply|
+ |lazyVariations| |radicalEigenvalues| |numberOfNormalPoly| |divisors|
+ |tryFunctionalDecomposition?| |s19adf| |functionIsOscillatory|
+ |rightUnit| |stFuncN| |readable?| |stoseInvertible?| |first| |d01fcf|
+ |halfExtendedSubResultantGcd1| |dn| |cyclicGroup| |cTanh|
+ |primPartElseUnitCanonical| |f07fdf| |outputArgs| |xor| |imag|
+ |diagonals| |solve1| |unitVector| |rest| |parametric?|
+ |indiceSubResultantEuclidean| |maxint| |OMputEndBVar|
+ |rightScalarTimes!| |directProduct| |normalElement| |besselI| |case|
+ |bracket| |e01bhf| |BumInSepFFE| |approximants|
+ |eisensteinIrreducible?| |degreeSubResultantEuclidean| |readIfCan!|
+ |symFunc| |bernoulli| |Zero| |removeRoughlyRedundantFactorsInPols|
+ |internalSubQuasiComponent?| |schwerpunkt| |bivariatePolynomials|
+ |charpol| |comp| |keys| |presub| |true| |chainSubResultants|
+ |composite| |att2Result| |void| |c02agf| |setValue!| |One| |top|
+ |removeZero| |patternVariable| |modifyPoint| |cup| |trigs2explogs|
+ |var1Steps| |sortConstraints| |fullPartialFraction|
+ |generalizedEigenvector| |continue| |critBonD| |romberg| |imagj|
+ |generic?| |tRange| |pToHdmp| |f01mcf| |primes| |putGraph| |sort|
+ |plusInfinity| |makeSin| |makeprod| |algebraicOf| |principalIdeal|
+ |divideExponents| |defineProperty| |trunc| |iisinh| |changeThreshhold|
+ |c02aff| |minusInfinity| |setScreenResolution3D| |internalSubPolSet?|
+ |connect| |iicoth| |quadraticForm| |padicallyExpand|
+ |univariatePolynomial| |Gamma| |create| |makeViewport3D|
+ |nthFractionalTerm| |pointColor| |listRepresentation| |reducedSystem|
+ |Frobenius| |id| |mainCharacterization| |leadingBasisTerm| |tubePlot|
+ |reverseLex| |lSpaceBasis| |laplacian| |refine| |iiasinh| |transform|
+ |roughSubIdeal?| |realEigenvalues| |elt| |rightRecip| |lo|
+ |coerceImages| |writeLine!| |lazyEvaluate| |basicSet| |littleEndian|
+ |random| |representationType| |quote| |deleteRoutine!| |rangeIsFinite|
+ |wronskianMatrix| |next| |iiacosh| |integralMatrix|
+ |OMsupportsSymbol?| |imagJ| |sayLength| |postfix| |df2st| |sqfrFactor|
+ |stoseInternalLastSubResultant| |diagonalProduct| |mapGen| |pushucoef|
+ |iiacot| |positive?| |f04qaf| |lllip| |numberOfPrimitivePoly|
+ |showArrayValues| |integralRepresents| |cyclic?| |OMgetBVar|
+ |compactFraction| |palgLODE| |complete| |fortranCompilerName| |dot|
+ |iicsc| |setAdaptive3D| |getRef| |latex| |ord| |s17dhf|
+ |categoryFrame| |bumptab| |float?| |exQuo| |unitCanonical|
+ |cyclicEqual?| |matrixGcd| |badNum| |corrPoly| |ode1| |readBytes!|
+ |BasicMethod| |hostByteOrder| |useEisensteinCriterion| |delay|
+ |adaptive| |e04ycf| |insert| |child| |complexZeros| |subSet|
+ |readInt16!| |leftDivide| |basisOfMiddleNucleus| |cAcsc| |maxColIndex|
+ |viewport3D| |physicalLength| |reducedDiscriminant| |leader|
+ |quadratic?| |positiveSolve| |degreeSubResultant| |extractClosed|
+ |mainForm| |restorePrecision| |getCurve| |pointColorPalette|
+ |consnewpol| |exprToUPS| |cschIfCan| |sinhcosh| |binaryTree|
+ |writable?| |addMatch| |setOrder| |pToDmp| |applyRules| |rootRadius|
+ |mkIntegral| |inGroundField?| |OMputBVar| |OMgetEndError|
+ |semiIndiceSubResultantEuclidean| |nary?| |lighting| |localAbs|
+ |lazyPremWithDefault| |changeBase| |viewWriteDefault| |cfirst|
+ |qfactor| |nextsubResultant2| |createPrimitiveNormalPoly|
+ |toseSquareFreePart| |calcRanges| |algebraicCoefficients?|
+ |leftTraceMatrix| |d03faf| |minPoints3D| |setright!| |normDeriv2|
+ |radicalOfLeftTraceForm| |LazardQuotient| |commutator| |reduceLODE|
+ |primitivePart!| |graphState| |shiftRoots| |possiblyInfinite?|
+ |palginfieldint| |zoom| |quotedOperators| |magnitude| |nullary?|
+ |node?| |lexico| |startPolynomial| |symbolTable| |eulerE| |normalise|
+ |quickSort| |bsolve| |gramschmidt| |splitConstant|
+ |scanOneDimSubspaces| |callForm?| |quartic| |primeFrobenius| |s17aff|
+ |balancedBinaryTree| |B1solve| |csch2sinh| |fortranDouble| |setTex!|
+ |tubeRadiusDefault| |escape| |pushFortranOutputStack| |numerators|
+ |invmultisect| |Si| |upperCase| |divideIfCan| |tablePow|
+ |pseudoDivide| |setRealSteps| |idealSimplify| |popFortranOutputStack|
+ |width| |trim| |simplifyExp| |rootOfIrreduciblePoly| |e02baf| |super|
+ |selectPolynomials| |open?| |fTable| |exponent| |f01maf|
+ |outputAsFortran| |rightMinimalPolynomial| |argumentList!| |cosIfCan|
+ |pol| |dequeue!| |exponentialOrder| Y |mapmult|
+ |variationOfParameters| |powers| |OMParseError?| |messagePrint|
+ |simplifyLog| |moduleSum| |monicDivide| |jacobian| |phiCoord|
+ |lazyPrem| |decompose| |eigenvector| |rotate| |expressIdealMember|
+ |noncommutativeJordanAlgebra?| |nthr| |infix| |selectPDERoutines|
+ |ellipticCylindrical| |f02fjf| |interpolate| |d01asf|
+ |selectMultiDimensionalRoutines| |remainder| |lowerBound| |bipolar|
+ |nil?| |clearCache| |sumSquares| |topPredicate| |readUInt16!| |lift|
+ |table| |tubeRadius| |completeHermite| |nextPrime| |maxPoints|
+ |isPower| |rename!| |reindex| |e04mbf| |addBadValue| |reduce| |new|
+ |upperCase!| |insert!| |fillPascalTriangle| |obj|
+ |selectOrPolynomials| |iisqrt3| |removeIrreducibleRedundantFactors|
+ |recolor| |socf2socdf| |integral| |reverse!| |solveid|
+ |removeConstantTerm| |cache| |stoseLastSubResultant|
+ |rightRegularRepresentation| |external?| |li| |vertConcat| |dark|
+ |cyclicSubmodule| |genericRightDiscriminant| |plot| |cycle| |expt|
+ |rootPoly| |factorOfDegree| |c06frf| |uncouplingMatrices|
+ |startTableGcd!| |linSolve| |leftRankPolynomial| |cAsin| |rk4a|
+ |raisePolynomial| |check| |allRootsOf| |approxSqrt| |duplicates?|
+ |factor| |cCosh| |moebius| |removeRedundantFactorsInPols| |checkRur|
+ |mindeg| |forLoop| |hexDigit?| |ref| |totalDifferential| |OMgetType|
+ |dmpToHdmp| |generalInfiniteProduct| |nonLinearPart| |endSubProgram|
+ |rCoord| |integralBasisAtInfinity| |gderiv| |multisect| |mapUp!|
+ |LiePolyIfCan| |tubePoints| |vector| |setErrorBound| |llprop| |iiexp|
+ |GospersMethod| |car| |inspect| |complex?| |euclideanGroebner| |list?|
+ |differentiate| |numberOfFactors| |userOrdered?| |tanh2trigh| |iomode|
+ |explimitedint| |coerceS| |predicate| |antiCommutator|
+ |basisOfLeftAnnihilator| |simpsono| |c06fuf| |airyBi| |mainKernel|
+ |setProperties| |e01baf| |lowerCase!| |roughBasicSet| |OMputObject|
+ |euler| |digit?| |SturmHabichtCoefficients| |binaryTournament| |size|
+ |irreducibleFactor| |safetyMargin| |left| ** |lyndon?| |monomial|
+ |laurentRep| |dom| |test| |logpart| |powern| |directSum| |box|
+ |leftTrace| |stoseInvertible?reg| |byte| |lfintegrate| |minIndex|
+ |multivariate| |right| |removeCosSq| |removeZeroes| |fixPredicate|
+ |palgintegrate| |zCoord| |extractSplittingLeaf| |cCsc|
+ |halfExtendedResultant2| |extendIfCan| |Aleph| |position!|
+ |retractIfCan| |subspace| |janko2| |rewriteSetWithReduction|
+ |basisOfCommutingElements| |rightZero| |lllp| |coefficients| |f02agf|
+ |close| |squareFree| |SturmHabichtMultiple| |linear| |highCommonTerms|
+ |weakBiRank| |mapUnivariateIfCan| |e02daf| |laplace| |mathieu24|
+ |computeCycleEntry| |OMputEndObject| |triangularSystems|
+ |stoseInvertibleSetreg| |sqrt| |rombergo| |dioSolve| |conjugate|
+ |setprevious!| |e02ajf| |updatF| |e04dgf| |leaves| |display|
+ |indicialEquation| |polynomial| |expPot| |real| |title| |rootPower|
+ |pade| |ravel| |resultant| |createNormalElement| |repeatUntilLoop|
+ |units| |repSq| |aromberg| |prefix| |tanSum| |cCsch| |deepExpand|
+ |writeInt8!| |iiabs| |newSubProgram| |symbolIfCan| |reshape|
+ |minimalPolynomial| |inputOutputBinaryFile| |points| |parameters|
+ |implies| |multinomial| |convergents| |s18dcf| |backOldPos| |s13aaf|
+ |scopes| |particularSolution| |int| |cSec| |s14abf| |blue| |e|
+ |mapdiv| |characteristicPolynomial| |OMopenString| F2FG |odd?| |node|
+ |linearAssociatedOrder| |leftRemainder| |decreasePrecision| |expint|
+ |e02bdf| |operators| |tryFunctionalDecomposition| |removeSinhSq|
+ |LowTriBddDenomInv| |var2StepsDefault| |SFunction| |createThreeSpace|
+ |input| |simplify| |setPrologue!| |map| |localUnquote| |numFunEvals|
+ |weight| |showTheSymbolTable| |fintegrate| |brace| |kernels| |code|
+ |testModulus| |OMgetApp| |palgRDE0| |library| |symmetric?| |lyndon|
+ |aspFilename| |solveLinearPolynomialEquationByRecursion| |constant?|
+ |e02adf| |update| |eq| |operator| |showSummary| |isEquiv| |fortran|
+ |s21bdf| |sample| |argumentListOf| |algebraic?| |schema|
+ |partialQuotients| |iicot| |atrapezoidal| |primPartElseUnitCanonical!|
+ |iter| |rootProduct| |optimize| |cSinh| |coerceL| |primextintfrac|
+ |constDsolve| |denominators| |infieldint| |associator|
+ |algebraicDecompose| |redmat| |isNot| |tanQ| |sequence| |selectfirst|
+ |hyperelliptic| |leastAffineMultiple| |ScanFloatIgnoreSpaces|
+ |continuedFraction| |multiple?| |assert| |cycleSplit!| |measure|
+ |asinIfCan| |myDegree| |optional?| |multMonom| |convert| |pomopo!|
+ |contract| |subResultantsChain| |OMputEndAtp| |signatureAst|
+ |showAttributes| |psolve| |rdregime| |split!| |order| |level|
+ |ldf2lst| |FormatArabic| |groebnerIdeal|
+ |semiLastSubResultantEuclidean| |zeroDim?| |position| |log2|
+ |nextIrreduciblePoly| |evenlambert| |areEquivalent?| |algSplitSimple|
+ |readUInt8!| |mergeDifference| |separant| |companionBlocks| |unit?|
+ |denomRicDE| |generalSqFr| |solveRetract| |RemainderList| |derivative|
+ |viewDeltaYDefault| |iiasec| |sncndn| |swap| |quotient| |fixedDivisor|
+ |setlast!| |createLowComplexityTable| |compile| |subMatrix|
+ |characteristicSerie| |status| |endOfFile?| |exp| |evaluateInverse|
+ |minPoly| |subNode?| |nlde| |zeroDimPrimary?| |createNormalPoly|
+ |separateFactors| |doubleFloatFormat|
+ |removeSuperfluousQuasiComponents| |equation| |lazyPseudoQuotient|
+ |rightGcd| |numeric| |invertible?| |initiallyReduced?| |curry| |iilog|
+ |setfirst!| |rightDivide| |extractPoint| |radical| |ParCond|
+ |sylvesterSequence| |removeSuperfluousCases| |LyndonCoordinates|
+ |f02wef| |rotatey| |build| |normalizedDivide| |badValues| |scale|
+ |rationalPoints| |shiftLeft| |before?| |rootSimp|
+ |setScreenResolution| |collectQuasiMonic| |e01bff| |OMgetString|
+ |irreducibleRepresentation| |script| |boundOfCauchy| |sh| |dmpToP|
+ |style| |noValueMode| |modulus| |f07aef| |cosSinInfo| |rootSplit|
+ |printInfo| |prinb| |vark| |sumOfSquares| |e04naf| |support|
+ |quasiMonicPolynomials| |any?| |OMputBind| |cyclotomic| |unparse|
+ |mix| |numberOfComponents| |fullDisplay| |iiasin| |symmetricSquare|
+ |localReal?| |bivariate?| |constantLeft| |tex| |arity|
+ |resetBadValues| |is?| |radicalSolve| |lepol| |nullSpace|
+ |relationsIdeal| |d01apf| |nothing| |overbar| |imagE| |vconcat|
+ |mindegTerm| |resultantReduitEuclidean| |zerosOf| |monomRDE| |optpair|
+ |setrest!| |mergeFactors| |size?| |atanIfCan|
+ |createMultiplicationMatrix| |univariatePolynomials| |figureUnits|
+ |rightMult| |problemPoints| |s18adf| |gcdPrimitive| |central?|
+ |addiag| |viewSizeDefault| |definingEquations| |complexEigenvectors|
+ |makeSUP| |monomialIntegrate| |decomposeFunc| |identity| |finiteBasis|
+ |saturate| |OMencodingBinary| |qelt| |ramifiedAtInfinity?|
+ |primintfldpoly| |generalizedContinuumHypothesisAssumed|
+ |getMultiplicationMatrix| |e01sbf| |oddInfiniteProduct| |type|
+ |qsetelt| |imagI| |sech2cosh| |eigenMatrix| |low| |rem|
+ |numberOfComputedEntries| |viewDeltaXDefault| |solve|
+ |localIntegralBasis| |fortranCharacter| |lazyIrreducibleFactors|
+ |dihedral| |freeOf?| |UP2ifCan| |quo| |xRange| |outputGeneral|
+ |initial| |LyndonWordsList| |errorKind| |prepareSubResAlgo|
+ |create3Space| |cons| |OMopenFile| |tanIfCan| |ParCondList| |yRange|
+ |ratDsolve| |mainVariables| |constantOperator| |LiePoly|
+ |symmetricTensors| |universe| |dim| |polyPart| |numericIfCan|
+ |getOrder| |div| |zRange| |leftNorm| |factorset| |chvar| |makeFR|
+ |hcrf| |e01daf| |appendPoint| |map!| |factorSquareFreeByRecursion|
+ |printStats!| |exquo| |pastel| |asimpson| |c06gbf| |isTimes|
+ |rationalPoint?| |makeGraphImage| |qsetelt!| |front| |stopTableGcd!|
+ ~= |tensorProduct| |cCos| |iiacsch| |f01qef| |octon| |orbit| |null?|
+ |subresultantSequence| |smith| |#| |nativeModuleExtension| |revert|
+ |shuffle| |subTriSet?| |infinite?| |extractIfCan| |constantRight|
+ |droot| |zero| |linearDependence| ~ |unit| |coerce|
+ |multiEuclideanTree| |curveColorPalette| |f01qcf| |fortranTypeOf|
+ |f04axf| |source| |flexibleArray| |radicalRoots| |stFunc2|
+ |maximumExponent| |construct| |fibonacci| |iroot| |mainVariable?|
+ |pushup| |And| |bipolarCylindrical| |represents| |leadingExponent|
+ |factorial| |iiperm| |positiveRemainder| |basisOfNucleus| |overlap|
+ |pdf2df| |nextPrimitivePoly| |/\\| |Or| |wordsForStrongGenerators|
+ |acsch| |region| |constantCoefficientRicDE| |coefChoose| |string?|
+ |frobenius| |real?| |f02adf| |elaborate| |Not| |iisec| |\\/| |rename|
+ |mkAnswer| |rationalApproximation| |normalDenom| |rk4qc|
+ |stoseSquareFreePart| |constantIfCan| |part?| |getExplanations|
+ |exprex| |rightQuotient| |closed| |viewport2D| |target| |normalized?|
+ |acothIfCan| |lazyResidueClass| |exprHasLogarithmicWeights|
+ |hypergeometric0F1| |genericRightTraceForm| |qroot|
+ |principalAncestors| |rst| |minRowIndex| |squareFreePrim| |imagK|
+ |sinh2csch| |indiceSubResultant| |indices| |leftScalarTimes!|
+ |getZechTable| |weierstrass| |bfKeys| |clipParametric| |addPointLast|
+ |leftOne| |monomials| |permanent| |abelianGroup|
+ |inverseIntegralMatrixAtInfinity| |genericLeftDiscriminant| |edf2fi|
+ |hessian| |exp1| |clearTheSymbolTable| |quadraticNorm| |acosIfCan|
+ |SturmHabicht| |transpose| |shiftRight|
+ |rightCharacteristicPolynomial| |second| |open| |irDef|
+ |setLabelValue| |integers| |univariate?| |computePowers| |minGbasis|
+ |integralDerivationMatrix| |tab1| |lintgcd|
+ |permutationRepresentation| |third| |sub| |rightAlternative?|
+ |readLineIfCan!| |twist| |getBadValues| |linear?| |bitLength|
+ |surface| |pow| |move| |crushedSet| |inverse| |pseudoRemainder|
+ |indicialEquations| |initiallyReduce| |paraboloidal| |reorder|
+ |characteristic| |contractSolve| |nilFactor| |modularGcdPrimitive|
+ |removeRoughlyRedundantFactorsInContents| |binomThmExpt| |evaluate|
+ |computeCycleLength| |cyclic| |rowEchLocal| |reset| |module|
+ |indicialEquationAtInfinity| |isExpt| |bright| |operations| |cSech|
+ |coshIfCan| |insertionSort!| |zeroVector| |empty?| |elem?| F
+ |morphism| |isAnd| |commutativeEquality| |remove!| |bounds| |conical|
+ |approxNthRoot| |prime?| |makeMulti| |cyclicEntries|
+ |standardBasisOfCyclicSubmodule| |graphStates| |pushNewContour|
+ |write| |simpson| |truncate| |inc| |cross| |eval|
+ |genericRightMinimalPolynomial| |graeffe| |initials| |gethi|
+ |mightHaveRoots| |setelt| |setRow!| |setPosition| |save| LODO2FUN
+ |capacity| |errorInfo| |iibinom| |routines| |lieAdmissible?|
+ |useEisensteinCriterion?| |rightExtendedGcd| |setMinPoints3D| |c06gqf|
+ |bigEndian| |attributeData| |alternative?| |zag| |iidsum| |overset?|
+ |sn| |getStream| |modifyPointData| |pseudoQuotient| |copy|
+ |viewThetaDefault| |infinityNorm| |slex| |c05pbf| |listexp| |error|
+ |lazy?| |acotIfCan| |expandLog| |just| |OMconnInDevice| |repeating?|
+ |extendedSubResultantGcd| EQ |unmakeSUP| |factorPolynomial|
+ |argscript| |write!| |monic?| |antiCommutative?| |complexRoots|
+ |fortranInteger| |norm| |euclideanSize| |rightRank| |diag| |extract!|
+ |leftRecip| |outputFloating| |factorsOfDegree| |safeFloor| |mathieu12|
+ |d02raf| |s17dgf| |s20adf| |genus| |hasSolution?| |kmax| |middle|
+ |parent| |cylindrical| |invmod| |legendre| |OMputSymbol|
+ |retractable?| |primeFactor| |pmComplexintegrate| |normInvertible?|
+ |removeSquaresIfCan| |match?| |interactiveEnv| |f02awf| |satisfy?|
+ |sin?| |gradient| |autoCoerce| |invertIfCan| |f04asf| |polyred|
+ |solveInField| |OMputEndAttr| |solveLinear| |heapSort|
+ |numberOfImproperPartitions| |singRicDE| |pile| |assign| |binding|
+ |countable?| |generalizedContinuumHypothesisAssumed?| |leaf?|
+ |mapCoef| |genericLeftMinimalPolynomial| |rightRemainder| |prologue|
+ |Nul| |numberOfOperations| |maxrow| |putProperties| |parseString|
+ |singular?| |unitNormalize| |powmod| |rightNorm| |explicitlyFinite?|
+ |fglmIfCan| |copy!| |f02bjf| |toScale| |someBasis| |genericLeftNorm|
+ |hdmpToDmp| |e04gcf| |column| |rur| |integer?| |unitNormal|
+ |unaryFunction| |changeName| |complexElementary| |entry|
+ |rightExactQuotient| |cAsinh| |ceiling| |edf2ef| |identityMatrix|
+ |totalLex| |traverse| |subtractIfCan| |semicolonSeparate|
+ |createZechTable| |innerEigenvectors| |d01akf| |exportedOperators|
+ |jordanAlgebra?| |cycles| |triangular?| |parametersOf| |df2fi| |eof?|
+ |tracePowMod| |showScalarValues| |uniform| |binomial| |null|
+ |symmetricDifference| |squareFreePart| |dflist| |times!|
+ |unprotectedRemoveRedundantFactors| |setAdaptive| |bezoutResultant|
+ |hasHi| |stiffnessAndStabilityOfODEIF| |twoFactor| |shade| |not|
+ |generators| |f2df| |d02kef| |gcdprim| |lastSubResultantEuclidean|
+ |bag| |negative?| |sdf2lst| |musserTrials| |associates?| |and|
+ |oddlambert| |variable?| |zero?| |recur| |toseInvertible?|
+ |categories| |unknownEndian| |expenseOfEvaluation| |cycleElt|
+ |palgRDE| |sincos| |or| |delete| |coerceListOfPairs|
+ |jordanAdmissible?| |extension| |gensym| |mainContent| |pole?|
+ |expenseOfEvaluationIF| |mapMatrixIfCan| |binarySearchTree|
+ |toseInvertibleSet| |toseLastSubResultant| |fracPart| |palglimint0|
+ |typeList| |radicalEigenvectors| |removeDuplicates| |leadingSupport|
+ |orbits| |setleft!| |e02agf| |s17acf| |integralMatrixAtInfinity|
+ |headAst| |rationalFunction| |bit?| |qualifier| |setStatus|
+ |mainExpression| |partitions| |composites| |f01rcf| |diagonalMatrix|
+ |makingStats?| |removeCoshSq| |argument| |substitute| |acscIfCan|
+ |round| |branchPoint?| |prolateSpheroidal| |mainPrimitivePart|
+ |e02dff| |lexGroebner| |ODESolve| |inconsistent?| |colorDef| |mat|
+ |ridHack1| |extend| |spherical| |double?| |randomLC| |newTypeLists|
+ |accuracyIF| |isQuotient| |rational| |idealiser| |algintegrate|
+ |copyInto!| |curryRight| |fortranLiteralLine| |purelyTranscendental?|
+ |HermiteIntegrate| |solveLinearPolynomialEquationByFractions| |c06ebf|
+ |rightLcm| |partialFraction| UTS2UP |f01brf| |patternMatchTimes|
+ |clipPointsDefault| |meatAxe| |polynomialZeros| |d01bbf| |lazyPquo|
+ |var2Steps| |selectIntegrationRoutines| |s19acf| |basisOfRightNucloid|
+ |bandedJacobian| |f01rdf| |f04mcf| |rotate!| |depth| |iiasech|
+ |showTheRoutinesTable| |karatsubaDivide| |credPol| |selectsecond|
+ |weighted| |completeEchelonBasis| |putColorInfo| |groebSolve| |cn|
+ |associatorDependence| |expintegrate| |intersect| |power!| |rotatez|
+ |regularRepresentation| |mkPrim| |OMgetAtp| |isConnected?| |height|
+ |OMlistSymbols| |inputBinaryFile| |changeWeightLevel| |ScanArabic|
+ |clearTable!| |makeop| |leftFactor| |setButtonValue| |e02gaf| |dec|
+ |fractionPart| |bitTruth| |opeval| |univariatePolynomialsGcds|
+ |linearlyDependent?| |combineFeatureCompatibility| |option?|
+ |rightDiscriminant| |numericalIntegration| |perfectNthRoot| |cPower|
+ |nextLatticePermutation| |setFormula!| |selectFiniteRoutines|
+ |lastSubResultantElseSplit| |merge| |stirling1| |connectTo| |log10|
+ |prefixRagits| |univcase| |rischDEsys| |headReduce| |iisech|
+ |sizeMultiplication| |choosemon| |readInt8!| |limitedIntegrate|
+ |bitand| |iiacos| |cubic| |lazyGintegrate| |midpoints|
+ |minimumExponent| |s17ahf| |splitDenominator| |d01anf|
+ |halfExtendedResultant1| |bubbleSort!| |distdfact|
+ |resultantEuclideannaif| |quasiRegular| |pointLists| |denomLODE|
+ |subQuasiComponent?| |parabolicCylindrical| |autoReduced?| |iicsch|
+ |genericRightNorm| |sinIfCan| |bombieriNorm| |readByte!| |functorData|
+ |rationalPower| |newLine| |fixedPointExquo| |finite?|
+ |fortranCarriageReturn| |pquo| |dAndcExp| |possiblyNewVariety?|
+ |squareFreePolynomial| |rewriteIdealWithRemainder| |const|
+ |coordinates| |debug| |rk4f| |failed| |An| |nextItem| |d02cjf|
+ |factorFraction| |semiResultantEuclideannaif| |taylorRep| |vectorise|
+ |substring?| D |asinhIfCan| |basisOfRightNucleus| |setClosed|
+ |leadingCoefficientRicDE| |palgextint| |belong?| |contours|
+ |initTable!| |decrease| |duplicates| |adaptive3D?| |controlPanel|
+ |sizeLess?| |leadingIndex| |pair?| |primitivePart| |suffix?|
+ |monicRightDivide| |select!| |nextSubsetGray| |green| |leftUnit|
+ |monicLeftDivide| |prevPrime| |sorted?| |swap!| |quatern| |component|
+ |ranges| |nil| |roman| |tail| |log| |associatedEquations|
+ |splitSquarefree| |univariate| |aQuadratic| |prefix?| |laurentIfCan|
+ |removeDuplicates!| |setnext!| |generalizedInverse| |discreteLog|
+ |init| |modularGcd| |property| |rspace|
+ |stoseIntegralLastSubResultant| |trapezoidal| |resultantnaif|
+ |macroExpand| |iiatanh| |expintfldpoly| |OMreceive| |arbitrary|
+ |homogeneous?| |minPoints| |useNagFunctions| |varList|
+ |pointSizeDefault| |lflimitedint| |besselY| |ocf2ocdf| |approximate|
+ |normal01| |partialNumerators| |e01sef| |showTheFTable| |limit|
+ |iprint| |row| |nand| |complex| |rquo| |printInfo!| |qqq|
+ |setFieldInfo| |palglimint| |subset?| |stopTableInvSet!| |normalize|
+ |zeroSquareMatrix| |screenResolution| |qPot| |setDifference|
+ |meshFun2Var| |basisOfRightAnnihilator| |buildSyntax|
+ |intPatternMatch| |print| |sechIfCan| |enqueue!| |determinant|
+ |properties| |iitanh| |outputFixed| |conditionsForIdempotents|
+ |infix?| |OMclose| |resolve| |lazyIntegrate| |coHeight| |translate|
+ |packageCall| |yCoord| |rightUnits| |mask| |axes| |declare|
+ |identitySquareMatrix| |singularAtInfinity?| |normalizeIfCan|
+ |stripCommentsAndBlanks| GF2FG |measure2Result| |supRittWu?|
+ |linGenPos| |pushdterm| |PDESolve| |adaptive?| |weights| |realZeros|
+ |reduced?| |frst| |split| |deleteProperty!| |members| |parabolic|
+ |iisqrt2| |rewriteSetByReducingWithParticularGenerators| |critT|
+ |alphabetic?| |rowEchelonLocal| |numberOfCycles| |completeEval| |high|
+ |e02zaf| GE |listLoops| |monicRightFactorIfCan| |randnum|
+ |setEpilogue!| |pack!| |e02bbf| |uniform01|
+ |semiDiscriminantEuclidean| |critMTonD1| |knownInfBasis| |slash| GT
+ |mapUnivariate| |cos2sec| |find| |d01aqf| |closedCurve?| |denominator|
+ |mainMonomials| |say| |constantToUnaryFunction|
+ |showIntensityFunctions| LE |interval| |chineseRemainder| |delta|
+ |f02aaf| |doubleComplex?| |compBound| |d02bhf| |OMlistCDs| LT
+ |equality| |exptMod| |reseed| |LazardQuotient2| |cycleTail| |iisin|
+ |comparison| |drawCurves| |hex| |entries| |plus| |reduceByQuasiMonic|
+ |bandedHessian| |subHeight| |ode2| |contains?| |moebiusMu|
+ |setsubMatrix!| |roughEqualIdeals?| |modularFactor| |s19aaf|
+ |youngGroup| |realRoots| |shift| |distance| |drawStyle| |nthFactor|
+ |primitiveElement| |conjugates| |iicosh| |eulerPhi| |member?| |remove|
+ |factorAndSplit| |internalZeroSetSplit| |df2mf| |tValues|
+ |prinpolINFO| |polar| |curveColor| |exprToXXP| |linearPolynomials|
+ |ScanRoman| |deriv| |rightRankPolynomial| |permutations| |environment|
+ |times| |expandPower| |insertMatch| |asecIfCan| |elRow1!| |last|
+ |largest| |insertTop!| |integral?| |copies| |iitan| |generator|
+ |adjoint| |dequeue| |internalIntegrate0| |mantissa| |aCubic| |more?|
+ |usingTable?| |assoc| |factorSquareFreePolynomial| |replaceKthElement|
+ |extendedint| |s21baf| |nthCoef| |elaboration| |d01amf| |gbasis|
+ |f02bbf| |medialSet| |beauzamyBound| |mainMonomial| |trapezoidalo|
+ |imagk| |quoted?| |listBranches| BY |hMonic| |rationalIfCan| |f04faf|
+ |condition| |froot| |nullity| |jacobi| |changeVar| |monom| |collect|
+ |cAcosh| |enterInCache| |linearDependenceOverZ| |range| |s17ajf|
+ |mainSquareFreePart| |realEigenvectors| |OMconnectTCP| |maxdeg|
+ |polygamma| |minus!| |abs| |dual| |getOperands| |cyclicParents|
+ |divide| |structuralConstants| |cap| |lyndonIfCan| |algDsolve|
+ |charthRoot| |insertBottom!| |erf| |space| |e01bef| |csc2sin|
+ |roughBase?| |output| |common| |maxRowIndex| |diagonal| |scaleRoots|
+ |leftExtendedGcd| |hue| |nextNormalPrimitivePoly| |iteratedInitials|
+ |plus!| |isImplies| |shanksDiscLogAlgorithm| |mathieu23| |eigenvalues|
+ |tan2cot| |heap| |constant| |getIdentifier| |getSyntaxFormsFromFile|
+ |padecf| |resetNew| |constructor| |ode| |s18def| |HenselLift|
+ |factor1| |brillhartIrreducible?| |dilog| |c06eaf| |padicFraction| NOT
+ |cCoth| |definingInequation| |incr| |showRegion| |headRemainder|
+ |subscriptedVariables| |f02xef| |htrigs| |sin| |function|
+ |OMcloseConn| |selectAndPolynomials| OR |OMputVariable| |fixedPoints|
+ |dualSignature| |hi| |d02bbf| |branchIfCan| |stoseInvertibleSet|
+ |drawComplexVectorField| |cos| |doublyTransitive?| |iifact|
+ |unrankImproperPartitions1| AND |rightTrim| |terms| |trace2PowMod|
+ |outputAsScript| |f2st| |setEmpty!| |antisymmetricTensors| |tan|
+ |iExquo| |key?| |numerator| |internalInfRittWu?| |leftTrim|
+ |exprHasWeightCosWXorSinWX| |explicitlyEmpty?|
+ |createMultiplicationTable| |quasiMonic?| |UnVectorise| |cot|
+ |setleaves!| |reducedContinuedFraction| |gcdcofact| |OMgetEndBVar|
+ |normal?| |coth2tanh| |lfextendedint| |trailingCoefficient|
+ |setStatus!| |sec| |solid| |clikeUniv| |seriesToOutputForm| |torsion?|
+ |chebyshevT| |clearTheIFTable| |iflist2Result| |OMgetEndApp|
+ |primextendedint| |csc| |symbol| |exprHasAlgebraicWeight|
+ |eigenvectors| |setLegalFortranSourceExtensions| |identification|
+ |difference| |polygon?| |firstUncouplingMatrix| |cotIfCan| |flexible?|
+ |asin| |expression| |delete!| |complement| |rk4| |floor| |f04jgf|
+ |normalizedAssociate| |closedCurve| |separate| |pdct| |acos|
+ |normalizeAtInfinity| |integer| |branchPointAtInfinity?| |destruct|
+ |redPol| |coleman| |rightFactorCandidate| |poisson| |taylorQuoByVar|
+ |minset| |irCtor| |showTheIFTable| |atan| |pdf2ef| |augment| |coord|
+ |taylorIfCan| |redPo| |integerBound| |stirling2| |screenResolution3D|
+ |selectNonFiniteRoutines| |outlineRender| |acot| |getMeasure|
+ |aLinear| |f02ajf| |components| |UpTriBddDenomInv| |lookupFunction|
+ |critM| |firstDenom| |nsqfree| |asec| |processTemplate| |empty| *
+ |OMbindTCP| |infLex?| |iiGamma| |lhs| |tanhIfCan| |hasPredicate?|
+ |trigs| |incrementKthElement| |acsc| |balancedFactorisation|
+ |singleFactorBound| |lcm| |nor| |expIfCan| |specialTrigs| |rhs|
+ |OMconnOutDevice| |lex| |removeSinSq| |groebgen| |sinh|
+ |getProperties| |mesh| |e01saf| |factorSFBRlcUnit| |f04arf| |generate|
+ |acschIfCan| |squareTop| |discriminant| |intcompBasis|
+ |multiEuclidean| |cosh| |primlimitedint| |append|
+ |semiResultantReduitEuclidean| |hash| |maxrank| = |currentEnv|
+ |minordet| |simpleBounds?| |preprocess| |lineColorDefault| |pattern|
+ |isOp| |tanh| |polarCoordinates| |minimize| |OMreadStr| |gcd| |count|
+ |pointPlot| |radPoly| |incrementBy| |commaSeparate| |ramified?|
+ |OMsend| |geometric| |clipBoolean| |coth| |ldf2vmf|
+ |listConjugateBases| |false| |lp| < |symbolTableOf| |expand|
+ |univariateSolve| |resetAttributeButtons| |category| |skewSFunction|
+ |supDimElseRittWu?| |ptree| |concat!| |genericLeftTraceForm| |flatten|
+ |semiSubResultantGcdEuclidean2| |addPoint2| > |tube| |s15adf|
+ |filterWhile| |domain| |extractProperty| |nextSublist| |crest|
+ |loadNativeModule| |zeroDimPrime?| |traceMatrix| |makeUnit|
+ |exponential| |e02ahf| <= |even?| |filterUntil| |oblateSpheroidal|
+ |package| |gcdcofactprim| |iCompose| |message| |ratPoly| |s01eaf|
+ |typeLists| |OMserve| >= |sequences| |lexTriangular| |select|
+ |dihedralGroup| |OMputAttr| |polyRDE| |Hausdorff| |byteBuffer|
+ |alternating| |groebner| |d01gbf| |rootOf| |omError| |double|
+ |euclideanNormalForm| |cAcos| |monicModulo| |Ci| |parts| |imaginary|
+ |OMunhandledSymbol| |getPickedPoints| |normalDeriv| |f02aef|
+ |primaryDecomp| |swapColumns!| |palgextint0| |secIfCan| |cot2trig|
+ |vedf2vef| |OMread| |totalDegree| |binaryFunction| + |OMgetEndBind|
+ |OMsetEncoding| |realElementary| |triangSolve| |tanNa| |parents|
+ |seriesSolve| |nthExponent| |xn| |binary| |trivialIdeal?| -
+ |linearAssociatedLog| |f01qdf| |innerint| |sec2cos|
+ |linearAssociatedExp| |call| |primlimintfrac| |showAll?| |recip|
+ |dmp2rfi| / |wordInGenerators| |leftCharacteristicPolynomial|
+ |children| |fprindINFO| |rule| |tubePointsDefault| |insertRoot!|
+ |elementary| |exponential1| |complexNormalize| |divergence|
+ |makeRecord| |symmetricPower| |untab| |readLine!|
+ |transcendenceDegree| |exponents| |reopen!| |useSingleFactorBound?|
+ |outerProduct| |hostPlatform| |createRandomElement| |rightTrace|
+ |wreath| |prime| |randomR| |fill!| |curryLeft| |finiteBound| |e01bgf|
+ |declare!| |supersub| |subResultantGcdEuclidean| |createGenericMatrix|
+ |maxIndex| |youngDiagram| |changeNameToObjf| |cycleRagits| |ideal|
+ |ignore?| |dimensions| |partialDenominators| |squareFreeFactors|
+ |LyndonBasis| |repeating| |inR?| |subPolSet?| |setTopPredicate|
+ |compose| |unexpand| |d01ajf| |OMputError| |updatD| |qinterval|
+ |blankSeparate| |isAbsolutelyIrreducible?| |rules| |s18aef|
+ |kroneckerDelta| |extractTop!| |removeRedundantFactorsInContents|
+ |whileLoop| |epilogue| |sqfree| |symmetricRemainder| |multiset|
+ |expextendedint| |numberOfComposites| |shallowCopy| |inRadical?|
+ |symbol?| |step| |firstNumer| |noLinearFactor?| |setPoly|
+ |LagrangeInterpolation| |stopTable!| |RittWuCompare| |cosh2sech|
+ |dimensionOfIrreducibleRepresentation| |tanh2coth| |csubst|
+ |inverseColeman| |OMputEndApp| |semiResultantEuclidean1| |noKaratsuba|
+ |conjunction| |listOfLists| |cAcot| |fractionFreeGauss!| |makeSketch|
+ |segment| |generalizedEigenvectors| |digits| |fortranDoubleComplex|
+ |hitherPlane| |alternatingGroup| |stosePrepareSubResAlgo|
+ |integralLastSubResultant| |transcendentalDecompose| |upperBound|
+ |henselFact| |numberOfFractionalTerms| |basisOfCentroid| |number?|
+ |moduloP| |prepareDecompose| |graphs| |monomRDEsys| |bat|
+ |leadingIdeal| |d03eef| |e02dcf| |collectUnder| |squareMatrix|
+ |mainCoefficients| |oneDimensionalArray| |primintegrate| |palgLODE0|
+ |differentialVariables| |polCase| |OMencodingSGML| |upDateBranches|
+ |monicCompleteDecompose| |setOfMinN| |rightPower| |currentSubProgram|
+ |plenaryPower| |f02axf| |lprop| |po| |quasiComponent| |block| |key|
+ |neglist| |mapExponents| |triangulate| |expandTrigProducts| |coerceP|
+ |bezoutDiscriminant| |viewZoomDefault| |leviCivitaSymbol|
+ |createNormalPrimitivePoly| |elRow2!| |tanAn| |rdHack1| |value|
+ |countRealRootsMultiple| |completeHensel| |mappingAst| |filename|
+ |getDatabase| |cothIfCan| |critB| |getOperator| |powerSum| |back|
+ |totolex| |aQuartic| |e02bcf| |optional| |OMputString|
+ |listYoungTableaus| |ratpart| |disjunction| |generalTwoFactor|
+ |irForm| |lfinfieldint| |doubleRank| |replace| |formula| |parse|
+ |generalPosition| |OMputApp| |sylvesterMatrix| |presuper| |upperCase?|
+ |divisorCascade| |curve| |pr2dmp| |nextPartition| |elaborateFile|
+ |reducedForm| |removeRoughlyRedundantFactorsInPol| |stop|
+ |multiplyCoefficients| |arguments| |currentScope| |pointColorDefault|
+ RF2UTS |mr| |leftMinimalPolynomial| |OMgetInteger|
+ |complexNumericIfCan| |superHeight| |principal?| |increment| |f01bsf|
+ |leftFactorIfCan| |leftMult| |c06ecf| |singularitiesOf| |iterationVar|
+ |withPredicates| |chebyshevU| |nullary| |OMmakeConn| |loopPoints|
+ |sts2stst| |e02akf| |FormatRoman| |increase| |safeCeiling| |nrows|
+ |result| |deref| |bumptab1| |yCoordinates|
+ |rewriteIdealWithQuasiMonicGenerators| |elseBranch|
+ |setAttributeButtonStep| |setref| |viewDefaults| |mesh?| |Vectorise|
+ |plotPolar| |ncols| |validExponential| |integralCoordinates|
+ |internalIntegrate| |scan| |updateStatus!| |summation| |cTan|
+ |numberOfIrreduciblePoly| |enterPointData| |generateIrredPoly|
+ |leastMonomial| |c06ekf| |prod| |e02ddf| |e04ucf| |tower|
+ |generalLambert| |linearMatrix| |lazyPseudoRemainder| |bernoulliB|
+ |basis| |setMaxPoints3D| |sizePascalTriangle| |imports| |groebner?|
+ |airyAi| |nthFlag| |bivariateSLPEBR| |notelem| |invertibleElseSplit?|
+ |makeVariable| |complexForm| |totalfract| |eyeDistance| |relerror|
+ |OMgetEndAttr| |prindINFO| |taylor| |comment| |setchildren!|
+ |jokerMode| |root?| |distFact| |compiledFunction| |mapDown!| |atom?|
+ |getMatch| |rootDirectory| |iiacoth| |laurent| |limitPlus|
+ |drawToScale| |prem| |countRealRoots| |stronglyReduced?| |fractRagits|
+ |printingInfo?| |optAttributes| |OMReadError?| |exprToGenUPS|
+ |puiseux| |ef2edf| |cAtanh| |explogs2trigs|
+ |unrankImproperPartitions0| |pureLex| |matrix| |index| |drawComplex|
+ |purelyAlgebraic?| |lowerCase?| |s17akf| |f02aff| |shellSort|
+ |critpOrder| |stoseInvertibleSetsqfreg| |entry?| |polygon|
+ |functionIsFracPolynomial?| |inf| |setPredicates|
+ |createIrreduciblePoly| |multiplyExponents| |inv| |content| |lambda|
+ |d01gaf| |s21bbf| |numFunEvals3D| |stopMusserTrials|
+ |startTableInvSet!| |whitePoint| |iiatan| |getCode| |karatsubaOnce|
+ |ground?| |setVariableOrder| |setvalue!| |interpretString| |dimension|
+ |outputSpacing| UP2UTS |lowerPolynomial| |e02aef| |pair|
+ |linkToFortran| |ground| |fortranLogical| |fixedPoint|
+ |makeYoungTableau| |scalarMatrix| |interReduce| |clipSurface|
+ |isOpen?| |recoverAfterFail| |solveLinearlyOverQ|
+ |clearFortranOutputStack| |OMgetObject| |directory| |cartesian|
+ |c06fqf| |lastSubResultant| |leftZero| |halfExtendedSubResultantGcd2|
+ |getGoodPrime| |leadingMonomial| |xCoord| |showFortranOutputStack|
+ |changeMeasure| |derivationCoordinates| |OMputEndBind| |sum|
+ |readInt32!| |reverse| |hspace| |quotientByP| |karatsuba| |compdegd|
+ |leadingCoefficient| |basisOfLeftNucloid| |getMultiplicationTable|
+ |quoByVar| |mathieu11| |factorSquareFree| |leftLcm| |constantOpIfCan|
+ |algebraicSort| |getConstant| |minimumDegree| |imagi|
+ |primitiveMonomials| |irreducible?| |lieAlgebra?| |midpoint|
+ |shrinkable| |rectangularMatrix| |retract| |push!| |divideIfCan!|
+ |innerSolve1| |shallowExpand| |mvar| |radix| |reductum| |setColumn!|
+ |alphanumeric?| |linears| |coth2trigh| |leftRegularRepresentation|
+ |fortranComplex| |queue| |exactQuotient| |inverseIntegralMatrix|
+ |commonDenominator| |reflect| |rootKerSimp| |coefficient|
+ |absolutelyIrreducible?| |OMputEndError| |unvectorise|
+ |viewPhiDefault| |rank| |e04jaf| |writeUInt8!| |makeFloatFunction|
+ |collectUpper| |explicitEntries?| |s17dlf| |primitive?| |superscript|
+ |trueEqual| |OMgetFloat| |lifting1| |over| |idealiserMatrix| |degree|
+ |zeroOf| |purelyAlgebraicLeadingMonomial?| |OMgetError| |rarrow|
+ |sumOfDivisors| |permutationGroup| |nil| |infinite|
+ |arbitraryExponent| |approximate| |complex| |shallowMutable|
+ |canonical| |noetherian| |central| |partiallyOrderedSet|
+ |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors|
+ |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown|
+ |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate|
+ |shallowlyMutable| |commutative|) 
\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index d588ea66..37a2c8a9 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5429 +1,5439 @@
 
-(3248531 . 3485856152)       
-((-1905 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3175 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3052 ((|#2| $ (-575) |#2|) NIL) ((|#2| $ (-1252 (-575)) |#2|) 44)) (-3086 (($ $) 80)) (-2302 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-2630 (((-575) (-1 (-112) |#2|) $) 27) (((-575) |#2| $) NIL) (((-575) |#2| $ (-575)) 96)) (-3999 (((-655 |#2|) $) 13)) (-4167 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-2844 (($ (-1 |#2| |#2|) $) 37)) (-2544 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-2129 (($ |#2| $ (-575)) NIL) (($ $ $ (-575)) 67)) (-1540 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-2718 (((-112) (-1 (-112) |#2|) $) 23)) (-2065 ((|#2| $ (-575) |#2|) NIL) ((|#2| $ (-575)) NIL) (($ $ (-1252 (-575))) 66)) (-3237 (($ $ (-575)) 76) (($ $ (-1252 (-575))) 75)) (-3922 (((-782) (-1 (-112) |#2|) $) 34) (((-782) |#2| $) NIL)) (-2617 (($ $ $ (-575)) 69)) (-3076 (($ $) 68)) (-2893 (($ (-655 |#2|)) 73)) (-1513 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-655 $)) 85)) (-2882 (((-873) $) 92)) (-4121 (((-112) (-1 (-112) |#2|) $) 22)) (-3913 (((-112) $ $) 95)) (-3940 (((-112) $ $) 99))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -3913 ((-112) |#1| |#1|)) (-15 -2882 ((-873) |#1|)) (-15 -3940 ((-112) |#1| |#1|)) (-15 -3175 (|#1| |#1|)) (-15 -3175 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3086 (|#1| |#1|)) (-15 -2617 (|#1| |#1| |#1| (-575))) (-15 -1905 ((-112) |#1|)) (-15 -4167 (|#1| |#1| |#1|)) (-15 -2630 ((-575) |#2| |#1| (-575))) (-15 -2630 ((-575) |#2| |#1|)) (-15 -2630 ((-575) (-1 (-112) |#2|) |#1|)) (-15 -1905 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -4167 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3052 (|#2| |#1| (-1252 (-575)) |#2|)) (-15 -2129 (|#1| |#1| |#1| (-575))) (-15 -2129 (|#1| |#2| |#1| (-575))) (-15 -3237 (|#1| |#1| (-1252 (-575)))) (-15 -3237 (|#1| |#1| (-575))) (-15 -2544 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1513 (|#1| (-655 |#1|))) (-15 -1513 (|#1| |#1| |#1|)) (-15 -1513 (|#1| |#2| |#1|)) (-15 -1513 (|#1| |#1| |#2|)) (-15 -2065 (|#1| |#1| (-1252 (-575)))) (-15 -2893 (|#1| (-655 |#2|))) (-15 -1540 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2065 (|#2| |#1| (-575))) (-15 -2065 (|#2| |#1| (-575) |#2|)) (-15 -3052 (|#2| |#1| (-575) |#2|)) (-15 -3922 ((-782) |#2| |#1|)) (-15 -3999 ((-655 |#2|) |#1|)) (-15 -3922 ((-782) (-1 (-112) |#2|) |#1|)) (-15 -2718 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -4121 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2844 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2544 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3076 (|#1| |#1|))) (-19 |#2|) (-1235)) (T -18)) 
+(3251813 . 3485863941)       
+((-3429 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-1426 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3028 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-1254 (-576)) |#2|) 44)) (-2338 (($ $) 80)) (-2326 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-2627 (((-576) (-1 (-112) |#2|) $) 27) (((-576) |#2| $) NIL) (((-576) |#2| $ (-576)) 96)) (-3975 (((-656 |#2|) $) 13)) (-3343 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-2822 (($ (-1 |#2| |#2|) $) 37)) (-2548 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-2163 (($ |#2| $ (-576)) NIL) (($ $ $ (-576)) 67)) (-3557 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-1910 (((-112) (-1 (-112) |#2|) $) 23)) (-2099 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-576)) NIL) (($ $ (-1254 (-576))) 66)) (-3213 (($ $ (-576)) 76) (($ $ (-1254 (-576))) 75)) (-3902 (((-783) (-1 (-112) |#2|) $) 34) (((-783) |#2| $) NIL)) (-3272 (($ $ $ (-576)) 69)) (-3052 (($ $) 68)) (-2869 (($ (-656 |#2|)) 73)) (-1534 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-656 $)) 85)) (-2858 (((-874) $) 92)) (-2714 (((-112) (-1 (-112) |#2|) $) 22)) (-3889 (((-112) $ $) 95)) (-3916 (((-112) $ $) 99))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -3889 ((-112) |#1| |#1|)) (-15 -2858 ((-874) |#1|)) (-15 -3916 ((-112) |#1| |#1|)) (-15 -1426 (|#1| |#1|)) (-15 -1426 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2338 (|#1| |#1|)) (-15 -3272 (|#1| |#1| |#1| (-576))) (-15 -3429 ((-112) |#1|)) (-15 -3343 (|#1| |#1| |#1|)) (-15 -2627 ((-576) |#2| |#1| (-576))) (-15 -2627 ((-576) |#2| |#1|)) (-15 -2627 ((-576) (-1 (-112) |#2|) |#1|)) (-15 -3429 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3343 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3028 (|#2| |#1| (-1254 (-576)) |#2|)) (-15 -2163 (|#1| |#1| |#1| (-576))) (-15 -2163 (|#1| |#2| |#1| (-576))) (-15 -3213 (|#1| |#1| (-1254 (-576)))) (-15 -3213 (|#1| |#1| (-576))) (-15 -2548 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1534 (|#1| (-656 |#1|))) (-15 -1534 (|#1| |#1| |#1|)) (-15 -1534 (|#1| |#2| |#1|)) (-15 -1534 (|#1| |#1| |#2|)) (-15 -2099 (|#1| |#1| (-1254 (-576)))) (-15 -2869 (|#1| (-656 |#2|))) (-15 -3557 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2099 (|#2| |#1| (-576))) (-15 -2099 (|#2| |#1| (-576) |#2|)) (-15 -3028 (|#2| |#1| (-576) |#2|)) (-15 -3902 ((-783) |#2| |#1|)) (-15 -3975 ((-656 |#2|) |#1|)) (-15 -3902 ((-783) (-1 (-112) |#2|) |#1|)) (-15 -1910 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2714 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2822 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2548 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3052 (|#1| |#1|))) (-19 |#2|) (-1237)) (T -18)) 
 NIL 
-(-10 -8 (-15 -3913 ((-112) |#1| |#1|)) (-15 -2882 ((-873) |#1|)) (-15 -3940 ((-112) |#1| |#1|)) (-15 -3175 (|#1| |#1|)) (-15 -3175 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3086 (|#1| |#1|)) (-15 -2617 (|#1| |#1| |#1| (-575))) (-15 -1905 ((-112) |#1|)) (-15 -4167 (|#1| |#1| |#1|)) (-15 -2630 ((-575) |#2| |#1| (-575))) (-15 -2630 ((-575) |#2| |#1|)) (-15 -2630 ((-575) (-1 (-112) |#2|) |#1|)) (-15 -1905 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -4167 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3052 (|#2| |#1| (-1252 (-575)) |#2|)) (-15 -2129 (|#1| |#1| |#1| (-575))) (-15 -2129 (|#1| |#2| |#1| (-575))) (-15 -3237 (|#1| |#1| (-1252 (-575)))) (-15 -3237 (|#1| |#1| (-575))) (-15 -2544 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1513 (|#1| (-655 |#1|))) (-15 -1513 (|#1| |#1| |#1|)) (-15 -1513 (|#1| |#2| |#1|)) (-15 -1513 (|#1| |#1| |#2|)) (-15 -2065 (|#1| |#1| (-1252 (-575)))) (-15 -2893 (|#1| (-655 |#2|))) (-15 -1540 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2302 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2065 (|#2| |#1| (-575))) (-15 -2065 (|#2| |#1| (-575) |#2|)) (-15 -3052 (|#2| |#1| (-575) |#2|)) (-15 -3922 ((-782) |#2| |#1|)) (-15 -3999 ((-655 |#2|) |#1|)) (-15 -3922 ((-782) (-1 (-112) |#2|) |#1|)) (-15 -2718 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -4121 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2844 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2544 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3076 (|#1| |#1|))) 
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-(((-19 |#1|) (-141) (-1235)) (T -19)) 
+(-10 -8 (-15 -3889 ((-112) |#1| |#1|)) (-15 -2858 ((-874) |#1|)) (-15 -3916 ((-112) |#1| |#1|)) (-15 -1426 (|#1| |#1|)) (-15 -1426 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2338 (|#1| |#1|)) (-15 -3272 (|#1| |#1| |#1| (-576))) (-15 -3429 ((-112) |#1|)) (-15 -3343 (|#1| |#1| |#1|)) (-15 -2627 ((-576) |#2| |#1| (-576))) (-15 -2627 ((-576) |#2| |#1|)) (-15 -2627 ((-576) (-1 (-112) |#2|) |#1|)) (-15 -3429 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3343 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3028 (|#2| |#1| (-1254 (-576)) |#2|)) (-15 -2163 (|#1| |#1| |#1| (-576))) (-15 -2163 (|#1| |#2| |#1| (-576))) (-15 -3213 (|#1| |#1| (-1254 (-576)))) (-15 -3213 (|#1| |#1| (-576))) (-15 -2548 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1534 (|#1| (-656 |#1|))) (-15 -1534 (|#1| |#1| |#1|)) (-15 -1534 (|#1| |#2| |#1|)) (-15 -1534 (|#1| |#1| |#2|)) (-15 -2099 (|#1| |#1| (-1254 (-576)))) (-15 -2869 (|#1| (-656 |#2|))) (-15 -3557 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2326 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2099 (|#2| |#1| (-576))) (-15 -2099 (|#2| |#1| (-576) |#2|)) (-15 -3028 (|#2| |#1| (-576) |#2|)) (-15 -3902 ((-783) |#2| |#1|)) (-15 -3975 ((-656 |#2|) |#1|)) (-15 -3902 ((-783) (-1 (-112) |#2|) |#1|)) (-15 -1910 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2714 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2822 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2548 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3052 (|#1| |#1|))) 
+((-2835 (((-112) $ $) 19 (|has| |#1| (-1119)))) (-3430 (((-1292) $ (-576) (-576)) 41 (|has| $ (-6 -4463)))) (-3429 (((-112) (-1 (-112) |#1| |#1|) $) 101) (((-112) $) 95 (|has| |#1| (-862)))) (-1426 (($ (-1 (-112) |#1| |#1|) $) 92 (|has| $ (-6 -4463))) (($ $) 91 (-12 (|has| |#1| (-862)) (|has| $ (-6 -4463))))) (-2059 (($ (-1 (-112) |#1| |#1|) $) 102) (($ $) 96 (|has| |#1| (-862)))) (-2746 (((-112) $ (-783)) 8)) (-3028 ((|#1| $ (-576) |#1|) 53 (|has| $ (-6 -4463))) ((|#1| $ (-1254 (-576)) |#1|) 60 (|has| $ (-6 -4463)))) (-3959 (($ (-1 (-112) |#1|) $) 77 (|has| $ (-6 -4462)))) (-2574 (($) 7 T CONST)) (-2338 (($ $) 93 (|has| $ (-6 -4463)))) (-4374 (($ $) 103)) (-3229 (($ $) 80 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-3607 (($ |#1| $) 79 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462)))) (($ (-1 (-112) |#1|) $) 76 (|has| $ (-6 -4462)))) (-2326 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 78 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 75 (|has| $ (-6 -4462))) ((|#1| (-1 |#1| |#1| |#1|) $) 74 (|has| $ (-6 -4462)))) (-2832 ((|#1| $ (-576) |#1|) 54 (|has| $ (-6 -4463)))) (-2767 ((|#1| $ (-576)) 52)) (-2627 (((-576) (-1 (-112) |#1|) $) 100) (((-576) |#1| $) 99 (|has| |#1| (-1119))) (((-576) |#1| $ (-576)) 98 (|has| |#1| (-1119)))) (-3975 (((-656 |#1|) $) 31 (|has| $ (-6 -4462)))) (-2327 (($ (-783) |#1|) 70)) (-3639 (((-112) $ (-783)) 9)) (-2440 (((-576) $) 44 (|has| (-576) (-862)))) (-1950 (($ $ $) 90 (|has| |#1| (-862)))) (-3343 (($ (-1 (-112) |#1| |#1|) $ $) 104) (($ $ $) 97 (|has| |#1| (-862)))) (-3531 (((-656 |#1|) $) 30 (|has| $ (-6 -4462)))) (-3606 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-4048 (((-576) $) 45 (|has| (-576) (-862)))) (-1492 (($ $ $) 89 (|has| |#1| (-862)))) (-2822 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4463)))) (-2548 (($ (-1 |#1| |#1|) $) 36) (($ (-1 |#1| |#1| |#1|) $ $) 65)) (-1684 (((-112) $ (-783)) 10)) (-2143 (((-1178) $) 22 (|has| |#1| (-1119)))) (-2163 (($ |#1| $ (-576)) 62) (($ $ $ (-576)) 61)) (-2928 (((-656 (-576)) $) 47)) (-1449 (((-112) (-576) $) 48)) (-3887 (((-1139) $) 21 (|has| |#1| (-1119)))) (-1989 ((|#1| $) 43 (|has| (-576) (-862)))) (-3557 (((-3 |#1| "failed") (-1 (-112) |#1|) $) 73)) (-4040 (($ $ |#1|) 42 (|has| $ (-6 -4463)))) (-1910 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4462)))) (-3022 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))))) (-1974 (((-112) $ $) 14)) (-4317 (((-112) |#1| $) 46 (-12 (|has| $ (-6 -4462)) (|has| |#1| (-1119))))) (-3584 (((-656 |#1|) $) 49)) (-3001 (((-112) $) 11)) (-3849 (($) 12)) (-2099 ((|#1| $ (-576) |#1|) 51) ((|#1| $ (-576)) 50) (($ $ (-1254 (-576))) 71)) (-3213 (($ $ (-576)) 64) (($ $ (-1254 (-576))) 63)) (-3902 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4462))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-3272 (($ $ $ (-576)) 94 (|has| $ (-6 -4463)))) (-3052 (($ $) 13)) (-2610 (((-548) $) 81 (|has| |#1| (-626 (-548))))) (-2869 (($ (-656 |#1|)) 72)) (-1534 (($ $ |#1|) 69) (($ |#1| $) 68) (($ $ $) 67) (($ (-656 $)) 66)) (-2858 (((-874) $) 18 (|has| |#1| (-625 (-874))))) (-2690 (((-112) $ $) 23 (|has| |#1| (-1119)))) (-2714 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4462)))) (-3956 (((-112) $ $) 87 (|has| |#1| (-862)))) (-3930 (((-112) $ $) 86 (|has| |#1| (-862)))) (-3889 (((-112) $ $) 20 (|has| |#1| (-1119)))) (-3944 (((-112) $ $) 88 (|has| |#1| (-862)))) (-3916 (((-112) $ $) 85 (|has| |#1| (-862)))) (-2845 (((-783) $) 6 (|has| $ (-6 -4462))))) 
+(((-19 |#1|) (-141) (-1237)) (T -19)) 
 NIL 
-(-13 (-383 |t#1|) (-10 -7 (-6 -4461))) 
-(((-34) . T) ((-102) -3763 (|has| |#1| (-1117)) (|has| |#1| (-861))) ((-624 (-873)) -3763 (|has| |#1| (-1117)) (|has| |#1| (-861)) (|has| |#1| (-624 (-873)))) ((-152 |#1|) . T) ((-625 (-547)) |has| |#1| (-625 (-547))) ((-295 #0=(-575) |#1|) . T) ((-295 (-1252 (-575)) $) . T) ((-297 #0# |#1|) . T) ((-318 |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117))) ((-383 |#1|) . T) ((-500 |#1|) . T) ((-615 #0# |#1|) . T) ((-525 |#1| |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117))) ((-662 |#1|) . T) ((-861) |has| |#1| (-861)) ((-1117) -3763 (|has| |#1| (-1117)) (|has| |#1| (-861))) ((-1235) . T)) 
-((-1708 (((-3 $ "failed") $ $) 12)) (-4027 (($ $) NIL) (($ $ $) 9)) (* (($ (-936) $) NIL) (($ (-782) $) 16) (($ (-575) $) 26))) 
-(((-20 |#1|) (-10 -8 (-15 -4027 (|#1| |#1| |#1|)) (-15 -4027 (|#1| |#1|)) (-15 * (|#1| (-575) |#1|)) (-15 -1708 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-782) |#1|)) (-15 * (|#1| (-936) |#1|))) (-21)) (T -20)) 
+(-13 (-384 |t#1|) (-10 -7 (-6 -4463))) 
+(((-34) . T) ((-102) -3739 (|has| |#1| (-1119)) (|has| |#1| (-862))) ((-625 (-874)) -3739 (|has| |#1| (-1119)) (|has| |#1| (-862)) (|has| |#1| (-625 (-874)))) ((-152 |#1|) . T) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-296 #0=(-576) |#1|) . T) ((-296 (-1254 (-576)) $) . T) ((-298 #0# |#1|) . T) ((-319 |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))) ((-384 |#1|) . T) ((-501 |#1|) . T) ((-616 #0# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))) ((-663 |#1|) . T) ((-862) |has| |#1| (-862)) ((-1119) -3739 (|has| |#1| (-1119)) (|has| |#1| (-862))) ((-1237) . T)) 
+((-3161 (((-3 $ "failed") $ $) 12)) (-4002 (($ $) NIL) (($ $ $) 9)) (* (($ (-938) $) NIL) (($ (-783) $) 16) (($ (-576) $) 26))) 
+(((-20 |#1|) (-10 -8 (-15 -4002 (|#1| |#1| |#1|)) (-15 -4002 (|#1| |#1|)) (-15 * (|#1| (-576) |#1|)) (-15 -3161 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-783) |#1|)) (-15 * (|#1| (-938) |#1|))) (-21)) (T -20)) 
 NIL 
-(-10 -8 (-15 -4027 (|#1| |#1| |#1|)) (-15 -4027 (|#1| |#1|)) (-15 * (|#1| (-575) |#1|)) (-15 -1708 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-782) |#1|)) (-15 * (|#1| (-936) |#1|))) 
-((-2859 (((-112) $ $) 7)) (-2045 (((-112) $) 17)) (-1708 (((-3 $ "failed") $ $) 20)) (-3261 (($) 18 T CONST)) (-4264 (((-1176) $) 10)) (-3912 (((-1137) $) 11)) (-2882 (((-873) $) 12)) (-3685 (((-112) $ $) 9)) (-1989 (($) 19 T CONST)) (-3913 (((-112) $ $) 6)) (-4027 (($ $) 23) (($ $ $) 22)) (-4015 (($ $ $) 15)) (* (($ (-936) $) 14) (($ (-782) $) 16) (($ (-575) $) 24))) 
+(-10 -8 (-15 -4002 (|#1| |#1| |#1|)) (-15 -4002 (|#1| |#1|)) (-15 * (|#1| (-576) |#1|)) (-15 -3161 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-783) |#1|)) (-15 * (|#1| (-938) |#1|))) 
+((-2835 (((-112) $ $) 7)) (-3203 (((-112) $) 17)) (-3161 (((-3 $ "failed") $ $) 20)) (-2574 (($) 18 T CONST)) (-2143 (((-1178) $) 10)) (-3887 (((-1139) $) 11)) (-2858 (((-874) $) 12)) (-2690 (((-112) $ $) 9)) (-2022 (($) 19 T CONST)) (-3889 (((-112) $ $) 6)) (-4002 (($ $) 23) (($ $ $) 22)) (-3990 (($ $ $) 15)) (* (($ (-938) $) 14) (($ (-783) $) 16) (($ (-576) $) 24))) 
 (((-21) (-141)) (T -21)) 
-((-4027 (*1 *1 *1) (-4 *1 (-21))) (-4027 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-132) (-657 (-575)) (-10 -8 (-15 -4027 ($ $)) (-15 -4027 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-624 (-873)) . T) ((-657 (-575)) . T) ((-1117) . T)) 
-((-2045 (((-112) $) 10)) (-3261 (($) 15)) (* (($ (-936) $) 14) (($ (-782) $) 19))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-782) |#1|)) (-15 -2045 ((-112) |#1|)) (-15 -3261 (|#1|)) (-15 * (|#1| (-936) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-782) |#1|)) (-15 -2045 ((-112) |#1|)) (-15 -3261 (|#1|)) (-15 * (|#1| (-936) |#1|))) 
-((-2859 (((-112) $ $) 7)) (-2045 (((-112) $) 17)) (-3261 (($) 18 T CONST)) (-4264 (((-1176) $) 10)) (-3912 (((-1137) $) 11)) (-2882 (((-873) $) 12)) (-3685 (((-112) $ $) 9)) (-1989 (($) 19 T CONST)) (-3913 (((-112) $ $) 6)) (-4015 (($ $ $) 15)) (* (($ (-936) $) 14) (($ (-782) $) 16))) 
+((-4002 (*1 *1 *1) (-4 *1 (-21))) (-4002 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-132) (-658 (-576)) (-10 -8 (-15 -4002 ($ $)) (-15 -4002 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-625 (-874)) . T) ((-658 (-576)) . T) ((-1119) . T)) 
+((-3203 (((-112) $) 10)) (-2574 (($) 15)) (* (($ (-938) $) 14) (($ (-783) $) 19))) 
+(((-22 |#1|) (-10 -8 (-15 * (|#1| (-783) |#1|)) (-15 -3203 ((-112) |#1|)) (-15 -2574 (|#1|)) (-15 * (|#1| (-938) |#1|))) (-23)) (T -22)) 
+NIL 
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243 (|has| |#1| (-146)))) (-4421 (((-782)) 32 T CONST)) (-2394 (($ (-655 $)) 161) (($ $) 160)) (-1825 (((-112) (-115)) 172)) (-3685 (((-112) $ $) 9)) (-3930 (((-112) $ $) 45)) (-1627 (($ (-1194) (-655 $)) 211) (($ (-1194) $ $ $ $) 210) (($ (-1194) $ $ $) 209) (($ (-1194) $ $) 208) (($ (-1194) $) 207)) (-1989 (($) 19 T CONST)) (-2005 (($) 34 T CONST)) (-3428 (($ $ (-655 (-1194)) (-655 (-782))) 254 (|has| |#1| (-1066))) (($ $ (-1194) (-782)) 253 (|has| |#1| (-1066))) (($ $ (-655 (-1194))) 252 (|has| |#1| (-1066))) (($ $ (-1194)) 248 (|has| |#1| (-1066)))) (-3913 (((-112) $ $) 6)) (-4038 (($ $ $) 73) (($ (-1142 |#1| (-623 $)) (-1142 |#1| (-623 $))) 234 (|has| |#1| (-567)))) (-4027 (($ $) 23) (($ $ $) 22)) (-4015 (($ $ $) 15)) (** (($ $ (-936)) 28) (($ $ (-782)) 36) (($ $ (-575)) 77) (($ $ (-418 (-575))) 98)) (* (($ (-936) $) 14) (($ (-782) $) 16) (($ (-575) $) 24) (($ $ $) 27) (($ $ (-418 (-575))) 76) (($ (-418 (-575)) $) 75) (($ $ |#1|) 242 (|has| |#1| (-174))) (($ |#1| $) 134 (|has| |#1| (-1066))))) 
-(((-29 |#1|) (-141) (-567)) (T -29)) 
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-(-13 (-27) (-441 |t#1|) (-10 -8 (-15 -3151 ($ $)) (-15 -4285 ((-655 $) $)) (-15 -3151 ($ $ (-1194))) (-15 -4285 ((-655 $) $ (-1194))) (-15 -3088 ($ $)) (-15 -2767 ((-655 $) $)) (-15 -3088 ($ $ (-1194))) (-15 -2767 ((-655 $) $ (-1194))))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-418 (-575))) . T) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) . T) ((-27) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) |has| |#1| (-174)) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-627 #0#) . T) ((-627 #1=(-418 (-967 |#1|))) |has| |#1| (-567)) ((-627 (-575)) . T) ((-627 #2=(-623 $)) . T) ((-627 #3=(-967 |#1|)) |has| |#1| (-1066)) ((-627 #4=(-1194)) . T) ((-627 |#1|) . T) ((-627 $) . T) ((-624 (-873)) . T) ((-174) . T) ((-625 (-547)) |has| |#1| (-625 (-547))) ((-625 (-904 (-389))) |has| |#1| (-625 (-904 (-389)))) ((-625 (-904 (-575))) |has| |#1| (-625 (-904 (-575)))) ((-248) . T) ((-299) . T) ((-316) . T) ((-318 $) . T) ((-311) . T) ((-373) . T) ((-387 |#1|) |has| |#1| (-1066)) ((-411 |#1|) . T) ((-422 |#1|) . T) ((-441 |#1|) . T) ((-463) . T) ((-484) |has| |#1| (-484)) ((-525 (-623 $) $) . T) ((-525 $ $) . T) ((-567) . T) ((-657 #0#) . T) ((-657 (-575)) . T) ((-657 |#1|) -3763 (|has| |#1| (-1066)) (|has| |#1| (-174))) ((-657 $) . T) ((-659 #0#) . T) ((-659 #5=(-575)) -12 (|has| |#1| (-650 (-575))) (|has| |#1| (-1066))) ((-659 |#1|) -3763 (|has| |#1| (-1066)) (|has| |#1| (-174))) ((-659 $) . T) ((-651 #0#) . T) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) . T) ((-650 #5#) -12 (|has| |#1| (-650 (-575))) (|has| |#1| (-1066))) ((-650 |#1|) |has| |#1| (-1066)) ((-728 #0#) . T) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) . T) ((-737) . T) ((-908 $ #6=(-1194)) |has| |#1| (-1066)) ((-913 #6#) |has| |#1| (-1066)) ((-915 #6#) |has| |#1| (-1066)) ((-898 (-389)) |has| |#1| (-898 (-389))) ((-898 (-575)) |has| |#1| (-898 (-575))) ((-896 |#1|) . T) ((-935) . T) ((-1019) . T) ((-1055 (-418 (-575))) -3763 (|has| |#1| (-1055 (-418 (-575)))) (-12 (|has| |#1| (-567)) (|has| |#1| (-1055 (-575))))) ((-1055 #1#) |has| |#1| (-567)) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 #2#) . T) ((-1055 #3#) |has| |#1| (-1066)) ((-1055 #4#) . T) ((-1055 |#1|) . T) ((-1068 #0#) . T) ((-1068 |#1|) |has| |#1| (-174)) ((-1068 $) . T) ((-1073 #0#) . T) ((-1073 |#1|) |has| |#1| (-174)) ((-1073 $) . T) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1235) . T) ((-1239) . T)) 
-((-2824 (((-1111 (-227)) $) NIL)) (-2812 (((-1111 (-227)) $) NIL)) (-2946 (($ $ (-227)) 164)) (-2999 (($ (-967 (-575)) (-1194) (-1194) (-1111 (-418 (-575))) (-1111 (-418 (-575)))) 104)) (-1612 (((-655 (-655 (-958 (-227)))) $) 180)) (-2882 (((-873) $) 194))) 
-(((-30) (-13 (-970) (-10 -8 (-15 -2999 ($ (-967 (-575)) (-1194) (-1194) (-1111 (-418 (-575))) (-1111 (-418 (-575))))) (-15 -2946 ($ $ (-227)))))) (T -30)) 
-((-2999 (*1 *1 *2 *3 *3 *4 *4) (-12 (-5 *2 (-967 (-575))) (-5 *3 (-1194)) (-5 *4 (-1111 (-418 (-575)))) (-5 *1 (-30)))) (-2946 (*1 *1 *1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-30))))) 
-(-13 (-970) (-10 -8 (-15 -2999 ($ (-967 (-575)) (-1194) (-1194) (-1111 (-418 (-575))) (-1111 (-418 (-575))))) (-15 -2946 ($ $ (-227))))) 
-((-2859 (((-112) $ $) NIL)) (-4264 (((-1176) $) NIL)) (-3912 (((-1137) $) NIL)) (-2882 (((-873) $) 17) (($ (-1199)) NIL) (((-1199) $) NIL)) (-1788 (((-1152) $) 11)) (-3685 (((-112) $ $) NIL)) (-1548 (((-1152) $) 9)) (-3913 (((-112) $ $) NIL))) 
-(((-31) (-13 (-1100) (-10 -8 (-15 -1548 ((-1152) $)) (-15 -1788 ((-1152) $))))) (T -31)) 
-((-1548 (*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-31)))) (-1788 (*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-31))))) 
-(-13 (-1100) (-10 -8 (-15 -1548 ((-1152) $)) (-15 -1788 ((-1152) $)))) 
-((-3151 ((|#2| (-1190 |#2|) (-1194)) 41)) (-2567 (((-115) (-115)) 55)) (-4088 (((-1190 |#2|) (-623 |#2|)) 149 (|has| |#1| (-1055 (-575))))) (-1778 ((|#2| |#1| (-575)) 137 (|has| |#1| (-1055 (-575))))) (-2771 ((|#2| (-1190 |#2|) |#2|) 29)) (-3264 (((-873) (-655 |#2|)) 86)) (-4436 ((|#2| |#2|) 144 (|has| |#1| (-1055 (-575))))) (-1825 (((-112) (-115)) 17)) (** ((|#2| |#2| (-418 (-575))) 103 (|has| |#1| (-1055 (-575)))))) 
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-((-1778 (*1 *2 *3 *4) (-12 (-5 *4 (-575)) (-4 *2 (-441 *3)) (-5 *1 (-32 *3 *2)) (-4 *3 (-1055 *4)) (-4 *3 (-567)))) (-4436 (*1 *2 *2) (-12 (-4 *3 (-1055 (-575))) (-4 *3 (-567)) (-5 *1 (-32 *3 *2)) (-4 *2 (-441 *3)))) (-4088 (*1 *2 *3) (-12 (-5 *3 (-623 *5)) (-4 *5 (-441 *4)) (-4 *4 (-1055 (-575))) (-4 *4 (-567)) (-5 *2 (-1190 *5)) (-5 *1 (-32 *4 *5)))) (** (*1 *2 *2 *3) (-12 (-5 *3 (-418 (-575))) (-4 *4 (-1055 (-575))) (-4 *4 (-567)) (-5 *1 (-32 *4 *2)) (-4 *2 (-441 *4)))) (-3264 (*1 *2 *3) (-12 (-5 *3 (-655 *5)) (-4 *5 (-441 *4)) (-4 *4 (-567)) (-5 *2 (-873)) (-5 *1 (-32 *4 *5)))) (-2771 (*1 *2 *3 *2) (-12 (-5 *3 (-1190 *2)) (-4 *2 (-441 *4)) (-4 *4 (-567)) (-5 *1 (-32 *4 *2)))) (-1825 (*1 *2 *3) (-12 (-5 *3 (-115)) (-4 *4 (-567)) (-5 *2 (-112)) (-5 *1 (-32 *4 *5)) (-4 *5 (-441 *4)))) (-2567 (*1 *2 *2) (-12 (-5 *2 (-115)) (-4 *3 (-567)) (-5 *1 (-32 *3 *4)) (-4 *4 (-441 *3)))) (-3151 (*1 *2 *3 *4) (-12 (-5 *3 (-1190 *2)) (-5 *4 (-1194)) (-4 *2 (-441 *5)) (-5 *1 (-32 *5 *2)) (-4 *5 (-567))))) 
-(-10 -7 (-15 -3151 (|#2| (-1190 |#2|) (-1194))) (-15 -2567 ((-115) (-115))) (-15 -1825 ((-112) (-115))) (-15 -2771 (|#2| (-1190 |#2|) |#2|)) (-15 -3264 ((-873) (-655 |#2|))) (IF (|has| |#1| (-1055 (-575))) (PROGN (-15 ** (|#2| |#2| (-418 (-575)))) (-15 -4088 ((-1190 |#2|) (-623 |#2|))) (-15 -4436 (|#2| |#2|)) (-15 -1778 (|#2| |#1| (-575)))) |%noBranch|)) 
-((-3133 (((-112) $ (-782)) 20)) (-3261 (($) 10)) (-3541 (((-112) $ (-782)) 19)) (-3218 (((-112) $ (-782)) 17)) (-2391 (((-112) $ $) 8)) (-2017 (((-112) $) 15))) 
-(((-33 |#1|) (-10 -8 (-15 -3261 (|#1|)) (-15 -3133 ((-112) |#1| (-782))) (-15 -3541 ((-112) |#1| (-782))) (-15 -3218 ((-112) |#1| (-782))) (-15 -2017 ((-112) |#1|)) (-15 -2391 ((-112) |#1| |#1|))) (-34)) (T -33)) 
-NIL 
-(-10 -8 (-15 -3261 (|#1|)) (-15 -3133 ((-112) |#1| (-782))) (-15 -3541 ((-112) |#1| (-782))) (-15 -3218 ((-112) |#1| (-782))) (-15 -2017 ((-112) |#1|)) (-15 -2391 ((-112) |#1| |#1|))) 
-((-3133 (((-112) $ (-782)) 8)) (-3261 (($) 7 T CONST)) (-3541 (((-112) $ (-782)) 9)) (-3218 (((-112) $ (-782)) 10)) (-2391 (((-112) $ $) 14)) (-2017 (((-112) $) 11)) (-1393 (($) 12)) (-3076 (($ $) 13)) (-2869 (((-782) $) 6 (|has| $ (-6 -4460))))) 
+((-3968 (*1 *1 *2) (-12 (-5 *2 (-969 *1)) (-4 *1 (-27)))) (-3968 (*1 *1 *2) (-12 (-5 *2 (-1192 *1)) (-4 *1 (-27)))) (-3968 (*1 *1 *2 *3) (-12 (-5 *2 (-1192 *1)) (-5 *3 (-1196)) (-4 *1 (-27)))) (-1665 (*1 *2 *3) (-12 (-5 *3 (-969 *1)) (-4 *1 (-27)) (-5 *2 (-656 *1)))) (-1665 (*1 *2 *3) (-12 (-5 *3 (-1192 *1)) (-4 *1 (-27)) (-5 *2 (-656 *1)))) (-1665 (*1 *2 *3 *4) (-12 (-5 *3 (-1192 *1)) (-5 *4 (-1196)) (-4 *1 (-27)) (-5 *2 (-656 *1)))) (-4437 (*1 *1 *2) (-12 (-5 *2 (-969 *1)) (-4 *1 (-27)))) (-4437 (*1 *1 *2) (-12 (-5 *2 (-1192 *1)) (-4 *1 (-27)))) (-4437 (*1 *1 *2 *3) (-12 (-5 *2 (-1192 *1)) (-5 *3 (-1196)) (-4 *1 (-27)))) (-2741 (*1 *2 *3) (-12 (-5 *3 (-969 *1)) (-4 *1 (-27)) (-5 *2 (-656 *1)))) (-2741 (*1 *2 *3) (-12 (-5 *3 (-1192 *1)) (-4 *1 (-27)) (-5 *2 (-656 *1)))) (-2741 (*1 *2 *3 *4) (-12 (-5 *3 (-1192 *1)) (-5 *4 (-1196)) (-4 *1 (-27)) (-5 *2 (-656 *1))))) 
+(-13 (-374) (-1021) (-10 -8 (-15 -3968 ($ (-969 $))) (-15 -3968 ($ (-1192 $))) (-15 -3968 ($ (-1192 $) (-1196))) (-15 -1665 ((-656 $) (-969 $))) (-15 -1665 ((-656 $) (-1192 $))) (-15 -1665 ((-656 $) (-1192 $) (-1196))) (-15 -4437 ($ (-969 $))) (-15 -4437 ($ (-1192 $))) (-15 -4437 ($ (-1192 $) (-1196))) (-15 -2741 ((-656 $) (-969 $))) (-15 -2741 ((-656 $) (-1192 $))) (-15 -2741 ((-656 $) (-1192 $) (-1196))))) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 $ $) . T) ((-132) . T) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 $) . T) ((-625 (-874)) . T) ((-174) . T) ((-248) . T) ((-300) . T) ((-317) . T) ((-374) . T) ((-464) . T) ((-568) . T) ((-658 #0#) . T) ((-658 (-576)) . T) ((-658 $) . T) ((-660 #0#) . T) ((-660 $) . T) ((-652 #0#) . T) ((-652 $) . T) ((-729 #0#) . T) ((-729 $) . T) ((-738) . T) ((-937) . T) ((-1021) . T) ((-1070 #0#) . T) ((-1070 $) . T) ((-1075 #0#) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1241) . T)) 
+((-2741 (((-656 $) (-969 $)) NIL) (((-656 $) (-1192 $)) NIL) (((-656 $) (-1192 $) (-1196)) 55) (((-656 $) $) 22) (((-656 $) $ (-1196)) 46)) (-4437 (($ (-969 $)) NIL) (($ (-1192 $)) NIL) (($ (-1192 $) (-1196)) 57) (($ $) 20) (($ $ (-1196)) 40)) (-1665 (((-656 $) (-969 $)) NIL) (((-656 $) (-1192 $)) NIL) (((-656 $) (-1192 $) (-1196)) 53) (((-656 $) $) 18) (((-656 $) $ (-1196)) 48)) (-3968 (($ (-969 $)) NIL) (($ (-1192 $)) NIL) (($ (-1192 $) (-1196)) NIL) (($ $) 15) (($ $ (-1196)) 42))) 
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+NIL 
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|#1| (-1068))))) 
+(((-29 |#1|) (-141) (-568)) (T -29)) 
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+NIL 
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 (((-38 |#1|) (-141) (-174)) (T -38)) 
 NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-132) . T) ((-627 (-575)) . T) ((-627 |#1|) . T) ((-624 (-873)) . T) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 |#1|) . T) ((-659 $) . T) ((-651 |#1|) . T) ((-728 |#1|) . T) ((-737) . T) ((-1068 |#1|) . T) ((-1073 |#1|) . T) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T)) 
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-NIL 
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+NIL 
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 (((-93) (-141)) (T -93)) 
 NIL 
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 NIL 
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 NIL 
 (((-98) (-141)) (T -98)) 
 NIL 
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-NIL 
-(-880 |#1|) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
-(-798) 
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-NIL 
-(-798) 
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-NIL 
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-(((-201) (-798)) (T -201)) 
-NIL 
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-(((-202) (-798)) (T -202)) 
-NIL 
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-NIL 
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-(((-231 |#1|) (-141) (-1117)) (T -231)) 
+(-13 (-1119) (-10 -8 (-15 -9 ($) -3712) (-15 -8 ($) -3712) (-15 -7 ($) -3712))) 
+((-2835 (((-112) $ $) NIL)) (-2996 (((-656 (-877)) $) NIL)) (-1811 (((-518) $) 8)) (-2143 (((-1178) $) NIL)) (-1584 (((-188) $) 10)) (-2729 (((-112) $ (-518)) NIL)) (-3887 (((-1139) $) NIL)) (-1340 (((-703 $) (-518)) 17)) (-3742 (((-656 (-112)) $) NIL)) (-2858 (((-874) $) NIL)) (-2690 (((-112) $ $) NIL)) (-2727 (((-55) $) 12)) (-3889 (((-112) $ $) NIL))) 
+(((-189) (-13 (-187) (-10 -8 (-15 -1340 ((-703 $) (-518)))))) (T -189)) 
+((-1340 (*1 *2 *3) (-12 (-5 *3 (-518)) (-5 *2 (-703 (-189))) (-5 *1 (-189))))) 
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+((-4152 (((-1287 (-701 (-969 |#1|))) (-1287 (-701 |#1|))) 26)) (-2858 (((-1287 (-701 (-419 (-969 |#1|)))) (-1287 (-701 |#1|))) 37))) 
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+((-2858 (*1 *2 *3) (-12 (-5 *3 (-1287 (-701 *4))) (-4 *4 (-174)) (-5 *2 (-1287 (-701 (-419 (-969 *4))))) (-5 *1 (-191 *4)))) (-4152 (*1 *2 *3) (-12 (-5 *3 (-1287 (-701 *4))) (-4 *4 (-174)) (-5 *2 (-1287 (-701 (-969 *4)))) (-5 *1 (-191 *4))))) 
+(-10 -7 (-15 -4152 ((-1287 (-701 (-969 |#1|))) (-1287 (-701 |#1|)))) (-15 -2858 ((-1287 (-701 (-419 (-969 |#1|)))) (-1287 (-701 |#1|))))) 
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+(-10 -7 (-15 -2137 ((-1198 (-419 (-576))) (-938))) (-15 -4169 ((-1198 (-419 (-576))) (-938))) (-15 -4021 ((-1198 (-419 (-576))) (-938))) (-15 -3965 ((-1198 (-419 (-576))) (-938))) (-15 -2989 ((-1198 (-419 (-576))) (-938))) (-15 -2787 ((-1198 (-419 (-576))) (-938))) (-15 -4121 ((-1198 (-419 (-576))) (-938))) (-15 -3686 ((-419 (-576)) (-1198 (-419 (-576))) (-1198 (-419 (-576))))) (-15 -2043 ((-1198 (-419 (-576))) (-1198 (-419 (-576))) (-1198 (-419 (-576))))) (-15 -3022 ((-419 (-576)) (-1198 (-419 (-576))))) (-15 -4037 ((-1198 (-419 (-576))) (-1198 (-419 (-576))) (-1198 (-419 (-576))))) (-15 -2543 ((-1198 (-419 (-576))) (-656 (-938)))) (-15 -3922 ((-1198 (-419 (-576))) (-656 (-576)) (-656 (-576))))) 
+((-1585 (((-430 (-1192 (-576))) (-576)) 38)) (-1368 (((-656 (-1192 (-576))) (-576)) 33)) (-2716 (((-1192 (-576)) (-576)) 28))) 
+(((-193) (-10 -7 (-15 -1368 ((-656 (-1192 (-576))) (-576))) (-15 -2716 ((-1192 (-576)) (-576))) (-15 -1585 ((-430 (-1192 (-576))) (-576))))) (T -193)) 
+((-1585 (*1 *2 *3) (-12 (-5 *2 (-430 (-1192 (-576)))) (-5 *1 (-193)) (-5 *3 (-576)))) (-2716 (*1 *2 *3) (-12 (-5 *2 (-1192 (-576))) (-5 *1 (-193)) (-5 *3 (-576)))) (-1368 (*1 *2 *3) (-12 (-5 *2 (-656 (-1192 (-576)))) (-5 *1 (-193)) (-5 *3 (-576))))) 
+(-10 -7 (-15 -1368 ((-656 (-1192 (-576))) (-576))) (-15 -2716 ((-1192 (-576)) (-576))) (-15 -1585 ((-430 (-1192 (-576))) (-576)))) 
+((-4215 (((-1176 (-227)) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 132)) (-3197 (((-656 (-1178)) (-1176 (-227))) NIL)) (-2111 (((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 109)) (-2752 (((-656 (-227)) (-326 (-227)) (-1196) (-1113 (-855 (-227)))) NIL)) (-2622 (((-656 (-1178)) (-656 (-227))) NIL)) (-1476 (((-227) (-1113 (-855 (-227)))) 31)) (-3026 (((-227) (-1113 (-855 (-227)))) 32)) (-1984 (((-390) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 126)) (-1392 (((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 67)) (-2120 (((-1178) (-227)) NIL)) (-3906 (((-1178) (-656 (-1178))) 27)) (-3151 (((-1054) (-1196) (-1196) (-1054)) 13))) 
+(((-194) (-10 -7 (-15 -2111 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -1392 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -1476 ((-227) (-1113 (-855 (-227))))) (-15 -3026 ((-227) (-1113 (-855 (-227))))) (-15 -1984 ((-390) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -2752 ((-656 (-227)) (-326 (-227)) (-1196) (-1113 (-855 (-227))))) (-15 -4215 ((-1176 (-227)) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -2120 ((-1178) (-227))) (-15 -2622 ((-656 (-1178)) (-656 (-227)))) (-15 -3197 ((-656 (-1178)) (-1176 (-227)))) (-15 -3906 ((-1178) (-656 (-1178)))) (-15 -3151 ((-1054) (-1196) (-1196) (-1054))))) (T -194)) 
+((-3151 (*1 *2 *3 *3 *2) (-12 (-5 *2 (-1054)) (-5 *3 (-1196)) (-5 *1 (-194)))) (-3906 (*1 *2 *3) (-12 (-5 *3 (-656 (-1178))) (-5 *2 (-1178)) (-5 *1 (-194)))) (-3197 (*1 *2 *3) (-12 (-5 *3 (-1176 (-227))) (-5 *2 (-656 (-1178))) (-5 *1 (-194)))) (-2622 (*1 *2 *3) (-12 (-5 *3 (-656 (-227))) (-5 *2 (-656 (-1178))) (-5 *1 (-194)))) (-2120 (*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1178)) (-5 *1 (-194)))) (-4215 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-1176 (-227))) (-5 *1 (-194)))) (-2752 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-326 (-227))) (-5 *4 (-1196)) (-5 *5 (-1113 (-855 (-227)))) (-5 *2 (-656 (-227))) (-5 *1 (-194)))) (-1984 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-390)) (-5 *1 (-194)))) (-3026 (*1 *2 *3) (-12 (-5 *3 (-1113 (-855 (-227)))) (-5 *2 (-227)) (-5 *1 (-194)))) (-1476 (*1 *2 *3) (-12 (-5 *3 (-1113 (-855 (-227)))) (-5 *2 (-227)) (-5 *1 (-194)))) (-1392 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-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 (-194)))) (-2111 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-194))))) 
+(-10 -7 (-15 -2111 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -1392 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -1476 ((-227) (-1113 (-855 (-227))))) (-15 -3026 ((-227) (-1113 (-855 (-227))))) (-15 -1984 ((-390) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -2752 ((-656 (-227)) (-326 (-227)) (-1196) (-1113 (-855 (-227))))) (-15 -4215 ((-1176 (-227)) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -2120 ((-1178) (-227))) (-15 -2622 ((-656 (-1178)) (-656 (-227)))) (-15 -3197 ((-656 (-1178)) (-1176 (-227)))) (-15 -3906 ((-1178) (-656 (-1178)))) (-15 -3151 ((-1054) (-1196) (-1196) (-1054)))) 
+((-2835 (((-112) $ $) NIL)) (-3336 (((-1054) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))) (-1054)) 61) (((-1054) (-2 (|:| |fn| (-326 (-227))) (|:| -3672 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227))) (-1054)) NIL)) (-2605 (((-2 (|:| -2605 (-390)) (|:| |explanations| (-1178)) (|:| |extra| (-1054))) (-1082) (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 33) (((-2 (|:| -2605 (-390)) (|:| |explanations| (-1178)) (|:| |extra| (-1054))) (-1082) (-2 (|:| |fn| (-326 (-227))) (|:| -3672 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) NIL)) (-2143 (((-1178) $) NIL)) (-3887 (((-1139) $) NIL)) (-2858 (((-874) $) NIL)) (-2690 (((-112) $ $) NIL)) (-3889 (((-112) $ $) NIL))) 
+(((-195) (-799)) (T -195)) 
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-NIL 
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-NIL 
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+NIL 
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 (((-248) (-141)) (T -248)) 
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-NIL 
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-NIL 
-(-13 (-243 |#1| |#3|) (-659 |#2|)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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 NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
-(-10 -8 (-15 -4027 (|#1| |#1| |#1|)) (-15 -4027 (|#1| |#1|))) 
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-NIL 
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-NIL 
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-((-1632 (*1 *1) (-5 *1 (-488)))) 
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-((-3878 (*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-489)))) (-3890 (*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-489))))) 
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+((-1947 ((|#4| |#4| (-656 |#4|)) 20 (|has| |#1| (-374)))) (-3966 (((-656 |#4|) (-656 |#4|) (-1178) (-1178)) 46) (((-656 |#4|) (-656 |#4|) (-1178)) 45) (((-656 |#4|) (-656 |#4|)) 34))) 
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+((-3862 (($ $ $) 14) (($ (-656 $)) 21)) (-1919 (((-1192 $) (-1192 $) (-1192 $)) 46)) (-3901 (($ $ $) NIL) (($ (-656 $)) 22))) 
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+NIL 
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+NIL 
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+NIL 
+(-1230 |#1| |#2| |#3| |#4|) 
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+((-1663 (*1 *1) (-5 *1 (-489)))) 
+(-13 (-374) (-148) (-1057 (-576)) (-1057 (-419 (-576))) (-1041) (-625 (-227)) (-625 (-390)) (-626 (-419 (-1192 (-576)))) (-626 (-548)) (-10 -8 (-15 -1663 ($)))) 
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+(((-490) (-13 (-1102) (-10 -8 (-15 -3854 ((-1154) $)) (-15 -3866 ((-1154) $))))) (T -490)) 
+((-3854 (*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-490)))) (-3866 (*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-490))))) 
+(-13 (-1102) (-10 -8 (-15 -3854 ((-1154) $)) (-15 -3866 ((-1154) $)))) 
+((-2835 (((-112) $ $) NIL (-3739 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)) (|has| |#2| (-1119))))) (-2316 (($) NIL) (($ (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL)) (-3430 (((-1292) $ |#1| |#1|) NIL (|has| $ (-6 -4463)))) (-2746 (((-112) $ (-783)) NIL)) (-3028 ((|#2| $ |#1| |#2|) 16)) (-3423 (($ (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462)))) (-3959 (($ (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462)))) (-1405 (((-3 |#2| "failed") |#1| $) 20)) (-2574 (($) NIL T CONST)) (-3229 (($ $) NIL (-12 (|has| $ (-6 -4462)) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119))))) (-3007 (($ (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) $) NIL (|has| $ (-6 -4462))) (($ (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462))) (((-3 |#2| "failed") |#1| $) 18)) (-3607 (($ (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) $) NIL (-12 (|has| $ (-6 -4462)) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (($ (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462)))) (-2326 (((-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $ (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) NIL (-12 (|has| $ (-6 -4462)) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (((-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $ (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) NIL (|has| $ (-6 -4462))) (((-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462)))) (-2832 ((|#2| $ |#1| |#2|) NIL (|has| $ (-6 -4463)))) (-2767 ((|#2| $ |#1|) NIL)) (-3975 (((-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462))) (((-656 |#2|) $) NIL (|has| $ (-6 -4462)))) (-3639 (((-112) $ (-783)) NIL)) (-2440 ((|#1| $) NIL (|has| |#1| (-862)))) (-3531 (((-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462))) (((-656 |#2|) $) NIL (|has| $ (-6 -4462)))) (-3606 (((-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) $) NIL (-12 (|has| $ (-6 -4462)) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119))))) (-4048 ((|#1| $) NIL (|has| |#1| (-862)))) (-2822 (($ (-1 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4463))) (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4463)))) (-2548 (($ (-1 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL) (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) NIL)) (-1684 (((-112) $ (-783)) NIL)) (-2143 (((-1178) $) NIL (-3739 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)) (|has| |#2| (-1119))))) 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(-304 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL (-12 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-319 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (($ $ (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) NIL (-12 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-319 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (($ $ (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL (-12 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-319 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (($ $ (-656 |#2|) (-656 |#2|)) NIL (-12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) (($ $ (-304 |#2|)) NIL (-12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) (($ $ (-656 (-304 |#2|))) NIL (-12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))))) (-1974 (((-112) $ $) NIL)) (-4317 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119))))) (-3584 (((-656 |#2|) $) NIL)) (-3001 (((-112) $) NIL)) (-3849 (($) 19)) (-2099 ((|#2| $ |#1|) NIL) ((|#2| $ |#1| |#2|) NIL)) (-1801 (($) NIL) (($ (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL)) (-3902 (((-783) (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462))) (((-783) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) $) NIL (-12 (|has| $ (-6 -4462)) (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)))) (((-783) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119)))) (((-783) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462)))) (-3052 (($ $) NIL)) (-2610 (((-548) $) NIL (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-626 (-548))))) (-2869 (($ (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL)) (-2858 (((-874) $) NIL (-3739 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-625 (-874))) (|has| |#2| (-625 (-874)))))) (-2690 (((-112) $ $) NIL (-3739 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)) (|has| |#2| (-1119))))) (-3195 (($ (-656 (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)))) NIL)) (-2714 (((-112) (-1 (-112) (-2 (|:| -4147 |#1|) (|:| -3153 |#2|))) $) NIL (|has| $ (-6 -4462))) (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462)))) (-3889 (((-112) $ $) 11 (-3739 (|has| (-2 (|:| -4147 |#1|) (|:| -3153 |#2|)) (-1119)) (|has| |#2| (-1119))))) (-2845 (((-783) $) 15 (|has| $ (-6 -4462))))) 
+(((-491 |#1| |#2| |#3|) (-13 (-1213 |#1| |#2|) (-10 -7 (-6 -4462))) (-1119) (-1119) (-1178)) (T -491)) 
+NIL 
+(-13 (-1213 |#1| |#2|) (-10 -7 (-6 -4462))) 
+((-1949 (((-576) (-576) (-576)) 19)) (-1388 (((-112) (-576) (-576) (-576) (-576)) 28)) (-3877 (((-1287 (-656 (-576))) (-783) (-783)) 41))) 
+(((-492) (-10 -7 (-15 -1949 ((-576) (-576) (-576))) (-15 -1388 ((-112) (-576) (-576) (-576) (-576))) (-15 -3877 ((-1287 (-656 (-576))) (-783) (-783))))) (T -492)) 
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 NIL 
 (-243 |#1| |#2|) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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 NIL 
 (-57 |#1| |#4| |#5|) 
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-NIL 
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-NIL 
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-NIL 
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 (((-175) . T)) 
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-(((-570) (-10 -8 (-15 -3933 ($)) (-15 -3915 ((-1290))) (-15 -1995 ((-655 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $)) (-15 -2662 ($ (-655 (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -3179 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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"))))))))) (-15 -4218 ($ (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -3179 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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")))))))) (-15 -2622 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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")))) "failed") (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -2697 ((-655 (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -3179 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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"))))))) $)) (-15 -3179 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))))) (T -570)) 
-((-3179 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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 (-570)))) (-2697 (*1 *2 *1) (-12 (-5 *2 (-655 (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -3179 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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 (-570)))) (-2622 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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 (-570)))) (-4218 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -3179 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1174 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1974 (-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 (-570)))) (-2662 (*1 *1 *2) (-12 (-5 *2 (-655 (-2 (|:| -4169 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| 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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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(|:| |coef2| $)) "failed") $ $ $) 122 (|has| |#1| (-373))) (((-2 (|:| |coef1| $) (|:| |coef2| $) (|:| -3657 $)) $ $) 121 (|has| |#1| (-373)))) (-2849 (((-3 $ "failed") $ $) 104 (|has| |#1| (-373)))) (-2880 (((-3 (-655 $) "failed") (-655 $) $) 115 (|has| |#1| (-373)))) (-1720 (((-782) $) 117 (|has| |#1| (-373)))) (-4416 (((-2 (|:| -3262 $) (|:| -4041 $)) $ $) 118 (|has| |#1| (-373)))) (-2801 ((|#1| (-1285 $)) 54) ((|#1|) 67)) (-2619 (((-782) $) 162 (|has| |#1| (-359))) (((-3 (-782) "failed") $ $) 150 (|has| |#1| (-359)))) (-2382 (($ $ (-782)) 147 (-3763 (-3224 (|has| |#1| (-237)) (|has| |#1| (-373))) (|has| |#1| (-359)))) (($ $) 145 (-3763 (-3224 (|has| |#1| (-237)) (|has| |#1| (-373))) (|has| |#1| (-359)))) (($ $ (-655 (-1194)) (-655 (-782))) 141 (-3224 (|has| |#1| (-915 (-1194))) (|has| |#1| (-373)))) (($ $ (-1194) (-782)) 140 (-3224 (|has| |#1| (-915 (-1194))) (|has| |#1| (-373)))) (($ $ (-655 (-1194))) 139 (-3224 (|has| |#1| (-915 (-1194))) (|has| |#1| (-373)))) (($ $ (-1194)) 137 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|#1| (-373))) (($ $ (-418 (-575))) 130 (|has| |#1| (-373))))) 
-(((-735 |#1| |#2|) (-141) (-174) (-1261 |t#1|)) (T -735)) 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-418 (-575))) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-38 |#1|) . T) ((-38 $) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-102) . T) ((-111 #0# #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -3763 (|has| |#1| (-359)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-627 #0#) -3763 (|has| |#1| (-1055 (-418 (-575)))) (|has| |#1| (-359)) (|has| |#1| (-373))) ((-627 (-575)) . T) ((-627 |#1|) . T) ((-627 $) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-624 (-873)) . T) ((-174) . T) ((-625 |#2|) . T) ((-234 $) -3763 (|has| |#1| (-359)) (-12 (|has| |#1| (-237)) (|has| |#1| (-373))) (-12 (|has| |#1| (-238)) (|has| |#1| (-373)))) ((-232 |#1|) |has| |#1| (-373)) ((-238) -3763 (|has| |#1| (-359)) (-12 (|has| |#1| (-238)) (|has| |#1| (-373)))) ((-237) -3763 (|has| |#1| (-359)) (-12 (|has| |#1| (-237)) (|has| |#1| (-373))) (-12 (|has| |#1| (-238)) (|has| |#1| (-373)))) ((-271 |#1|) |has| |#1| (-373)) ((-248) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-299) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-316) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-373) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-413) |has| |#1| (-359)) ((-378) -3763 (|has| |#1| (-378)) (|has| |#1| (-359))) ((-359) |has| |#1| (-359)) ((-380 |#1| |#2|) . T) ((-420 |#1| |#2|) . T) ((-387 |#1|) . T) ((-422 |#1|) . T) ((-463) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-567) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-657 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-659 #1=(-575)) |has| |#1| (-650 (-575))) ((-659 |#1|) . T) ((-659 $) . T) ((-651 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-651 |#1|) . T) ((-651 $) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-650 #1#) |has| |#1| (-650 (-575))) ((-650 |#1|) . T) ((-728 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-728 |#1|) . T) ((-728 $) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-737) . T) ((-908 $ #2=(-1194)) -3763 (-12 (|has| |#1| (-373)) (|has| |#1| (-915 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#1| (-913 (-1194))))) ((-913 (-1194)) -12 (|has| |#1| (-373)) (|has| |#1| (-913 (-1194)))) ((-915 #2#) -3763 (-12 (|has| |#1| (-373)) (|has| |#1| (-915 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#1| (-913 (-1194))))) ((-935) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 |#1|) . T) ((-1068 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1068 |#1|) . T) ((-1068 $) . T) ((-1073 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1073 |#1|) . T) ((-1073 $) . T) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) |has| |#1| (-359)) ((-1235) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1239) -3763 (|has| |#1| (-359)) (|has| |#1| (-373)))) 
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-NIL 
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-(((-737) (-141)) (T -737)) 
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-NIL 
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+((-2326 ((|#5| (-1 |#5| |#1| |#5|) |#4| |#5|) 39)) (-2548 (((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|) 37) ((|#8| (-1 |#5| |#1|) |#4|) 31))) 
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+NIL 
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|#1| (-374))) (($ $ (-419 (-576))) 130 (|has| |#1| (-374))))) 
+(((-736 |#1| |#2|) (-141) (-174) (-1263 |t#1|)) (T -736)) 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-102) . T) ((-111 #0# #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -3739 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -3739 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) . T) ((-626 |#2|) . T) ((-234 $) -3739 (|has| |#1| (-360)) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-232 |#1|) |has| |#1| (-374)) ((-238) -3739 (|has| |#1| (-360)) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-237) -3739 (|has| |#1| (-360)) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-272 |#1|) |has| |#1| (-374)) ((-248) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-300) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-317) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-374) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -3739 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| |#2|) . T) ((-421 |#1| |#2|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-568) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2=(-1196)) -3739 (-12 (|has| |#1| (-374)) (|has| |#1| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#1| (-915 (-1196))))) ((-915 (-1196)) -12 (|has| |#1| (-374)) (|has| |#1| (-915 (-1196)))) ((-917 #2#) -3739 (-12 (|has| |#1| (-374)) (|has| |#1| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#1| (-915 (-1196))))) ((-937) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1237) -3739 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1241) -3739 (|has| |#1| (-360)) (|has| |#1| (-374)))) 
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+NIL 
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 NIL 
 (-243 |#1| |#2|) 
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-NIL 
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-NIL 
-(-997 |#1|) 
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-NIL 
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-NIL 
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+NIL 
+(-353 |#1| |#2| |#3|) 
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 NIL 
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-NIL 
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-((-4264 (((-1176) $) 10)) (-3912 (((-1137) $) 8)) (-3685 (((-112) $ $) 12))) 
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-NIL 
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-(((-102) . T) ((-624 (-873)) . T)) 
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-(((-1119 |#1|) (-436 |#1|) (-1117)) (T -1119)) 
-NIL 
-(-436 |#1|) 
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-(((-1120 |#1| |#2| |#3| |#4| |#5|) (-141) (-1117) (-1117) (-1117) (-1117) (-1117)) (T -1120)) 
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-(((-102) . T) ((-624 (-873)) . T) ((-629 (-655 $)) . T) ((-629 |#1|) . T) ((-629 |#2|) . T) ((-629 |#3|) . T) ((-629 |#4|) . T) ((-629 |#5|) . T) ((-295 (-575) $) . T) ((-295 (-655 (-575)) $) . T) ((-1117) . T) ((-1235) . T)) 
-((-2859 (((-112) $ $) NIL)) (-3704 (((-112) $) NIL)) (-3816 (((-1194) $) NIL)) (-2437 (((-112) $) NIL)) (-1650 (((-1176) $) NIL)) (-3049 (((-112) $) NIL)) (-1618 (((-112) $) NIL)) (-1503 (((-112) $) NIL)) (-4264 (((-1176) $) NIL)) (-3255 (((-112) $) NIL)) (-3839 (((-575) $) NIL)) (-3912 (((-1137) $) NIL)) (-4344 (((-112) $) NIL)) (-1539 (((-227) $) NIL)) (-1401 (((-873) $) NIL)) (-2566 (((-112) $ $) NIL)) (-2065 (($ $ (-575)) NIL) (($ $ (-655 (-575))) NIL)) (-3841 (((-655 $) $) NIL)) (-2613 (($ (-1176)) NIL) (($ (-1194)) NIL) (($ (-575)) NIL) (($ (-227)) NIL) (($ (-873)) NIL) (($ (-655 $)) NIL)) (-2882 (((-873) $) NIL)) (-1450 (($ $) NIL)) (-4207 (($ $) NIL)) (-3685 (((-112) $ $) NIL)) (-4154 (((-112) $) NIL)) (-3913 (((-112) $ $) NIL)) (-2869 (((-575) $) NIL))) 
-(((-1121) (-1120 (-1176) (-1194) (-575) (-227) (-873))) (T -1121)) 
-NIL 
-(-1120 (-1176) (-1194) (-575) (-227) (-873)) 
-((-2859 (((-112) $ $) NIL)) (-3704 (((-112) $) 45)) (-3816 ((|#2| $) 48)) (-2437 (((-112) $) 20)) (-1650 ((|#1| $) 21)) (-3049 (((-112) $) 42)) (-1618 (((-112) $) 14)) (-1503 (((-112) $) 44)) (-4264 (((-1176) $) NIL)) (-3255 (((-112) $) 46)) (-3839 ((|#3| $) 50)) (-3912 (((-1137) $) NIL)) (-4344 (((-112) $) 47)) (-1539 ((|#4| $) 49)) (-1401 ((|#5| $) 51)) (-2566 (((-112) $ $) 41)) (-2065 (($ $ (-575)) 62) (($ $ (-655 (-575))) 64)) (-3841 (((-655 $) $) 27)) (-2613 (($ |#1|) 53) (($ |#2|) 54) (($ |#3|) 55) (($ |#4|) 56) (($ |#5|) 57) (($ (-655 $)) 52)) (-2882 (((-873) $) 28)) (-1450 (($ $) 26)) (-4207 (($ $) 58)) (-3685 (((-112) $ $) NIL)) (-4154 (((-112) $) 23)) (-3913 (((-112) $ $) 40)) (-2869 (((-575) $) 60))) 
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-NIL 
-(-1120 |#1| |#2| |#3| |#4| |#5|) 
-((-2244 (((-1290) $) 22)) (-2571 (($ (-1194) (-445) |#2|) 11)) (-2882 (((-873) $) 16))) 
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+NIL 
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+NIL 
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+((-2572 (*1 *1 *2 *3 *4) (-12 (-5 *2 (-1196)) (-5 *3 (-446)) (-4 *5 (-1119)) (-5 *1 (-1125 *5 *4)) (-4 *4 (-442 *5))))) 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-4464 "*"))) ((-102) . T) ((-111 |#2| |#2|) . T) ((-132) . T) ((-628 #0=(-419 (-576))) |has| |#2| (-1057 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#2|) . T) ((-625 (-874)) . T) ((-234 $) -3739 (|has| |#2| (-237)) (|has| |#2| (-238))) ((-232 |#2|) . T) ((-238) |has| |#2| (-238)) ((-237) -3739 (|has| |#2| (-237)) (|has| |#2| (-238))) ((-272 |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-388 |#2|) . T) ((-423 |#2|) . T) ((-501 |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) . T) ((-658 |#2|) . T) ((-658 $) . T) ((-660 #1=(-576)) |has| |#2| (-651 (-576))) ((-660 |#2|) . T) ((-660 $) . T) ((-652 |#2|) -3739 (|has| |#2| (-174)) (|has| |#2| (-6 (-4464 "*")))) ((-651 #1#) |has| |#2| (-651 (-576))) ((-651 |#2|) . T) ((-729 |#2|) -3739 (|has| |#2| (-174)) (|has| |#2| (-6 (-4464 "*")))) ((-738) . T) ((-909 $ #2=(-1196)) -3739 (|has| |#2| (-917 (-1196))) (|has| |#2| (-915 (-1196)))) ((-915 (-1196)) |has| |#2| (-915 (-1196))) ((-917 #2#) -3739 (|has| |#2| (-917 (-1196))) (|has| |#2| (-915 (-1196)))) ((-1072 |#1| |#1| |#2| |#3| |#4|) . T) ((-1057 #0#) |has| |#2| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#2| (-1057 (-576))) ((-1057 |#2|) . T) ((-1070 |#2|) . T) ((-1075 |#2|) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1237) . T)) 
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-NIL 
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-NIL 
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T) ((-295 |#2| $) -12 (|has| |#1| (-373)) (|has| |#2| (-295 |#2| |#2|))) ((-295 $ $) |has| (-575) (-1129)) ((-299) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-316) |has| |#1| (-373)) ((-318 |#2|) -12 (|has| |#1| (-373)) (|has| |#2| (-318 |#2|))) ((-373) |has| |#1| (-373)) ((-348 |#2|) |has| |#1| (-373)) ((-387 |#2|) |has| |#1| (-373)) ((-411 |#2|) |has| |#1| (-373)) ((-463) |has| |#1| (-373)) ((-504) |has| |#1| (-38 (-418 (-575)))) ((-525 (-1194) |#2|) -12 (|has| |#1| (-373)) (|has| |#2| (-525 (-1194) |#2|))) ((-525 |#2| |#2|) -12 (|has| |#1| (-373)) (|has| |#2| (-318 |#2|))) ((-567) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-657 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 |#2|) |has| |#1| (-373)) ((-657 $) . T) ((-659 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-659 #3=(-575)) -12 (|has| |#1| (-373)) (|has| |#2| (-650 (-575)))) ((-659 |#1|) . T) ((-659 |#2|) |has| |#1| (-373)) ((-659 $) . T) ((-651 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-651 |#1|) |has| |#1| (-174)) ((-651 |#2|) |has| |#1| (-373)) ((-651 $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-650 #3#) -12 (|has| |#1| (-373)) (|has| |#2| (-650 (-575)))) ((-650 |#2|) |has| |#1| (-373)) ((-728 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-728 |#1|) |has| |#1| (-174)) ((-728 |#2|) |has| |#1| (-373)) ((-728 $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-737) . 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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
-(-13 (-174) (-378) (-625 (-575)) (-1169)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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(NIL T T) -8 NIL NIL NIL) (-1247 2984966 2997091 2997153 "ULSCCAT" 2997791 NIL ULSCCAT (NIL T T) -9 NIL 2998080 NIL) (-1246 2984016 2984261 2984649 "ULSCCAT-" 2984654 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1245 2973080 2979563 2979606 "ULSCAT" 2980469 NIL ULSCAT (NIL T) -9 NIL 2981200 NIL) (-1244 2972510 2972589 2972768 "ULS2" 2972995 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 2971629 2972139 2972246 "UINT8" 2972357 T UINT8 (NIL) -8 NIL NIL 2972442) (-1242 2970747 2971257 2971364 "UINT64" 2971475 T UINT64 (NIL) -8 NIL NIL 2971560) (-1241 2969865 2970375 2970482 "UINT32" 2970593 T UINT32 (NIL) -8 NIL NIL 2970678) (-1240 2968983 2969493 2969600 "UINT16" 2969711 T UINT16 (NIL) -8 NIL NIL 2969796) (-1239 2967286 2968243 2968273 "UFD" 2968485 T UFD (NIL) -9 NIL 2968599 NIL) (-1238 2967080 2967126 2967221 "UFD-" 2967226 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1237 2966162 2966345 2966561 "UDVO" 2966886 T UDVO (NIL) -7 NIL NIL NIL) (-1236 2963978 2964387 2964858 "UDPO" 2965726 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1235 2963911 2963916 2963946 "TYPE" 2963951 T TYPE (NIL) -9 NIL NIL NIL) (-1234 2963671 2963866 2963897 "TYPEAST" 2963902 T TYPEAST (NIL) -8 NIL NIL NIL) (-1233 2962642 2962844 2963084 "TWOFACT" 2963465 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1232 2961665 2962051 2962286 "TUPLE" 2962442 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1231 2959356 2959875 2960414 "TUBETOOL" 2961148 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1230 2958205 2958410 2958651 "TUBE" 2959149 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1229 2952934 2957177 2957460 "TS" 2957957 NIL TS (NIL T) -8 NIL NIL NIL) (-1228 2941574 2945693 2945790 "TSETCAT" 2951059 NIL TSETCAT (NIL T T T T) -9 NIL 2952590 NIL) (-1227 2936306 2937906 2939797 "TSETCAT-" 2939802 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1226 2930945 2931792 2932721 "TRMANIP" 2935442 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1225 2930386 2930449 2930612 "TRIMAT" 2930877 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1224 2928252 2928489 2928846 "TRIGMNIP" 2930135 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1223 2927772 2927885 2927915 "TRIGCAT" 2928128 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1222 2927441 2927520 2927661 "TRIGCAT-" 2927666 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1221 2924286 2926299 2926580 "TREE" 2927195 NIL TREE (NIL T) -8 NIL NIL NIL) (-1220 2923560 2924088 2924118 "TRANFUN" 2924153 T TRANFUN (NIL) -9 NIL 2924219 NIL) (-1219 2922839 2923030 2923310 "TRANFUN-" 2923315 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1218 2922643 2922675 2922736 "TOPSP" 2922800 T TOPSP (NIL) -7 NIL NIL NIL) (-1217 2921991 2922106 2922260 "TOOLSIGN" 2922524 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1216 2920625 2921168 2921407 "TEXTFILE" 2921774 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1215 2918537 2919078 2919507 "TEX" 2920218 T TEX (NIL) -8 NIL NIL NIL) (-1214 2918318 2918349 2918421 "TEX1" 2918500 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1213 2917966 2918029 2918119 "TEMUTL" 2918250 T TEMUTL (NIL) -7 NIL NIL NIL) (-1212 2916120 2916400 2916725 "TBCMPPK" 2917689 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1211 2907897 2914280 2914336 "TBAGG" 2914736 NIL TBAGG (NIL T T) -9 NIL 2914947 NIL) (-1210 2902967 2904455 2906209 "TBAGG-" 2906214 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1209 2902351 2902458 2902603 "TANEXP" 2902856 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1208 2901862 2902126 2902216 "TALGOP" 2902296 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1207 2895252 2901719 2901812 "TABLE" 2901817 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1206 2894664 2894763 2894901 "TABLEAU" 2895149 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1205 2889272 2890492 2891740 "TABLBUMP" 2893450 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1204 2888494 2888641 2888822 "SYSTEM" 2889113 T SYSTEM (NIL) -8 NIL NIL NIL) (-1203 2884953 2885652 2886435 "SYSSOLP" 2887745 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1202 2884751 2884908 2884939 "SYSPTR" 2884944 T SYSPTR (NIL) -8 NIL NIL NIL) (-1201 2883787 2884292 2884411 "SYSNNI" 2884597 NIL SYSNNI (NIL NIL) -8 NIL NIL 2884682) (-1200 2883086 2883545 2883624 "SYSINT" 2883684 NIL SYSINT (NIL NIL) -8 NIL NIL 2883729) (-1199 2879418 2880364 2881074 "SYNTAX" 2882398 T SYNTAX (NIL) -8 NIL NIL NIL) (-1198 2876576 2877178 2877810 "SYMTAB" 2878808 T SYMTAB (NIL) -8 NIL NIL NIL) (-1197 2871825 2872727 2873710 "SYMS" 2875615 T SYMS (NIL) -8 NIL NIL NIL) (-1196 2869060 2871283 2871513 "SYMPOLY" 2871630 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1195 2868577 2868652 2868775 "SYMFUNC" 2868972 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1194 2864597 2865889 2866702 "SYMBOL" 2867786 T SYMBOL (NIL) -8 NIL NIL NIL) (-1193 2858136 2859825 2861545 "SWITCH" 2862899 T SWITCH (NIL) -8 NIL NIL NIL) (-1192 2851480 2857092 2857386 "SUTS" 2857900 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2843656 2850862 2851126 "SUPXS" 2851274 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1190 2835326 2843274 2843400 "SUP" 2843565 NIL SUP (NIL T) -8 NIL NIL NIL) (-1189 2834485 2834612 2834829 "SUPFRACF" 2835194 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1188 2834106 2834165 2834278 "SUP2" 2834420 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1187 2832554 2832828 2833184 "SUMRF" 2833805 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1186 2831889 2831955 2832147 "SUMFS" 2832475 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1185 2814963 2831201 2831443 "SULS" 2831705 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2814565 2814785 2814855 "SUCHTAST" 2814915 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1183 2813860 2814090 2814230 "SUCH" 2814473 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1182 2807727 2808766 2809725 "SUBSPACE" 2812948 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1181 2807157 2807247 2807411 "SUBRESP" 2807615 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1180 2800525 2801822 2803133 "STTF" 2805893 NIL STTF (NIL T) -7 NIL NIL NIL) (-1179 2794698 2795818 2796965 "STTFNC" 2799425 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1178 2786011 2787880 2789674 "STTAYLOR" 2792939 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1177 2779141 2785875 2785958 "STRTBL" 2785963 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1176 2774505 2779096 2779127 "STRING" 2779132 T STRING (NIL) -8 NIL NIL NIL) (-1175 2769334 2773848 2773878 "STRICAT" 2773937 T STRICAT (NIL) -9 NIL 2773999 NIL) (-1174 2762087 2766953 2767564 "STREAM" 2768758 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1173 2761597 2761674 2761818 "STREAM3" 2762004 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1172 2760579 2760762 2760997 "STREAM2" 2761410 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1171 2760267 2760319 2760412 "STREAM1" 2760521 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1170 2759283 2759464 2759695 "STINPROD" 2760083 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1169 2758835 2759045 2759075 "STEP" 2759155 T STEP (NIL) -9 NIL 2759233 NIL) (-1168 2758022 2758324 2758472 "STEPAST" 2758709 T STEPAST (NIL) -8 NIL NIL NIL) (-1167 2751454 2757921 2757998 "STBL" 2758003 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1166 2746549 2750645 2750688 "STAGG" 2750841 NIL STAGG (NIL T) -9 NIL 2750930 NIL) (-1165 2744251 2744853 2745725 "STAGG-" 2745730 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1164 2742398 2744021 2744113 "STACK" 2744194 NIL STACK (NIL T) -8 NIL NIL NIL) (-1163 2735093 2740539 2740995 "SREGSET" 2742028 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1162 2727518 2728887 2730400 "SRDCMPK" 2733699 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1161 2720403 2724928 2724958 "SRAGG" 2726261 T SRAGG (NIL) -9 NIL 2726869 NIL) (-1160 2719420 2719675 2720054 "SRAGG-" 2720059 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1159 2713791 2718367 2718788 "SQMATRIX" 2719046 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1158 2707476 2710509 2711236 "SPLTREE" 2713136 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1157 2703439 2704132 2704778 "SPLNODE" 2706902 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1156 2702486 2702719 2702749 "SPFCAT" 2703193 T SPFCAT (NIL) -9 NIL NIL NIL) (-1155 2701223 2701433 2701697 "SPECOUT" 2702244 T SPECOUT (NIL) -7 NIL NIL NIL) (-1154 2692333 2694205 2694235 "SPADXPT" 2698911 T SPADXPT (NIL) -9 NIL 2701075 NIL) (-1153 2692094 2692134 2692203 "SPADPRSR" 2692286 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1152 2690143 2692049 2692080 "SPADAST" 2692085 T SPADAST (NIL) -8 NIL NIL NIL) (-1151 2682088 2683861 2683904 "SPACEC" 2688277 NIL SPACEC (NIL T) -9 NIL 2690093 NIL) (-1150 2680218 2682020 2682069 "SPACE3" 2682074 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1149 2678970 2679141 2679432 "SORTPAK" 2680023 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1148 2677062 2677365 2677777 "SOLVETRA" 2678634 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1147 2676112 2676334 2676595 "SOLVESER" 2676835 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1146 2671416 2672304 2673299 "SOLVERAD" 2675164 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1145 2667231 2667840 2668569 "SOLVEFOR" 2670783 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1144 2661501 2666580 2666677 "SNTSCAT" 2666682 NIL SNTSCAT (NIL T T T T) -9 NIL 2666752 NIL) (-1143 2655607 2659824 2660215 "SMTS" 2661191 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1142 2650203 2655495 2655572 "SMP" 2655577 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1141 2648362 2648663 2649061 "SMITH" 2649900 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1140 2640653 2644941 2645044 "SMATCAT" 2646395 NIL SMATCAT (NIL NIL T T T) -9 NIL 2646945 NIL) (-1139 2637371 2638256 2639514 "SMATCAT-" 2639519 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1138 2635037 2636607 2636650 "SKAGG" 2636911 NIL SKAGG (NIL T) -9 NIL 2637046 NIL) (-1137 2631313 2634510 2634694 "SINT" 2634846 T SINT (NIL) -8 NIL NIL 2635008) (-1136 2631085 2631123 2631189 "SIMPAN" 2631269 T SIMPAN (NIL) -7 NIL NIL NIL) (-1135 2630364 2630620 2630760 "SIG" 2630967 T SIG (NIL) -8 NIL NIL NIL) (-1134 2629202 2629423 2629698 "SIGNRF" 2630123 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1133 2628035 2628186 2628470 "SIGNEF" 2629031 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1132 2627341 2627618 2627742 "SIGAST" 2627933 T SIGAST (NIL) -8 NIL NIL NIL) (-1131 2625031 2625485 2625991 "SHP" 2626882 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1130 2619036 2624932 2625008 "SHDP" 2625013 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1129 2618609 2618801 2618831 "SGROUP" 2618924 T SGROUP (NIL) -9 NIL 2618986 NIL) (-1128 2618467 2618493 2618566 "SGROUP-" 2618571 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1127 2615258 2615956 2616679 "SGCF" 2617766 T SGCF (NIL) -7 NIL NIL NIL) (-1126 2609626 2614705 2614802 "SFRTCAT" 2614807 NIL SFRTCAT (NIL T T T T) -9 NIL 2614846 NIL) (-1125 2603047 2604065 2605201 "SFRGCD" 2608609 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1124 2596173 2597246 2598432 "SFQCMPK" 2601980 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1123 2595793 2595882 2595993 "SFORT" 2596114 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1122 2594911 2595633 2595754 "SEXOF" 2595759 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1121 2594018 2594792 2594860 "SEX" 2594865 T SEX (NIL) -8 NIL NIL NIL) (-1120 2589799 2590514 2590609 "SEXCAT" 2593231 NIL SEXCAT (NIL T T T T T) -9 NIL 2593791 NIL) (-1119 2586952 2589733 2589781 "SET" 2589786 NIL SET (NIL T) -8 NIL NIL NIL) (-1118 2585176 2585665 2585970 "SETMN" 2586693 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1117 2584672 2584824 2584854 "SETCAT" 2585030 T SETCAT (NIL) -9 NIL 2585140 NIL) (-1116 2584364 2584442 2584572 "SETCAT-" 2584577 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1115 2580725 2582825 2582868 "SETAGG" 2583738 NIL SETAGG (NIL T) -9 NIL 2584078 NIL) (-1114 2580183 2580299 2580536 "SETAGG-" 2580541 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1113 2579626 2579879 2579980 "SEQAST" 2580104 T SEQAST (NIL) -8 NIL NIL NIL) (-1112 2578825 2579119 2579180 "SEGXCAT" 2579466 NIL SEGXCAT (NIL T T) -9 NIL 2579586 NIL) (-1111 2577831 2578491 2578673 "SEG" 2578678 NIL SEG (NIL T) -8 NIL NIL NIL) (-1110 2576810 2577024 2577067 "SEGCAT" 2577589 NIL SEGCAT (NIL T) -9 NIL 2577810 NIL) (-1109 2575742 2576173 2576381 "SEGBIND" 2576637 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1108 2575363 2575422 2575535 "SEGBIND2" 2575677 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1107 2574936 2575164 2575241 "SEGAST" 2575308 T SEGAST (NIL) -8 NIL NIL NIL) (-1106 2574155 2574281 2574485 "SEG2" 2574780 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1105 2573526 2574090 2574137 "SDVAR" 2574142 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1104 2565964 2573296 2573426 "SDPOL" 2573431 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1103 2564557 2564823 2565142 "SCPKG" 2565679 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1102 2563721 2563893 2564085 "SCOPE" 2564387 T SCOPE (NIL) -8 NIL NIL NIL) (-1101 2562941 2563075 2563254 "SCACHE" 2563576 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1100 2562587 2562773 2562803 "SASTCAT" 2562808 T SASTCAT (NIL) -9 NIL 2562821 NIL) (-1099 2562074 2562422 2562498 "SAOS" 2562533 T SAOS (NIL) -8 NIL NIL NIL) (-1098 2561639 2561674 2561847 "SAERFFC" 2562033 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1097 2555489 2561536 2561616 "SAE" 2561621 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1096 2555082 2555117 2555276 "SAEFACT" 2555448 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1095 2553403 2553717 2554118 "RURPK" 2554748 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1094 2552040 2552346 2552651 "RULESET" 2553237 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1093 2549263 2549793 2550251 "RULE" 2551721 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1092 2548875 2549057 2549140 "RULECOLD" 2549215 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1091 2548665 2548693 2548764 "RTVALUE" 2548826 T RTVALUE (NIL) -8 NIL NIL NIL) (-1090 2548136 2548382 2548476 "RSTRCAST" 2548593 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1089 2542984 2543779 2544699 "RSETGCD" 2547335 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1088 2532214 2537293 2537390 "RSETCAT" 2541509 NIL RSETCAT (NIL T T T T) -9 NIL 2542606 NIL) (-1087 2530141 2530680 2531504 "RSETCAT-" 2531509 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1086 2522527 2523903 2525423 "RSDCMPK" 2528740 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1085 2520506 2520973 2521047 "RRCC" 2522133 NIL RRCC (NIL T T) -9 NIL 2522477 NIL) (-1084 2519857 2520031 2520310 "RRCC-" 2520315 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1083 2519300 2519553 2519654 "RPTAST" 2519778 T RPTAST (NIL) -8 NIL NIL NIL) (-1082 2492963 2502412 2502479 "RPOLCAT" 2513145 NIL RPOLCAT (NIL T T T) -9 NIL 2516305 NIL) (-1081 2484461 2486801 2489923 "RPOLCAT-" 2489928 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1080 2475392 2482672 2483154 "ROUTINE" 2484001 T ROUTINE (NIL) -8 NIL NIL NIL) (-1079 2472139 2475018 2475158 "ROMAN" 2475274 T ROMAN (NIL) -8 NIL NIL NIL) (-1078 2470383 2470999 2471259 "ROIRC" 2471944 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1077 2466615 2468899 2468929 "RNS" 2469233 T RNS (NIL) -9 NIL 2469507 NIL) (-1076 2465124 2465507 2466041 "RNS-" 2466116 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1075 2464527 2464935 2464965 "RNG" 2464970 T RNG (NIL) -9 NIL 2464991 NIL) (-1074 2463530 2463892 2464094 "RNGBIND" 2464378 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1073 2462929 2463317 2463360 "RMODULE" 2463365 NIL RMODULE (NIL T) -9 NIL 2463392 NIL) (-1072 2461765 2461859 2462195 "RMCAT2" 2462830 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1071 2458615 2461111 2461408 "RMATRIX" 2461527 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1070 2451442 2453702 2453817 "RMATCAT" 2457176 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2458158 NIL) (-1069 2450817 2450964 2451271 "RMATCAT-" 2451276 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1068 2450218 2450439 2450482 "RLINSET" 2450676 NIL RLINSET (NIL T) -9 NIL 2450767 NIL) (-1067 2449785 2449860 2449988 "RINTERP" 2450137 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1066 2448843 2449397 2449427 "RING" 2449483 T RING (NIL) -9 NIL 2449575 NIL) (-1065 2448635 2448679 2448776 "RING-" 2448781 NIL RING- (NIL T) -8 NIL NIL NIL) (-1064 2447476 2447713 2447971 "RIDIST" 2448399 T RIDIST (NIL) -7 NIL NIL NIL) (-1063 2438765 2446944 2447150 "RGCHAIN" 2447324 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1062 2438115 2438521 2438562 "RGBCSPC" 2438620 NIL RGBCSPC (NIL T) -9 NIL 2438672 NIL) (-1061 2437273 2437654 2437695 "RGBCMDL" 2437927 NIL RGBCMDL (NIL T) -9 NIL 2438041 NIL) (-1060 2434267 2434881 2435551 "RF" 2436637 NIL RF (NIL T) -7 NIL NIL NIL) (-1059 2433913 2433976 2434079 "RFFACTOR" 2434198 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1058 2433638 2433673 2433770 "RFFACT" 2433872 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1057 2431755 2432119 2432501 "RFDIST" 2433278 T RFDIST (NIL) -7 NIL NIL NIL) (-1056 2431208 2431300 2431463 "RETSOL" 2431657 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1055 2430844 2430924 2430967 "RETRACT" 2431100 NIL RETRACT (NIL T) -9 NIL 2431187 NIL) (-1054 2430693 2430718 2430805 "RETRACT-" 2430810 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1053 2430295 2430515 2430585 "RETAST" 2430645 T RETAST (NIL) -8 NIL NIL NIL) (-1052 2423033 2429948 2430075 "RESULT" 2430190 T RESULT (NIL) -8 NIL NIL NIL) (-1051 2421624 2422302 2422501 "RESRING" 2422936 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1050 2421260 2421309 2421407 "RESLATC" 2421561 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1049 2420965 2421000 2421107 "REPSQ" 2421219 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1048 2418387 2418967 2419569 "REP" 2420385 T REP (NIL) -7 NIL NIL NIL) (-1047 2418084 2418119 2418230 "REPDB" 2418346 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1046 2411984 2413373 2414596 "REP2" 2416896 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1045 2408361 2409042 2409850 "REP1" 2411211 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1044 2401057 2406502 2406958 "REGSET" 2407991 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1043 2399822 2400205 2400455 "REF" 2400842 NIL REF (NIL T) -8 NIL NIL NIL) (-1042 2399199 2399302 2399469 "REDORDER" 2399706 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1041 2395167 2398412 2398639 "RECLOS" 2399027 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1040 2394219 2394400 2394615 "REALSOLV" 2394974 T REALSOLV (NIL) -7 NIL NIL NIL) (-1039 2394065 2394106 2394136 "REAL" 2394141 T REAL (NIL) -9 NIL 2394176 NIL) (-1038 2390548 2391350 2392234 "REAL0Q" 2393230 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1037 2386149 2387137 2388198 "REAL0" 2389529 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1036 2385620 2385866 2385960 "RDUCEAST" 2386077 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1035 2385025 2385097 2385304 "RDIV" 2385542 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1034 2384093 2384267 2384480 "RDIST" 2384847 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1033 2382690 2382977 2383349 "RDETRS" 2383801 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1032 2380502 2380956 2381494 "RDETR" 2382232 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1031 2379127 2379405 2379802 "RDEEFS" 2380218 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1030 2377636 2377942 2378367 "RDEEF" 2378815 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1029 2371697 2374617 2374647 "RCFIELD" 2375942 T RCFIELD (NIL) -9 NIL 2376673 NIL) (-1028 2369761 2370265 2370961 "RCFIELD-" 2371036 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1027 2366030 2367862 2367905 "RCAGG" 2368989 NIL RCAGG (NIL T) -9 NIL 2369454 NIL) (-1026 2365658 2365752 2365915 "RCAGG-" 2365920 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1025 2364993 2365105 2365270 "RATRET" 2365542 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1024 2364546 2364613 2364734 "RATFACT" 2364921 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1023 2363854 2363974 2364126 "RANDSRC" 2364416 T RANDSRC (NIL) -7 NIL NIL NIL) (-1022 2363588 2363632 2363705 "RADUTIL" 2363803 T RADUTIL (NIL) -7 NIL NIL NIL) (-1021 2356609 2362419 2362730 "RADIX" 2363311 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1020 2347277 2356451 2356581 "RADFF" 2356586 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1019 2346924 2346999 2347029 "RADCAT" 2347189 T RADCAT (NIL) -9 NIL NIL NIL) (-1018 2346706 2346754 2346854 "RADCAT-" 2346859 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1017 2344804 2346476 2346568 "QUEUE" 2346649 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1016 2341252 2344737 2344785 "QUAT" 2344790 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1015 2340883 2340926 2341057 "QUATCT2" 2341203 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2333896 2337333 2337375 "QUATCAT" 2338166 NIL QUATCAT (NIL T) -9 NIL 2338932 NIL) (-1013 2330035 2331072 2332462 "QUATCAT-" 2332558 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2327500 2329111 2329154 "QUAGG" 2329535 NIL QUAGG (NIL T) -9 NIL 2329710 NIL) (-1011 2327102 2327322 2327392 "QQUTAST" 2327452 T QQUTAST (NIL) -8 NIL NIL NIL) (-1010 2326115 2326615 2326780 "QFORM" 2326983 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1009 2316689 2322017 2322059 "QFCAT" 2322727 NIL QFCAT (NIL T) -9 NIL 2323728 NIL) (-1008 2312034 2313297 2314971 "QFCAT-" 2315067 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1007 2311665 2311708 2311839 "QFCAT2" 2311985 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2311120 2311230 2311362 "QEQUAT" 2311555 T QEQUAT (NIL) -8 NIL NIL NIL) (-1005 2304246 2305319 2306505 "QCMPACK" 2310053 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1004 2301784 2302232 2302662 "QALGSET" 2303901 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1003 2301019 2301195 2301431 "QALGSET2" 2301602 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1002 2299704 2299928 2300247 "PWFFINTB" 2300792 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1001 2297879 2298047 2298403 "PUSHVAR" 2299518 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1000 2293768 2294822 2294865 "PTRANFN" 2296776 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-999 2292170 2292461 2292783 "PTPACK" 2293479 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-998 2291802 2291859 2291968 "PTFUNC2" 2292107 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-997 2286247 2290644 2290685 "PTCAT" 2290981 NIL PTCAT (NIL T) -9 NIL 2291134 NIL) (-996 2285905 2285940 2286064 "PSQFR" 2286206 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-995 2284500 2284798 2285132 "PSEUDLIN" 2285603 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-994 2271263 2273634 2275958 "PSETPK" 2282260 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-993 2264281 2267021 2267117 "PSETCAT" 2270138 NIL PSETCAT (NIL T T T T) -9 NIL 2270952 NIL) (-992 2262117 2262751 2263572 "PSETCAT-" 2263577 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-991 2261466 2261631 2261659 "PSCURVE" 2261927 T PSCURVE (NIL) -9 NIL 2262094 NIL) (-990 2257464 2258980 2259045 "PSCAT" 2259889 NIL PSCAT (NIL T T T) -9 NIL 2260129 NIL) (-989 2256527 2256743 2257143 "PSCAT-" 2257148 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-988 2254886 2255596 2255859 "PRTITION" 2256284 T PRTITION (NIL) -8 NIL NIL NIL) (-987 2254361 2254607 2254699 "PRTDAST" 2254814 T PRTDAST (NIL) -8 NIL NIL NIL) (-986 2243451 2245665 2247853 "PRS" 2252223 NIL PRS (NIL T T) -7 NIL NIL NIL) (-985 2241262 2242801 2242841 "PRQAGG" 2243024 NIL PRQAGG (NIL T) -9 NIL 2243126 NIL) (-984 2240598 2240903 2240931 "PROPLOG" 2241070 T PROPLOG (NIL) -9 NIL 2241185 NIL) (-983 2240202 2240259 2240382 "PROPFUN2" 2240521 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-982 2239517 2239638 2239810 "PROPFUN1" 2240063 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-981 2237698 2238264 2238561 "PROPFRML" 2239253 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-980 2237167 2237274 2237402 "PROPERTY" 2237590 T PROPERTY (NIL) -8 NIL NIL NIL) (-979 2231225 2235333 2236153 "PRODUCT" 2236393 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-978 2228503 2230683 2230917 "PR" 2231036 NIL PR (NIL T T) -8 NIL NIL NIL) (-977 2228299 2228331 2228390 "PRINT" 2228464 T PRINT (NIL) -7 NIL NIL NIL) (-976 2227639 2227756 2227908 "PRIMES" 2228179 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-975 2225704 2226105 2226571 "PRIMELT" 2227218 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-974 2225433 2225482 2225510 "PRIMCAT" 2225634 T PRIMCAT (NIL) -9 NIL NIL NIL) (-973 2221548 2225371 2225416 "PRIMARR" 2225421 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-972 2220555 2220733 2220961 "PRIMARR2" 2221366 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-971 2220198 2220254 2220365 "PREASSOC" 2220493 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-970 2219673 2219806 2219834 "PPCURVE" 2220039 T PPCURVE (NIL) -9 NIL 2220175 NIL) (-969 2219268 2219468 2219551 "PORTNUM" 2219610 T PORTNUM (NIL) -8 NIL NIL NIL) (-968 2216627 2217026 2217618 "POLYROOT" 2218849 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-967 2210720 2216231 2216391 "POLY" 2216500 NIL POLY (NIL T) -8 NIL NIL NIL) (-966 2210103 2210161 2210395 "POLYLIFT" 2210656 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-965 2206378 2206827 2207456 "POLYCATQ" 2209648 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-964 2192907 2198125 2198190 "POLYCAT" 2201704 NIL POLYCAT (NIL T T T) -9 NIL 2203582 NIL) (-963 2186134 2188058 2190522 "POLYCAT-" 2190527 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-962 2185721 2185789 2185909 "POLY2UP" 2186060 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-961 2185353 2185410 2185519 "POLY2" 2185658 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-960 2184038 2184277 2184553 "POLUTIL" 2185127 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-959 2182393 2182670 2183001 "POLTOPOL" 2183760 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-958 2177858 2182329 2182375 "POINT" 2182380 NIL POINT (NIL T) -8 NIL NIL NIL) (-957 2176045 2176402 2176777 "PNTHEORY" 2177503 T PNTHEORY (NIL) -7 NIL NIL NIL) (-956 2174503 2174800 2175199 "PMTOOLS" 2175743 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-955 2174096 2174174 2174291 "PMSYM" 2174419 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-954 2173604 2173673 2173848 "PMQFCAT" 2174021 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-953 2172959 2173069 2173225 "PMPRED" 2173481 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-952 2172352 2172438 2172600 "PMPREDFS" 2172860 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-951 2171016 2171224 2171602 "PMPLCAT" 2172114 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-950 2170548 2170627 2170779 "PMLSAGG" 2170931 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-949 2170021 2170097 2170279 "PMKERNEL" 2170466 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-948 2169638 2169713 2169826 "PMINS" 2169940 NIL PMINS (NIL T) -7 NIL NIL NIL) (-947 2169080 2169149 2169358 "PMFS" 2169563 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-946 2168308 2168426 2168631 "PMDOWN" 2168957 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-945 2167475 2167633 2167814 "PMASS" 2168147 T PMASS (NIL) -7 NIL NIL NIL) (-944 2166748 2166858 2167021 "PMASSFS" 2167362 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-943 2166403 2166471 2166565 "PLOTTOOL" 2166674 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-942 2161010 2162214 2163362 "PLOT" 2165275 T PLOT (NIL) -8 NIL NIL NIL) (-941 2156814 2157858 2158779 "PLOT3D" 2160109 T PLOT3D (NIL) -8 NIL NIL NIL) (-940 2155726 2155903 2156138 "PLOT1" 2156618 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-939 2131117 2135792 2140643 "PLEQN" 2150992 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-938 2130435 2130557 2130737 "PINTERP" 2130982 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-937 2130128 2130175 2130278 "PINTERPA" 2130382 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-936 2129344 2129892 2129979 "PI" 2130019 T PI (NIL) -8 NIL NIL 2130086) (-935 2127641 2128616 2128644 "PID" 2128826 T PID (NIL) -9 NIL 2128960 NIL) (-934 2127392 2127429 2127504 "PICOERCE" 2127598 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-933 2126712 2126851 2127027 "PGROEB" 2127248 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-932 2122299 2123113 2124018 "PGE" 2125827 T PGE (NIL) -7 NIL NIL NIL) (-931 2120422 2120669 2121035 "PGCD" 2122016 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-930 2119760 2119863 2120024 "PFRPAC" 2120306 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-929 2116400 2118308 2118661 "PFR" 2119439 NIL PFR (NIL T) -8 NIL NIL NIL) (-928 2114789 2115033 2115358 "PFOTOOLS" 2116147 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-927 2113322 2113561 2113912 "PFOQ" 2114546 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-926 2111823 2112035 2112391 "PFO" 2113106 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-925 2108376 2111712 2111781 "PF" 2111786 NIL PF (NIL NIL) -8 NIL NIL NIL) (-924 2105710 2106981 2107009 "PFECAT" 2107594 T PFECAT (NIL) -9 NIL 2107978 NIL) (-923 2105155 2105309 2105523 "PFECAT-" 2105528 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-922 2103758 2104010 2104311 "PFBRU" 2104904 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-921 2101624 2101976 2102408 "PFBR" 2103409 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-920 2097670 2099136 2099783 "PERM" 2101010 NIL PERM (NIL T) -8 NIL NIL NIL) (-919 2092904 2093877 2094747 "PERMGRP" 2096833 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-918 2091023 2091983 2092024 "PERMCAT" 2092424 NIL PERMCAT (NIL T) -9 NIL 2092722 NIL) (-917 2090676 2090717 2090841 "PERMAN" 2090976 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-916 2088164 2090341 2090463 "PENDTREE" 2090587 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-915 2087093 2087308 2087349 "PDSPC" 2087882 NIL PDSPC (NIL T) -9 NIL 2088127 NIL) (-914 2086196 2086414 2086776 "PDSPC-" 2086781 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-913 2085078 2085846 2085887 "PDRING" 2085892 NIL PDRING (NIL T) -9 NIL 2085920 NIL) (-912 2082293 2083071 2083739 "PDEPROB" 2084430 T PDEPROB (NIL) -8 NIL NIL NIL) (-911 2079838 2080342 2080897 "PDEPACK" 2081758 T PDEPACK (NIL) -7 NIL NIL NIL) (-910 2078750 2078940 2079191 "PDECOMP" 2079637 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-909 2076329 2077172 2077200 "PDECAT" 2077987 T PDECAT (NIL) -9 NIL 2078700 NIL) (-908 2075958 2076013 2076067 "PDDOM" 2076232 NIL PDDOM (NIL T T) -9 NIL 2076312 NIL) (-907 2075777 2075807 2075914 "PDDOM-" 2075919 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-906 2075528 2075561 2075651 "PCOMP" 2075738 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-905 2073706 2074329 2074626 "PBWLB" 2075257 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-904 2066179 2067779 2069117 "PATTERN" 2072389 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-903 2065811 2065868 2065977 "PATTERN2" 2066116 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-902 2063568 2063956 2064413 "PATTERN1" 2065400 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-901 2060936 2061517 2061998 "PATRES" 2063133 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-900 2060500 2060567 2060699 "PATRES2" 2060863 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-899 2058383 2058788 2059195 "PATMATCH" 2060167 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-898 2057893 2058102 2058143 "PATMAB" 2058250 NIL PATMAB (NIL T) -9 NIL 2058333 NIL) (-897 2056411 2056747 2057005 "PATLRES" 2057698 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-896 2055957 2056080 2056121 "PATAB" 2056126 NIL PATAB (NIL T) -9 NIL 2056298 NIL) (-895 2054139 2054534 2054957 "PARTPERM" 2055554 T PARTPERM (NIL) -7 NIL NIL NIL) (-894 2053760 2053823 2053925 "PARSURF" 2054070 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-893 2053392 2053449 2053558 "PARSU2" 2053697 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-892 2053156 2053196 2053263 "PARSER" 2053345 T PARSER (NIL) -7 NIL NIL NIL) (-891 2052777 2052840 2052942 "PARSCURV" 2053087 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-890 2052409 2052466 2052575 "PARSC2" 2052714 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-889 2052048 2052106 2052203 "PARPCURV" 2052345 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-888 2051680 2051737 2051846 "PARPC2" 2051985 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-887 2050741 2051053 2051235 "PARAMAST" 2051518 T PARAMAST (NIL) -8 NIL NIL NIL) (-886 2050261 2050347 2050466 "PAN2EXPR" 2050642 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-885 2049038 2049382 2049610 "PALETTE" 2050053 T PALETTE (NIL) -8 NIL NIL NIL) (-884 2047431 2048043 2048403 "PAIR" 2048724 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-883 2041210 2046688 2046883 "PADICRC" 2047285 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-882 2034334 2040554 2040739 "PADICRAT" 2041057 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-881 2032649 2034271 2034316 "PADIC" 2034321 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-880 2029759 2031323 2031363 "PADICCT" 2031944 NIL PADICCT (NIL NIL) -9 NIL 2032226 NIL) (-879 2028716 2028916 2029184 "PADEPAC" 2029546 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-878 2027928 2028061 2028267 "PADE" 2028578 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-877 2026315 2027136 2027416 "OWP" 2027732 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-876 2025808 2026021 2026118 "OVERSET" 2026238 T OVERSET (NIL) -8 NIL NIL NIL) (-875 2024854 2025413 2025585 "OVAR" 2025676 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-874 2024118 2024239 2024400 "OUT" 2024713 T OUT (NIL) -7 NIL NIL NIL) (-873 2012990 2015227 2017427 "OUTFORM" 2021938 T OUTFORM (NIL) -8 NIL NIL NIL) (-872 2012326 2012587 2012714 "OUTBFILE" 2012883 T OUTBFILE (NIL) -8 NIL NIL NIL) (-871 2011633 2011798 2011826 "OUTBCON" 2012144 T OUTBCON (NIL) -9 NIL 2012310 NIL) (-870 2011234 2011346 2011503 "OUTBCON-" 2011508 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-869 2010614 2010963 2011052 "OSI" 2011165 T OSI (NIL) -8 NIL NIL NIL) (-868 2010144 2010482 2010510 "OSGROUP" 2010515 T OSGROUP (NIL) -9 NIL 2010537 NIL) (-867 2008889 2009116 2009401 "ORTHPOL" 2009891 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-866 2006440 2008724 2008845 "OREUP" 2008850 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-865 2003843 2006131 2006258 "ORESUP" 2006382 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-864 2001371 2001871 2002432 "OREPCTO" 2003332 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-863 1995057 1997258 1997299 "OREPCAT" 1999647 NIL OREPCAT (NIL T) -9 NIL 2000751 NIL) (-862 1992204 1992986 1994044 "OREPCAT-" 1994049 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-861 1991355 1991653 1991681 "ORDSET" 1991990 T ORDSET (NIL) -9 NIL 1992154 NIL) (-860 1990786 1990934 1991158 "ORDSET-" 1991163 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-859 1989351 1990142 1990170 "ORDRING" 1990372 T ORDRING (NIL) -9 NIL 1990497 NIL) (-858 1988996 1989090 1989234 "ORDRING-" 1989239 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-857 1988376 1988839 1988867 "ORDMON" 1988872 T ORDMON (NIL) -9 NIL 1988893 NIL) (-856 1987538 1987685 1987880 "ORDFUNS" 1988225 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-855 1986876 1987295 1987323 "ORDFIN" 1987388 T ORDFIN (NIL) -9 NIL 1987462 NIL) (-854 1983435 1985462 1985871 "ORDCOMP" 1986500 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-853 1982701 1982828 1983014 "ORDCOMP2" 1983295 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-852 1979282 1980192 1981006 "OPTPROB" 1981907 T OPTPROB (NIL) -8 NIL NIL NIL) (-851 1976084 1976723 1977427 "OPTPACK" 1978598 T OPTPACK (NIL) -7 NIL NIL NIL) (-850 1973771 1974537 1974565 "OPTCAT" 1975384 T OPTCAT (NIL) -9 NIL 1976034 NIL) (-849 1973155 1973448 1973553 "OPSIG" 1973686 T OPSIG (NIL) -8 NIL NIL NIL) (-848 1972923 1972962 1973028 "OPQUERY" 1973109 T OPQUERY (NIL) -7 NIL NIL NIL) (-847 1970054 1971234 1971738 "OP" 1972452 NIL OP (NIL T) -8 NIL NIL NIL) (-846 1969428 1969654 1969695 "OPERCAT" 1969907 NIL OPERCAT (NIL T) -9 NIL 1970004 NIL) (-845 1969183 1969239 1969356 "OPERCAT-" 1969361 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-844 1965996 1967980 1968349 "ONECOMP" 1968847 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-843 1965301 1965416 1965590 "ONECOMP2" 1965868 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1964720 1964826 1964956 "OMSERVER" 1965191 T OMSERVER (NIL) -7 NIL NIL NIL) (-841 1961582 1964160 1964200 "OMSAGG" 1964261 NIL OMSAGG (NIL T) -9 NIL 1964325 NIL) (-840 1960205 1960468 1960750 "OMPKG" 1961320 T OMPKG (NIL) -7 NIL NIL NIL) (-839 1959635 1959738 1959766 "OM" 1960065 T OM (NIL) -9 NIL NIL NIL) (-838 1958182 1959184 1959353 "OMLO" 1959516 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-837 1957142 1957289 1957509 "OMEXPR" 1958008 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-836 1956433 1956688 1956824 "OMERR" 1957026 T OMERR (NIL) -8 NIL NIL NIL) (-835 1955584 1955854 1956014 "OMERRK" 1956293 T OMERRK (NIL) -8 NIL NIL NIL) (-834 1955035 1955261 1955369 "OMENC" 1955496 T OMENC (NIL) -8 NIL NIL NIL) (-833 1948930 1950115 1951286 "OMDEV" 1953884 T OMDEV (NIL) -8 NIL NIL NIL) (-832 1947999 1948170 1948364 "OMCONN" 1948756 T OMCONN (NIL) -8 NIL NIL NIL) (-831 1946520 1947496 1947524 "OINTDOM" 1947529 T OINTDOM (NIL) -9 NIL 1947550 NIL) (-830 1943858 1945208 1945545 "OFMONOID" 1946215 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-829 1943230 1943795 1943840 "ODVAR" 1943845 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-828 1940653 1942975 1943130 "ODR" 1943135 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-827 1933145 1940429 1940555 "ODPOL" 1940560 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-826 1927120 1933017 1933122 "ODP" 1933127 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-825 1925886 1926101 1926376 "ODETOOLS" 1926894 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-824 1922853 1923511 1924227 "ODESYS" 1925219 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-823 1917735 1918643 1919668 "ODERTRIC" 1921928 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-822 1917161 1917243 1917437 "ODERED" 1917647 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-821 1914049 1914597 1915274 "ODERAT" 1916584 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-820 1911008 1911473 1912070 "ODEPRRIC" 1913578 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-819 1908951 1909547 1910033 "ODEPROB" 1910542 T ODEPROB (NIL) -8 NIL NIL NIL) (-818 1905471 1905956 1906603 "ODEPRIM" 1908430 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-817 1904720 1904822 1905082 "ODEPAL" 1905363 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-816 1900882 1901673 1902537 "ODEPACK" 1903876 T ODEPACK (NIL) -7 NIL NIL NIL) (-815 1899943 1900050 1900272 "ODEINT" 1900771 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-814 1894044 1895469 1896916 "ODEIFTBL" 1898516 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-813 1889442 1890228 1891180 "ODEEF" 1893203 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-812 1888791 1888880 1889103 "ODECONST" 1889347 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-811 1886916 1887577 1887605 "ODECAT" 1888210 T ODECAT (NIL) -9 NIL 1888741 NIL) (-810 1883771 1886621 1886743 "OCT" 1886826 NIL OCT (NIL T) -8 NIL NIL NIL) (-809 1883409 1883452 1883579 "OCTCT2" 1883722 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-808 1878020 1880455 1880495 "OC" 1881592 NIL OC (NIL T) -9 NIL 1882450 NIL) (-807 1875247 1875995 1876985 "OC-" 1877079 NIL OC- (NIL T T) -8 NIL NIL NIL) (-806 1874599 1875067 1875095 "OCAMON" 1875100 T OCAMON (NIL) -9 NIL 1875121 NIL) (-805 1874130 1874471 1874499 "OASGP" 1874504 T OASGP (NIL) -9 NIL 1874524 NIL) (-804 1873391 1873880 1873908 "OAMONS" 1873948 T OAMONS (NIL) -9 NIL 1873991 NIL) (-803 1872805 1873238 1873266 "OAMON" 1873271 T OAMON (NIL) -9 NIL 1873291 NIL) (-802 1872063 1872581 1872609 "OAGROUP" 1872614 T OAGROUP (NIL) -9 NIL 1872634 NIL) (-801 1871753 1871803 1871891 "NUMTUBE" 1872007 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-800 1865326 1866844 1868380 "NUMQUAD" 1870237 T NUMQUAD (NIL) -7 NIL NIL NIL) (-799 1861082 1862070 1863095 "NUMODE" 1864321 T NUMODE (NIL) -7 NIL NIL NIL) (-798 1858437 1859317 1859345 "NUMINT" 1860268 T NUMINT (NIL) -9 NIL 1861032 NIL) (-797 1857385 1857582 1857800 "NUMFMT" 1858239 T NUMFMT (NIL) -7 NIL NIL NIL) (-796 1843744 1846689 1849221 "NUMERIC" 1854892 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-795 1838114 1843193 1843288 "NTSCAT" 1843293 NIL NTSCAT (NIL T T T T) -9 NIL 1843332 NIL) (-794 1837308 1837473 1837666 "NTPOLFN" 1837953 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-793 1825296 1834133 1834945 "NSUP" 1836529 NIL NSUP (NIL T) -8 NIL NIL NIL) (-792 1824928 1824985 1825094 "NSUP2" 1825233 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-791 1815065 1824702 1824835 "NSMP" 1824840 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-790 1813497 1813798 1814155 "NREP" 1814753 NIL NREP (NIL T) -7 NIL NIL NIL) (-789 1812088 1812340 1812698 "NPCOEF" 1813240 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-788 1811154 1811269 1811485 "NORMRETR" 1811969 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-787 1809195 1809485 1809894 "NORMPK" 1810862 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-786 1808880 1808908 1809032 "NORMMA" 1809161 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-785 1808680 1808837 1808866 "NONE" 1808871 T NONE (NIL) -8 NIL NIL NIL) (-784 1808469 1808498 1808567 "NONE1" 1808644 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-783 1807966 1808028 1808207 "NODE1" 1808401 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-782 1806247 1807098 1807353 "NNI" 1807700 T NNI (NIL) -8 NIL NIL 1807935) (-781 1804667 1804980 1805344 "NLINSOL" 1805915 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-780 1800908 1801903 1802802 "NIPROB" 1803788 T NIPROB (NIL) -8 NIL NIL NIL) (-779 1799665 1799899 1800201 "NFINTBAS" 1800670 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-778 1798839 1799315 1799356 "NETCLT" 1799528 NIL NETCLT (NIL T) -9 NIL 1799610 NIL) (-777 1797547 1797778 1798059 "NCODIV" 1798607 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-776 1797309 1797346 1797421 "NCNTFRAC" 1797504 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-775 1795489 1795853 1796273 "NCEP" 1796934 NIL NCEP (NIL T) -7 NIL NIL NIL) (-774 1794340 1795113 1795141 "NASRING" 1795251 T NASRING (NIL) -9 NIL 1795331 NIL) (-773 1794135 1794179 1794273 "NASRING-" 1794278 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-772 1793242 1793767 1793795 "NARNG" 1793912 T NARNG (NIL) -9 NIL 1794003 NIL) (-771 1792934 1793001 1793135 "NARNG-" 1793140 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-770 1791813 1792020 1792255 "NAGSP" 1792719 T NAGSP (NIL) -7 NIL NIL NIL) (-769 1783085 1784769 1786442 "NAGS" 1790160 T NAGS (NIL) -7 NIL NIL NIL) (-768 1781633 1781941 1782272 "NAGF07" 1782774 T NAGF07 (NIL) -7 NIL NIL NIL) (-767 1776171 1777462 1778769 "NAGF04" 1780346 T NAGF04 (NIL) -7 NIL NIL NIL) (-766 1769139 1770753 1772386 "NAGF02" 1774558 T NAGF02 (NIL) -7 NIL NIL NIL) (-765 1764363 1765463 1766580 "NAGF01" 1768042 T NAGF01 (NIL) -7 NIL NIL NIL) (-764 1757991 1759557 1761142 "NAGE04" 1762798 T NAGE04 (NIL) -7 NIL NIL NIL) (-763 1749160 1751281 1753411 "NAGE02" 1755881 T NAGE02 (NIL) -7 NIL NIL NIL) (-762 1745113 1746060 1747024 "NAGE01" 1748216 T NAGE01 (NIL) -7 NIL NIL NIL) (-761 1742908 1743442 1744000 "NAGD03" 1744575 T NAGD03 (NIL) -7 NIL NIL NIL) (-760 1734658 1736586 1738540 "NAGD02" 1740974 T NAGD02 (NIL) -7 NIL NIL NIL) (-759 1728469 1729894 1731334 "NAGD01" 1733238 T NAGD01 (NIL) -7 NIL NIL NIL) (-758 1724678 1725500 1726337 "NAGC06" 1727652 T NAGC06 (NIL) -7 NIL NIL NIL) (-757 1723143 1723475 1723831 "NAGC05" 1724342 T NAGC05 (NIL) -7 NIL NIL NIL) (-756 1722519 1722638 1722782 "NAGC02" 1723019 T NAGC02 (NIL) -7 NIL NIL NIL) (-755 1721478 1722061 1722101 "NAALG" 1722180 NIL NAALG (NIL T) -9 NIL 1722241 NIL) (-754 1721313 1721342 1721432 "NAALG-" 1721437 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-753 1715263 1716371 1717558 "MULTSQFR" 1720209 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-752 1714582 1714657 1714841 "MULTFACT" 1715175 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-751 1707253 1711167 1711220 "MTSCAT" 1712290 NIL MTSCAT (NIL T T) -9 NIL 1712805 NIL) (-750 1706965 1707019 1707111 "MTHING" 1707193 NIL MTHING (NIL T) -7 NIL NIL NIL) (-749 1706757 1706790 1706850 "MSYSCMD" 1706925 T MSYSCMD (NIL) -7 NIL NIL NIL) (-748 1702839 1705512 1705832 "MSET" 1706470 NIL MSET (NIL T) -8 NIL NIL NIL) (-747 1699908 1702400 1702441 "MSETAGG" 1702446 NIL MSETAGG (NIL T) -9 NIL 1702480 NIL) (-746 1695750 1697287 1698032 "MRING" 1699208 NIL MRING (NIL T T) -8 NIL NIL NIL) (-745 1695316 1695383 1695514 "MRF2" 1695677 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-744 1694934 1694969 1695113 "MRATFAC" 1695275 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-743 1692546 1692841 1693272 "MPRFF" 1694639 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-742 1686754 1692400 1692497 "MPOLY" 1692502 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-741 1686244 1686279 1686487 "MPCPF" 1686713 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-740 1685758 1685801 1685985 "MPC3" 1686195 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1684953 1685034 1685255 "MPC2" 1685673 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1683254 1683591 1683981 "MONOTOOL" 1684613 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-737 1682479 1682796 1682824 "MONOID" 1683043 T MONOID (NIL) -9 NIL 1683190 NIL) (-736 1682025 1682144 1682325 "MONOID-" 1682330 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-735 1671760 1677803 1677862 "MONOGEN" 1678536 NIL MONOGEN (NIL T T) -9 NIL 1678992 NIL) (-734 1668978 1669713 1670713 "MONOGEN-" 1670832 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-733 1667811 1668257 1668285 "MONADWU" 1668677 T MONADWU (NIL) -9 NIL 1668915 NIL) (-732 1667183 1667342 1667590 "MONADWU-" 1667595 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-731 1666542 1666786 1666814 "MONAD" 1667021 T MONAD (NIL) -9 NIL 1667133 NIL) (-730 1666227 1666305 1666437 "MONAD-" 1666442 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-729 1664516 1665140 1665419 "MOEBIUS" 1665980 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-728 1663794 1664198 1664238 "MODULE" 1664243 NIL MODULE (NIL T) -9 NIL 1664282 NIL) (-727 1663362 1663458 1663648 "MODULE-" 1663653 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-726 1661042 1661726 1662053 "MODRING" 1663186 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-725 1657986 1659147 1659668 "MODOP" 1660571 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-724 1656574 1657053 1657330 "MODMONOM" 1657849 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-723 1646529 1654865 1655279 "MODMON" 1656211 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-722 1643685 1645373 1645649 "MODFIELD" 1646404 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-721 1642662 1642966 1643156 "MMLFORM" 1643515 T MMLFORM (NIL) -8 NIL NIL NIL) (-720 1642188 1642231 1642410 "MMAP" 1642613 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-719 1640267 1641034 1641075 "MLO" 1641498 NIL MLO (NIL T) -9 NIL 1641740 NIL) (-718 1637633 1638149 1638751 "MLIFT" 1639748 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-717 1637024 1637108 1637262 "MKUCFUNC" 1637544 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-716 1636623 1636693 1636816 "MKRECORD" 1636947 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-715 1635670 1635832 1636060 "MKFUNC" 1636434 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-714 1635058 1635162 1635318 "MKFLCFN" 1635553 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-713 1634335 1634437 1634622 "MKBCFUNC" 1634951 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-712 1631010 1633889 1634025 "MINT" 1634219 T MINT (NIL) -8 NIL NIL NIL) (-711 1629822 1630065 1630342 "MHROWRED" 1630765 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-710 1625202 1628357 1628762 "MFLOAT" 1629437 T MFLOAT (NIL) -8 NIL NIL NIL) (-709 1624559 1624635 1624806 "MFINFACT" 1625114 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-708 1620874 1621722 1622606 "MESH" 1623695 T MESH (NIL) -7 NIL NIL NIL) (-707 1619264 1619576 1619929 "MDDFACT" 1620561 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-706 1616059 1618423 1618464 "MDAGG" 1618719 NIL MDAGG (NIL T) -9 NIL 1618862 NIL) (-705 1604946 1615352 1615559 "MCMPLX" 1615872 T MCMPLX (NIL) -8 NIL NIL NIL) (-704 1604083 1604229 1604430 "MCDEN" 1604795 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-703 1601973 1602243 1602623 "MCALCFN" 1603813 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-702 1600898 1601138 1601371 "MAYBE" 1601779 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-701 1598510 1599033 1599595 "MATSTOR" 1600369 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-700 1594467 1597882 1598130 "MATRIX" 1598295 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-699 1590233 1590940 1591676 "MATLIN" 1593824 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-698 1580339 1583525 1583602 "MATCAT" 1588482 NIL MATCAT (NIL T T T) -9 NIL 1589899 NIL) (-697 1576695 1577716 1579072 "MATCAT-" 1579077 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-696 1575289 1575442 1575775 "MATCAT2" 1576530 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-695 1573401 1573725 1574109 "MAPPKG3" 1574964 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-694 1572382 1572555 1572777 "MAPPKG2" 1573225 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-693 1570881 1571165 1571492 "MAPPKG1" 1572088 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-692 1569960 1570287 1570464 "MAPPAST" 1570724 T MAPPAST (NIL) -8 NIL NIL NIL) (-691 1569571 1569629 1569752 "MAPHACK3" 1569896 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-690 1569163 1569224 1569338 "MAPHACK2" 1569503 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-689 1568601 1568704 1568846 "MAPHACK1" 1569054 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-688 1566680 1567301 1567605 "MAGMA" 1568329 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-687 1566159 1566404 1566495 "MACROAST" 1566609 T MACROAST (NIL) -8 NIL NIL NIL) (-686 1562577 1564398 1564859 "M3D" 1565731 NIL M3D (NIL T) -8 NIL NIL NIL) (-685 1556652 1560916 1560957 "LZSTAGG" 1561739 NIL LZSTAGG (NIL T) -9 NIL 1562034 NIL) (-684 1552610 1553783 1555240 "LZSTAGG-" 1555245 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-683 1549697 1550501 1550988 "LWORD" 1552155 NIL LWORD (NIL T) -8 NIL NIL NIL) (-682 1549273 1549501 1549576 "LSTAST" 1549642 T LSTAST (NIL) -8 NIL NIL NIL) (-681 1542350 1549044 1549178 "LSQM" 1549183 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-680 1541574 1541713 1541941 "LSPP" 1542205 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-679 1539386 1539687 1540143 "LSMP" 1541263 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-678 1536165 1536839 1537569 "LSMP1" 1538688 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-677 1530011 1535302 1535343 "LSAGG" 1535405 NIL LSAGG (NIL T) -9 NIL 1535483 NIL) (-676 1526706 1527630 1528843 "LSAGG-" 1528848 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-675 1524305 1525850 1526099 "LPOLY" 1526501 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-674 1523887 1523972 1524095 "LPEFRAC" 1524214 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-673 1522208 1522981 1523234 "LO" 1523719 NIL LO (NIL T T T) -8 NIL NIL NIL) (-672 1521860 1521972 1522000 "LOGIC" 1522111 T LOGIC (NIL) -9 NIL 1522192 NIL) (-671 1521722 1521745 1521816 "LOGIC-" 1521821 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-670 1520915 1521055 1521248 "LODOOPS" 1521578 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-669 1518338 1520831 1520897 "LODO" 1520902 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-668 1516876 1517111 1517464 "LODOF" 1518085 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-667 1513080 1515511 1515552 "LODOCAT" 1515990 NIL LODOCAT (NIL T) -9 NIL 1516201 NIL) (-666 1512813 1512871 1512998 "LODOCAT-" 1513003 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-665 1510133 1512654 1512772 "LODO2" 1512777 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-664 1507568 1510070 1510115 "LODO1" 1510120 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-663 1506449 1506614 1506919 "LODEEF" 1507391 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-662 1501752 1504643 1504684 "LNAGG" 1505546 NIL LNAGG (NIL T) -9 NIL 1505981 NIL) (-661 1500899 1501113 1501455 "LNAGG-" 1501460 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-660 1497035 1497824 1498463 "LMOPS" 1500314 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-659 1496438 1496826 1496867 "LMODULE" 1496872 NIL LMODULE (NIL T) -9 NIL 1496898 NIL) (-658 1493636 1496083 1496206 "LMDICT" 1496348 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-657 1493042 1493263 1493304 "LLINSET" 1493495 NIL LLINSET (NIL T) -9 NIL 1493586 NIL) (-656 1492741 1492950 1493010 "LITERAL" 1493015 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-655 1485904 1491675 1491979 "LIST" 1492470 NIL LIST (NIL T) -8 NIL NIL NIL) (-654 1485429 1485503 1485642 "LIST3" 1485824 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-653 1484436 1484614 1484842 "LIST2" 1485247 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-652 1482570 1482882 1483281 "LIST2MAP" 1484083 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-651 1482166 1482403 1482444 "LINSET" 1482449 NIL LINSET (NIL T) -9 NIL 1482483 NIL) (-650 1480895 1481428 1481469 "LINEXP" 1481820 NIL LINEXP (NIL T) -9 NIL 1482011 NIL) (-649 1479472 1479732 1480043 "LINDEP" 1480647 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-648 1476239 1476958 1477735 "LIMITRF" 1478727 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-647 1474542 1474838 1475247 "LIMITPS" 1475934 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-646 1468970 1474053 1474281 "LIE" 1474363 NIL LIE (NIL T T) -8 NIL NIL NIL) (-645 1467918 1468387 1468427 "LIECAT" 1468567 NIL LIECAT (NIL T) -9 NIL 1468718 NIL) (-644 1467759 1467786 1467874 "LIECAT-" 1467879 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-643 1460346 1467299 1467455 "LIB" 1467623 T LIB (NIL) -8 NIL NIL NIL) (-642 1455981 1456864 1457799 "LGROBP" 1459463 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-641 1453979 1454253 1454603 "LF" 1455702 NIL LF (NIL T T) -7 NIL NIL NIL) (-640 1452819 1453511 1453539 "LFCAT" 1453746 T LFCAT (NIL) -9 NIL 1453885 NIL) (-639 1449721 1450351 1451039 "LEXTRIPK" 1452183 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-638 1446465 1447291 1447794 "LEXP" 1449301 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-637 1445941 1446186 1446278 "LETAST" 1446393 T LETAST (NIL) -8 NIL NIL NIL) (-636 1444339 1444652 1445053 "LEADCDET" 1445623 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-635 1443529 1443603 1443832 "LAZM3PK" 1444260 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-634 1438446 1441606 1442144 "LAUPOL" 1443041 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-633 1438025 1438069 1438230 "LAPLACE" 1438396 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-632 1435964 1437126 1437377 "LA" 1437858 NIL LA (NIL T T T) -8 NIL NIL NIL) (-631 1434958 1435542 1435583 "LALG" 1435645 NIL LALG (NIL T) -9 NIL 1435704 NIL) (-630 1434672 1434731 1434867 "LALG-" 1434872 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-629 1434507 1434531 1434572 "KVTFROM" 1434634 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-628 1433430 1433874 1434059 "KTVLOGIC" 1434342 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-627 1433265 1433289 1433330 "KRCFROM" 1433392 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-626 1432169 1432356 1432655 "KOVACIC" 1433065 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-625 1432004 1432028 1432069 "KONVERT" 1432131 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-624 1431839 1431863 1431904 "KOERCE" 1431966 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-623 1429670 1430432 1430809 "KERNEL" 1431495 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-622 1429166 1429247 1429379 "KERNEL2" 1429584 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-621 1422936 1427705 1427759 "KDAGG" 1428136 NIL KDAGG (NIL T T) -9 NIL 1428342 NIL) (-620 1422465 1422589 1422794 "KDAGG-" 1422799 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-619 1415613 1422126 1422281 "KAFILE" 1422343 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-618 1410041 1415124 1415352 "JORDAN" 1415434 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1409420 1409690 1409811 "JOINAST" 1409940 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1409266 1409325 1409380 "JAVACODE" 1409385 T JAVACODE (NIL) -8 NIL NIL NIL) (-615 1405518 1407471 1407525 "IXAGG" 1408454 NIL IXAGG (NIL T T) -9 NIL 1408913 NIL) (-614 1404437 1404743 1405162 "IXAGG-" 1405167 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1399967 1404359 1404418 "IVECTOR" 1404423 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-612 1398733 1398970 1399236 "ITUPLE" 1399734 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-611 1397235 1397412 1397707 "ITRIGMNP" 1398555 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-610 1395980 1396184 1396467 "ITFUN3" 1397011 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-609 1395612 1395669 1395778 "ITFUN2" 1395917 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-608 1394771 1395092 1395266 "ITFORM" 1395458 T ITFORM (NIL) -8 NIL NIL NIL) (-607 1392732 1393791 1394069 "ITAYLOR" 1394526 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-606 1381677 1386869 1388032 "ISUPS" 1391602 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-605 1380781 1380921 1381157 "ISUMP" 1381524 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-604 1376156 1380726 1380767 "ISTRING" 1380772 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-603 1375632 1375877 1375969 "ISAST" 1376084 T ISAST (NIL) -8 NIL NIL NIL) (-602 1374841 1374923 1375139 "IRURPK" 1375546 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-601 1373777 1373978 1374218 "IRSN" 1374621 T IRSN (NIL) -7 NIL NIL NIL) (-600 1371848 1372203 1372632 "IRRF2F" 1373415 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-599 1371595 1371633 1371709 "IRREDFFX" 1371804 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-598 1370210 1370469 1370768 "IROOT" 1371328 NIL IROOT (NIL T) -7 NIL NIL NIL) (-597 1366814 1367894 1368586 "IR" 1369550 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1366019 1366307 1366458 "IRFORM" 1366683 T IRFORM (NIL) -8 NIL NIL NIL) (-595 1363632 1364127 1364693 "IR2" 1365497 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-594 1362732 1362845 1363059 "IR2F" 1363515 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-593 1362523 1362557 1362617 "IPRNTPK" 1362692 T IPRNTPK (NIL) -7 NIL NIL NIL) (-592 1359104 1362412 1362481 "IPF" 1362486 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-591 1357431 1359029 1359086 "IPADIC" 1359091 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-590 1356743 1356991 1357121 "IP4ADDR" 1357321 T IP4ADDR (NIL) -8 NIL NIL NIL) (-589 1356117 1356372 1356504 "IOMODE" 1356631 T IOMODE (NIL) -8 NIL NIL NIL) (-588 1355190 1355714 1355841 "IOBFILE" 1356010 T IOBFILE (NIL) -8 NIL NIL NIL) (-587 1354678 1355094 1355122 "IOBCON" 1355127 T IOBCON (NIL) -9 NIL 1355148 NIL) (-586 1354189 1354247 1354430 "INVLAPLA" 1354614 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-585 1343837 1346191 1348577 "INTTR" 1351853 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-584 1340172 1340914 1341779 "INTTOOLS" 1343022 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-583 1339758 1339849 1339966 "INTSLPE" 1340075 T INTSLPE (NIL) -7 NIL NIL NIL) (-582 1337711 1339681 1339740 "INTRVL" 1339745 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-581 1335313 1335825 1336400 "INTRF" 1337196 NIL INTRF (NIL T) -7 NIL NIL NIL) (-580 1334724 1334821 1334963 "INTRET" 1335211 NIL INTRET (NIL T) -7 NIL NIL NIL) (-579 1332721 1333110 1333580 "INTRAT" 1334332 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-578 1329984 1330567 1331186 "INTPM" 1332206 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-577 1326729 1327328 1328066 "INTPAF" 1329370 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-576 1321908 1322870 1323921 "INTPACK" 1325698 T INTPACK (NIL) -7 NIL NIL NIL) (-575 1318806 1321705 1321814 "INT" 1321819 T INT (NIL) -8 NIL NIL NIL) (-574 1318058 1318210 1318418 "INTHERTR" 1318648 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-573 1317497 1317577 1317765 "INTHERAL" 1317972 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-572 1315343 1315786 1316243 "INTHEORY" 1317060 T INTHEORY (NIL) -7 NIL NIL NIL) (-571 1306749 1308370 1310142 "INTG0" 1313695 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-570 1287322 1292112 1296922 "INTFTBL" 1301959 T INTFTBL (NIL) -8 NIL NIL NIL) (-569 1286571 1286709 1286882 "INTFACT" 1287181 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-568 1283998 1284444 1285001 "INTEF" 1286125 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-567 1282365 1283104 1283132 "INTDOM" 1283433 T INTDOM (NIL) -9 NIL 1283640 NIL) (-566 1281734 1281908 1282150 "INTDOM-" 1282155 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-565 1278122 1280050 1280104 "INTCAT" 1280903 NIL INTCAT (NIL T) -9 NIL 1281224 NIL) (-564 1277594 1277697 1277825 "INTBIT" 1278014 T INTBIT (NIL) -7 NIL NIL NIL) (-563 1276293 1276447 1276754 "INTALG" 1277439 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-562 1275776 1275866 1276023 "INTAF" 1276197 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-561 1269119 1275586 1275726 "INTABL" 1275731 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-560 1268452 1268918 1268983 "INT8" 1269017 T INT8 (NIL) -8 NIL NIL 1269062) (-559 1267784 1268250 1268315 "INT64" 1268349 T INT64 (NIL) -8 NIL NIL 1268394) (-558 1267116 1267582 1267647 "INT32" 1267681 T INT32 (NIL) -8 NIL NIL 1267726) (-557 1266448 1266914 1266979 "INT16" 1267013 T INT16 (NIL) -8 NIL NIL 1267058) (-556 1261243 1264009 1264037 "INS" 1264971 T INS (NIL) -9 NIL 1265636 NIL) (-555 1258483 1259254 1260228 "INS-" 1260301 NIL INS- (NIL T) -8 NIL NIL NIL) (-554 1257258 1257485 1257783 "INPSIGN" 1258236 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-553 1256376 1256493 1256690 "INPRODPF" 1257138 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-552 1255270 1255387 1255624 "INPRODFF" 1256256 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-551 1254270 1254422 1254682 "INNMFACT" 1255106 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-550 1253467 1253564 1253752 "INMODGCD" 1254169 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-549 1251975 1252220 1252544 "INFSP" 1253212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-548 1251159 1251276 1251459 "INFPROD0" 1251855 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-547 1248014 1249224 1249739 "INFORM" 1250652 T INFORM (NIL) -8 NIL NIL NIL) (-546 1247624 1247684 1247782 "INFORM1" 1247949 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-545 1247147 1247236 1247350 "INFINITY" 1247530 T INFINITY (NIL) -7 NIL NIL NIL) (-544 1246323 1246867 1246968 "INETCLTS" 1247066 T INETCLTS (NIL) -8 NIL NIL NIL) (-543 1244939 1245189 1245510 "INEP" 1246071 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-542 1244188 1244836 1244901 "INDE" 1244906 NIL INDE (NIL T) -8 NIL NIL NIL) (-541 1243752 1243820 1243937 "INCRMAPS" 1244115 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-540 1242570 1243021 1243227 "INBFILE" 1243566 T INBFILE (NIL) -8 NIL NIL NIL) (-539 1237869 1238806 1239750 "INBFF" 1241658 NIL INBFF (NIL T) -7 NIL NIL NIL) (-538 1236777 1237046 1237074 "INBCON" 1237587 T INBCON (NIL) -9 NIL 1237853 NIL) (-537 1236029 1236252 1236528 "INBCON-" 1236533 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-536 1235508 1235753 1235844 "INAST" 1235958 T INAST (NIL) -8 NIL NIL NIL) (-535 1234935 1235187 1235293 "IMPTAST" 1235422 T IMPTAST (NIL) -8 NIL NIL NIL) (-534 1231381 1234779 1234883 "IMATRIX" 1234888 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-533 1230089 1230212 1230528 "IMATQF" 1231237 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-532 1228309 1228536 1228873 "IMATLIN" 1229845 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-531 1222887 1228233 1228291 "ILIST" 1228296 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-530 1220792 1222747 1222860 "IIARRAY2" 1222865 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-529 1216190 1220703 1220767 "IFF" 1220772 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-528 1215537 1215807 1215923 "IFAST" 1216094 T IFAST (NIL) -8 NIL NIL NIL) (-527 1210532 1214829 1215017 "IFARRAY" 1215394 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-526 1209712 1210436 1210509 "IFAMON" 1210514 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-525 1209296 1209361 1209415 "IEVALAB" 1209622 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-524 1208971 1209039 1209199 "IEVALAB-" 1209204 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-523 1208602 1208885 1208948 "IDPO" 1208953 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-522 1207852 1208491 1208566 "IDPOAMS" 1208571 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-521 1207159 1207741 1207816 "IDPOAM" 1207821 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-520 1206218 1206494 1206547 "IDPC" 1206960 NIL IDPC (NIL T T) -9 NIL 1207109 NIL) (-519 1205687 1206110 1206183 "IDPAM" 1206188 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-518 1205063 1205579 1205652 "IDPAG" 1205657 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-517 1204708 1204899 1204974 "IDENT" 1205008 T IDENT (NIL) -8 NIL NIL NIL) (-516 1200963 1201811 1202706 "IDECOMP" 1203865 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-515 1193800 1194886 1195933 "IDEAL" 1199999 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-514 1192960 1193072 1193272 "ICDEN" 1193684 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-513 1192031 1192440 1192587 "ICARD" 1192833 T ICARD (NIL) -8 NIL NIL NIL) (-512 1190091 1190404 1190809 "IBPTOOLS" 1191708 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-511 1185698 1189711 1189824 "IBITS" 1190010 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-510 1182421 1182997 1183692 "IBATOOL" 1185115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-509 1180200 1180662 1181195 "IBACHIN" 1181956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-508 1178029 1180046 1180149 "IARRAY2" 1180154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-507 1174135 1177955 1178012 "IARRAY1" 1178017 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-506 1168173 1172547 1173028 "IAN" 1173674 T IAN (NIL) -8 NIL NIL NIL) (-505 1167684 1167741 1167914 "IALGFACT" 1168110 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-504 1167212 1167325 1167353 "HYPCAT" 1167560 T HYPCAT (NIL) -9 NIL NIL NIL) (-503 1166750 1166867 1167053 "HYPCAT-" 1167058 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-502 1166345 1166545 1166628 "HOSTNAME" 1166687 T HOSTNAME (NIL) -8 NIL NIL NIL) (-501 1166190 1166227 1166268 "HOMOTOP" 1166273 NIL HOMOTOP (NIL T) -9 NIL 1166306 NIL) (-500 1162822 1164200 1164241 "HOAGG" 1165222 NIL HOAGG (NIL T) -9 NIL 1165901 NIL) (-499 1161416 1161815 1162341 "HOAGG-" 1162346 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-498 1155325 1161009 1161159 "HEXADEC" 1161286 T HEXADEC (NIL) -8 NIL NIL NIL) (-497 1154073 1154295 1154558 "HEUGCD" 1155102 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-496 1153149 1153910 1154040 "HELLFDIV" 1154045 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-495 1151328 1152926 1153014 "HEAP" 1153093 NIL HEAP (NIL T) -8 NIL NIL NIL) (-494 1150591 1150880 1151014 "HEADAST" 1151214 T HEADAST (NIL) -8 NIL NIL NIL) (-493 1144610 1150506 1150568 "HDP" 1150573 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-492 1138509 1144245 1144397 "HDMP" 1144511 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-491 1137833 1137973 1138137 "HB" 1138365 T HB (NIL) -7 NIL NIL NIL) (-490 1131219 1137679 1137783 "HASHTBL" 1137788 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-489 1130695 1130940 1131032 "HASAST" 1131147 T HASAST (NIL) -8 NIL NIL NIL) (-488 1128473 1130317 1130499 "HACKPI" 1130533 T HACKPI (NIL) -8 NIL NIL NIL) (-487 1124141 1128326 1128439 "GTSET" 1128444 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-486 1117556 1124019 1124117 "GSTBL" 1124122 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-485 1109943 1116721 1116977 "GSERIES" 1117356 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-484 1109084 1109501 1109529 "GROUP" 1109732 T GROUP (NIL) -9 NIL 1109866 NIL) (-483 1108450 1108609 1108860 "GROUP-" 1108865 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-482 1106817 1107138 1107525 "GROEBSOL" 1108127 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-481 1105731 1106019 1106070 "GRMOD" 1106599 NIL GRMOD (NIL T T) -9 NIL 1106767 NIL) (-480 1105499 1105535 1105663 "GRMOD-" 1105668 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-479 1100789 1101853 1102853 "GRIMAGE" 1104519 T GRIMAGE (NIL) -8 NIL NIL NIL) (-478 1099255 1099516 1099840 "GRDEF" 1100485 T GRDEF (NIL) -7 NIL NIL NIL) (-477 1098699 1098815 1098956 "GRAY" 1099134 T GRAY (NIL) -7 NIL NIL NIL) (-476 1097886 1098292 1098343 "GRALG" 1098496 NIL GRALG (NIL T T) -9 NIL 1098589 NIL) (-475 1097547 1097620 1097783 "GRALG-" 1097788 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-474 1094324 1097132 1097310 "GPOLSET" 1097454 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-473 1093678 1093735 1093993 "GOSPER" 1094261 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-472 1089410 1090116 1090642 "GMODPOL" 1093377 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-471 1088415 1088599 1088837 "GHENSEL" 1089222 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-470 1082571 1083414 1084434 "GENUPS" 1087499 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-469 1082268 1082319 1082408 "GENUFACT" 1082514 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-468 1081680 1081757 1081922 "GENPGCD" 1082186 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-467 1081154 1081189 1081402 "GENMFACT" 1081639 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-466 1079720 1079977 1080284 "GENEEZ" 1080897 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-465 1073779 1079331 1079493 "GDMP" 1079643 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-464 1063122 1067550 1068656 "GCNAALG" 1072762 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-463 1061449 1062311 1062339 "GCDDOM" 1062594 T GCDDOM (NIL) -9 NIL 1062751 NIL) (-462 1060919 1061046 1061261 "GCDDOM-" 1061266 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-461 1059591 1059776 1060080 "GB" 1060698 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1048207 1050537 1052929 "GBINTERN" 1057282 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-459 1046044 1046336 1046757 "GBF" 1047882 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-458 1044825 1044990 1045257 "GBEUCLID" 1045860 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-457 1044174 1044299 1044448 "GAUSSFAC" 1044696 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-456 1042541 1042843 1043157 "GALUTIL" 1043893 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-455 1040849 1041123 1041447 "GALPOLYU" 1042268 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-454 1038214 1038504 1038911 "GALFACTU" 1040546 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-453 1030020 1031519 1033127 "GALFACT" 1036646 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-452 1027408 1028066 1028094 "FVFUN" 1029250 T FVFUN (NIL) -9 NIL 1029970 NIL) (-451 1026674 1026856 1026884 "FVC" 1027175 T FVC (NIL) -9 NIL 1027358 NIL) (-450 1026317 1026499 1026567 "FUNDESC" 1026626 T FUNDESC (NIL) -8 NIL NIL NIL) (-449 1025932 1026114 1026195 "FUNCTION" 1026269 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-448 1023676 1024254 1024720 "FT" 1025486 T FT (NIL) -8 NIL NIL NIL) (-447 1022467 1022977 1023180 "FTEM" 1023493 T FTEM (NIL) -8 NIL NIL NIL) (-446 1020758 1021047 1021444 "FSUPFACT" 1022158 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-445 1019155 1019444 1019776 "FST" 1020446 T FST (NIL) -8 NIL NIL NIL) (-444 1018354 1018460 1018648 "FSRED" 1019037 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-443 1017053 1017309 1017656 "FSPRMELT" 1018069 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-442 1014359 1014797 1015283 "FSPECF" 1016616 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-441 995661 1004133 1004174 "FS" 1008058 NIL FS (NIL T) -9 NIL 1010347 NIL) (-440 984304 987297 991354 "FS-" 991654 NIL FS- (NIL T T) -8 NIL NIL NIL) (-439 983832 983886 984056 "FSINT" 984245 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-438 982124 982825 983128 "FSERIES" 983611 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-437 981166 981282 981506 "FSCINT" 982004 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-436 977374 980110 980151 "FSAGG" 980521 NIL FSAGG (NIL T) -9 NIL 980780 NIL) (-435 975136 975737 976533 "FSAGG-" 976628 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-434 974178 974321 974548 "FSAGG2" 974989 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-433 971856 972136 972684 "FS2UPS" 973896 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-432 971490 971533 971662 "FS2" 971807 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-431 970368 970539 970841 "FS2EXPXP" 971315 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-430 969794 969909 970061 "FRUTIL" 970248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-429 961207 965289 966647 "FR" 968468 NIL FR (NIL T) -8 NIL NIL NIL) (-428 956221 958896 958936 "FRNAALG" 960256 NIL FRNAALG (NIL T) -9 NIL 960854 NIL) (-427 951894 952970 954245 "FRNAALG-" 954995 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-426 951532 951575 951702 "FRNAAF2" 951845 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-425 949907 950381 950677 "FRMOD" 951344 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-424 947650 948282 948600 "FRIDEAL" 949698 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-423 946841 946928 947219 "FRIDEAL2" 947557 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-422 945974 946388 946429 "FRETRCT" 946434 NIL FRETRCT (NIL T) -9 NIL 946610 NIL) (-421 945086 945317 945668 "FRETRCT-" 945673 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-420 942174 943384 943443 "FRAMALG" 944325 NIL FRAMALG (NIL T T) -9 NIL 944617 NIL) (-419 940308 940763 941393 "FRAMALG-" 941616 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-418 934138 939781 940058 "FRAC" 940063 NIL FRAC (NIL T) -8 NIL NIL NIL) (-417 933774 933831 933938 "FRAC2" 934075 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-416 933410 933467 933574 "FR2" 933711 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-415 927923 930816 930844 "FPS" 931963 T FPS (NIL) -9 NIL 932520 NIL) (-414 927372 927481 927645 "FPS-" 927791 NIL FPS- (NIL T) -8 NIL NIL NIL) (-413 924674 926343 926371 "FPC" 926596 T FPC (NIL) -9 NIL 926738 NIL) (-412 924467 924507 924604 "FPC-" 924609 NIL FPC- (NIL T) -8 NIL NIL NIL) (-411 923257 923955 923996 "FPATMAB" 924001 NIL FPATMAB (NIL T) -9 NIL 924153 NIL) (-410 921496 921999 922346 "FPARFRAC" 922973 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-409 916890 917388 918070 "FORTRAN" 920928 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-408 914606 915106 915645 "FORT" 916371 T FORT (NIL) -7 NIL NIL NIL) (-407 912282 912844 912872 "FORTFN" 913932 T FORTFN (NIL) -9 NIL 914556 NIL) (-406 912046 912096 912124 "FORTCAT" 912183 T FORTCAT (NIL) -9 NIL 912245 NIL) (-405 910152 910662 911052 "FORMULA" 911676 T FORMULA (NIL) -8 NIL NIL NIL) (-404 909940 909970 910039 "FORMULA1" 910116 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-403 909463 909515 909688 "FORDER" 909882 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-402 908559 908723 908916 "FOP" 909290 T FOP (NIL) -7 NIL NIL NIL) (-401 907140 907839 908013 "FNLA" 908441 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-400 905869 906284 906312 "FNCAT" 906772 T FNCAT (NIL) -9 NIL 907032 NIL) (-399 905408 905828 905856 "FNAME" 905861 T FNAME (NIL) -8 NIL NIL NIL) (-398 903971 904934 904962 "FMTC" 904967 T FMTC (NIL) -9 NIL 905003 NIL) (-397 902717 903907 903953 "FMONOID" 903958 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-396 899545 900713 900754 "FMONCAT" 901971 NIL FMONCAT (NIL T) -9 NIL 902576 NIL) (-395 898737 899287 899436 "FM" 899441 NIL FM (NIL T T) -8 NIL NIL NIL) (-394 896161 896807 896835 "FMFUN" 897979 T FMFUN (NIL) -9 NIL 898687 NIL) (-393 895430 895611 895639 "FMC" 895929 T FMC (NIL) -9 NIL 896111 NIL) (-392 892509 893369 893423 "FMCAT" 894618 NIL FMCAT (NIL T T) -9 NIL 895113 NIL) (-391 891375 892275 892375 "FM1" 892454 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-390 889149 889565 890059 "FLOATRP" 890926 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-389 882727 886878 887499 "FLOAT" 888548 T FLOAT (NIL) -8 NIL NIL NIL) (-388 880165 880665 881243 "FLOATCP" 882194 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-387 879012 879771 879812 "FLINEXP" 879817 NIL FLINEXP (NIL T) -9 NIL 879910 NIL) (-386 877944 878241 878649 "FLINEXP-" 878654 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-385 877020 877164 877388 "FLASORT" 877796 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-384 874136 875004 875056 "FLALG" 876283 NIL FLALG (NIL T T) -9 NIL 876750 NIL) (-383 867840 871592 871633 "FLAGG" 872895 NIL FLAGG (NIL T) -9 NIL 873547 NIL) (-382 866566 866905 867395 "FLAGG-" 867400 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-381 865608 865751 865978 "FLAGG2" 866419 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-380 862459 863467 863526 "FINRALG" 864654 NIL FINRALG (NIL T T) -9 NIL 865162 NIL) (-379 861619 861848 862187 "FINRALG-" 862192 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-378 860999 861238 861266 "FINITE" 861462 T FINITE (NIL) -9 NIL 861569 NIL) (-377 853356 855543 855583 "FINAALG" 859250 NIL FINAALG (NIL T) -9 NIL 860703 NIL) (-376 848688 849738 850882 "FINAALG-" 852261 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-375 848056 848443 848546 "FILE" 848618 NIL FILE (NIL T) -8 NIL NIL NIL) (-374 846714 847052 847106 "FILECAT" 847790 NIL FILECAT (NIL T T) -9 NIL 848006 NIL) (-373 844430 845958 845986 "FIELD" 846026 T FIELD (NIL) -9 NIL 846106 NIL) (-372 843050 843435 843946 "FIELD-" 843951 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-371 840900 841685 842032 "FGROUP" 842736 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-370 839990 840154 840374 "FGLMICPK" 840732 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-369 835822 839915 839972 "FFX" 839977 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-368 835423 835484 835619 "FFSLPE" 835755 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-367 831413 832195 832991 "FFPOLY" 834659 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-366 830917 830953 831162 "FFPOLY2" 831371 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-365 826763 830836 830899 "FFP" 830904 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-364 822161 826674 826738 "FF" 826743 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-363 817287 821504 821694 "FFNBX" 822015 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-362 812215 816422 816680 "FFNBP" 817141 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-361 806848 811499 811710 "FFNB" 812048 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-360 805680 805878 806193 "FFINTBAS" 806645 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-359 801706 803927 803955 "FFIELDC" 804575 T FFIELDC (NIL) -9 NIL 804951 NIL) (-358 800368 800739 801236 "FFIELDC-" 801241 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-357 799937 799983 800107 "FFHOM" 800310 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-356 797632 798119 798636 "FFF" 799452 NIL FFF (NIL T) -7 NIL NIL NIL) (-355 793250 797374 797475 "FFCGX" 797575 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-354 788872 792982 793089 "FFCGP" 793193 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-353 784055 788599 788707 "FFCG" 788808 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-352 763736 773731 773817 "FFCAT" 778982 NIL FFCAT (NIL T T T) -9 NIL 780433 NIL) (-351 758933 759981 761295 "FFCAT-" 762525 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-350 758344 758387 758622 "FFCAT2" 758884 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-349 747667 751316 752536 "FEXPR" 757196 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-348 746629 747064 747105 "FEVALAB" 747189 NIL FEVALAB (NIL T) -9 NIL 747450 NIL) (-347 745788 745998 746336 "FEVALAB-" 746341 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-346 744354 745171 745374 "FDIV" 745687 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 741374 742115 742230 "FDIVCAT" 743798 NIL FDIVCAT (NIL T T T T) -9 NIL 744235 NIL) (-344 741136 741163 741333 "FDIVCAT-" 741338 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-343 740356 740443 740720 "FDIV2" 741043 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-342 739330 739651 739853 "FCTRDATA" 740174 T FCTRDATA (NIL) -8 NIL NIL NIL) (-341 738016 738275 738564 "FCPAK1" 739061 T FCPAK1 (NIL) -7 NIL NIL NIL) (-340 737115 737516 737657 "FCOMP" 737907 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-339 720820 724265 727803 "FC" 733597 T FC (NIL) -8 NIL NIL NIL) (-338 713099 717127 717167 "FAXF" 718969 NIL FAXF (NIL T) -9 NIL 719661 NIL) (-337 710376 711033 711858 "FAXF-" 712323 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-336 705428 709752 709928 "FARRAY" 710233 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-335 700322 702389 702442 "FAMR" 703465 NIL FAMR (NIL T T) -9 NIL 703925 NIL) (-334 699212 699514 699949 "FAMR-" 699954 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-333 698381 699134 699187 "FAMONOID" 699192 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-332 696167 696877 696930 "FAMONC" 697871 NIL FAMONC (NIL T T) -9 NIL 698257 NIL) (-331 694831 695921 696058 "FAGROUP" 696063 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-330 692626 692945 693348 "FACUTIL" 694512 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-329 691725 691910 692132 "FACTFUNC" 692436 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-328 684147 691028 691227 "EXPUPXS" 691581 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-327 681630 682170 682756 "EXPRTUBE" 683581 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-326 677901 678493 679223 "EXPRODE" 680969 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-325 663620 676550 676979 "EXPR" 677505 NIL EXPR (NIL T) -8 NIL NIL NIL) (-324 658174 658761 659567 "EXPR2UPS" 662918 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-323 657806 657863 657972 "EXPR2" 658111 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-322 649059 656957 657248 "EXPEXPAN" 657642 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-321 648859 649016 649045 "EXIT" 649050 T EXIT (NIL) -8 NIL NIL NIL) (-320 648339 648583 648674 "EXITAST" 648788 T EXITAST (NIL) -8 NIL NIL NIL) (-319 647966 648028 648141 "EVALCYC" 648271 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-318 647507 647625 647666 "EVALAB" 647836 NIL EVALAB (NIL T) -9 NIL 647940 NIL) (-317 646988 647110 647331 "EVALAB-" 647336 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-316 644356 645658 645686 "EUCDOM" 646241 T EUCDOM (NIL) -9 NIL 646591 NIL) (-315 642761 643203 643793 "EUCDOM-" 643798 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-314 630300 633059 635809 "ESTOOLS" 640031 T ESTOOLS (NIL) -7 NIL NIL NIL) (-313 629932 629989 630098 "ESTOOLS2" 630237 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-312 629683 629725 629805 "ESTOOLS1" 629884 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-311 623720 625328 625356 "ES" 628124 T ES (NIL) -9 NIL 629534 NIL) (-310 618667 619954 621771 "ES-" 621935 NIL ES- (NIL T) -8 NIL NIL NIL) (-309 615041 615802 616582 "ESCONT" 617907 T ESCONT (NIL) -7 NIL NIL NIL) (-308 614786 614818 614900 "ESCONT1" 615003 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-307 614461 614511 614611 "ES2" 614730 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-306 614091 614149 614258 "ES1" 614397 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-305 613307 613436 613612 "ERROR" 613935 T ERROR (NIL) -7 NIL NIL NIL) (-304 606699 613166 613257 "EQTBL" 613262 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-303 599202 602013 603462 "EQ" 605283 NIL -3091 (NIL T) -8 NIL NIL NIL) (-302 598834 598891 599000 "EQ2" 599139 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-301 594125 595172 596265 "EP" 597773 NIL EP (NIL T) -7 NIL NIL NIL) (-300 592725 593016 593322 "ENV" 593839 T ENV (NIL) -8 NIL NIL NIL) (-299 591819 592373 592401 "ENTIRER" 592406 T ENTIRER (NIL) -9 NIL 592452 NIL) (-298 588513 590001 590362 "EMR" 591627 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-297 587643 587828 587882 "ELTAGG" 588262 NIL ELTAGG (NIL T T) -9 NIL 588473 NIL) (-296 587362 587424 587565 "ELTAGG-" 587570 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-295 587126 587155 587209 "ELTAB" 587293 NIL ELTAB (NIL T T) -9 NIL 587345 NIL) (-294 586252 586398 586597 "ELFUTS" 586977 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-293 585994 586050 586078 "ELEMFUN" 586183 T ELEMFUN (NIL) -9 NIL NIL NIL) (-292 585864 585885 585953 "ELEMFUN-" 585958 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-291 580678 583934 583975 "ELAGG" 584915 NIL ELAGG (NIL T) -9 NIL 585378 NIL) (-290 578963 579397 580060 "ELAGG-" 580065 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-289 578275 578412 578568 "ELABOR" 578827 T ELABOR (NIL) -8 NIL NIL NIL) (-288 576936 577215 577509 "ELABEXPR" 578001 T ELABEXPR (NIL) -8 NIL NIL NIL) (-287 569770 571573 572402 "EFUPXS" 576211 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-286 563218 565019 565830 "EFULS" 569045 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-285 560703 561061 561533 "EFSTRUC" 562850 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-284 550494 552060 553608 "EF" 559218 NIL EF (NIL T T) -7 NIL NIL NIL) (-283 549568 549979 550128 "EAB" 550365 T EAB (NIL) -8 NIL NIL NIL) (-282 548750 549527 549555 "E04UCFA" 549560 T E04UCFA (NIL) -8 NIL NIL NIL) (-281 547932 548709 548737 "E04NAFA" 548742 T E04NAFA (NIL) -8 NIL NIL NIL) (-280 547114 547891 547919 "E04MBFA" 547924 T E04MBFA (NIL) -8 NIL NIL NIL) (-279 546296 547073 547101 "E04JAFA" 547106 T E04JAFA (NIL) -8 NIL NIL NIL) (-278 545480 546255 546283 "E04GCFA" 546288 T E04GCFA (NIL) -8 NIL NIL NIL) (-277 544664 545439 545467 "E04FDFA" 545472 T E04FDFA (NIL) -8 NIL NIL NIL) (-276 543846 544623 544651 "E04DGFA" 544656 T E04DGFA (NIL) -8 NIL NIL NIL) (-275 538019 539371 540735 "E04AGNT" 542502 T E04AGNT (NIL) -7 NIL NIL NIL) (-274 536790 537333 537373 "DVARCAT" 537714 NIL DVARCAT (NIL T) -9 NIL 537877 NIL) (-273 535994 536206 536520 "DVARCAT-" 536525 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-272 529042 535793 535922 "DSMP" 535927 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-271 527465 528184 528225 "DSEXT" 528588 NIL DSEXT (NIL T) -9 NIL 528882 NIL) (-270 525750 526178 526844 "DSEXT-" 526849 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-269 520531 521695 522763 "DROPT" 524702 T DROPT (NIL) -8 NIL NIL NIL) (-268 520196 520255 520353 "DROPT1" 520466 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-267 515311 516437 517574 "DROPT0" 519079 T DROPT0 (NIL) -7 NIL NIL NIL) (-266 513656 513981 514367 "DRAWPT" 514945 T DRAWPT (NIL) -7 NIL NIL NIL) (-265 508243 509166 510245 "DRAW" 512630 NIL DRAW (NIL T) -7 NIL NIL NIL) (-264 507876 507929 508047 "DRAWHACK" 508184 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-263 506607 506876 507167 "DRAWCX" 507605 T DRAWCX (NIL) -7 NIL NIL NIL) (-262 506122 506191 506342 "DRAWCURV" 506533 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-261 496590 498552 500667 "DRAWCFUN" 504027 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-260 493354 495283 495324 "DQAGG" 495953 NIL DQAGG (NIL T) -9 NIL 496227 NIL) (-259 481006 487565 487648 "DPOLCAT" 489500 NIL DPOLCAT (NIL T T T T) -9 NIL 490045 NIL) (-258 475843 477191 479149 "DPOLCAT-" 479154 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-257 469425 475704 475802 "DPMO" 475807 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-256 462910 469205 469372 "DPMM" 469377 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-255 462480 462694 462783 "DOMTMPLT" 462841 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-254 461913 462282 462362 "DOMCTOR" 462420 T DOMCTOR (NIL) -8 NIL NIL NIL) (-253 461125 461393 461544 "DOMAIN" 461782 T DOMAIN (NIL) -8 NIL NIL NIL) (-252 455024 460760 460912 "DMP" 461026 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-251 454624 454680 454824 "DLP" 454962 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 448446 453951 454141 "DLIST" 454466 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 445243 447299 447340 "DLAGG" 447890 NIL DLAGG (NIL T) -9 NIL 448120 NIL) (-248 443919 444583 444611 "DIVRING" 444703 T DIVRING (NIL) -9 NIL 444786 NIL) (-247 443156 443346 443646 "DIVRING-" 443651 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 441258 441615 442021 "DISPLAY" 442770 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 435297 441172 441235 "DIRPROD" 441240 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 434145 434348 434613 "DIRPROD2" 435090 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 423073 428931 428984 "DIRPCAT" 429242 NIL DIRPCAT (NIL NIL T) -9 NIL 430117 NIL) (-242 420177 420881 421842 "DIRPCAT-" 422179 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 419464 419624 419810 "DIOSP" 420011 T DIOSP (NIL) -7 NIL NIL NIL) (-240 416119 418376 418417 "DIOPS" 418851 NIL DIOPS (NIL T) -9 NIL 419080 NIL) (-239 415668 415782 415973 "DIOPS-" 415978 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 414719 415347 415375 "DIFRING" 415380 T DIFRING (NIL) -9 NIL 415402 NIL) (-237 414391 414465 414493 "DIFFSPC" 414612 T DIFFSPC (NIL) -9 NIL 414687 NIL) (-236 414036 414114 414266 "DIFFSPC-" 414271 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 413192 413670 413710 "DIFFMOD" 413715 NIL DIFFMOD (NIL T) -9 NIL 413742 NIL) (-234 412900 412945 412986 "DIFFDOM" 413107 NIL DIFFDOM (NIL T) -9 NIL 413175 NIL) (-233 412753 412777 412861 "DIFFDOM-" 412866 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 410685 411957 411998 "DIFEXT" 412003 NIL DIFEXT (NIL T) -9 NIL 412156 NIL) (-231 407960 410217 410258 "DIAGG" 410263 NIL DIAGG (NIL T) -9 NIL 410283 NIL) (-230 407344 407501 407753 "DIAGG-" 407758 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 402761 406303 406580 "DHMATRIX" 407113 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 398373 399282 400292 "DFSFUN" 401771 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 393453 397304 397616 "DFLOAT" 398081 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 391716 391997 392386 "DFINTTLS" 393161 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 388745 389737 390137 "DERHAM" 391382 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 386546 388520 388609 "DEQUEUE" 388689 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 385800 385933 386116 "DEGRED" 386408 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 382230 382975 383821 "DEFINTRF" 385028 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 379785 380254 380846 "DEFINTEF" 381749 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 379135 379405 379520 "DEFAST" 379690 T DEFAST (NIL) -8 NIL NIL NIL) (-219 373044 378728 378878 "DECIMAL" 379005 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 370556 371014 371520 "DDFACT" 372588 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 370152 370195 370346 "DBLRESP" 370507 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 368020 368382 368743 "DBASE" 369918 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 367262 367500 367646 "DATAARY" 367919 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 366368 367221 367249 "D03FAFA" 367254 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 365475 366327 366355 "D03EEFA" 366360 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 363425 363891 364380 "D03AGNT" 365006 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 362714 363384 363412 "D02EJFA" 363417 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 362003 362673 362701 "D02CJFA" 362706 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 361292 361962 361990 "D02BHFA" 361995 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 360581 361251 361279 "D02BBFA" 361284 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 353778 355367 356973 "D02AGNT" 358995 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 351546 352069 352615 "D01WGTS" 353252 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 350613 351505 351533 "D01TRNS" 351538 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 349681 350572 350600 "D01GBFA" 350605 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 348749 349640 349668 "D01FCFA" 349673 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 347817 348708 348736 "D01ASFA" 348741 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 346885 347776 347804 "D01AQFA" 347809 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 345953 346844 346872 "D01APFA" 346877 T D01APFA (NIL) -8 NIL NIL NIL) (-199 345021 345912 345940 "D01ANFA" 345945 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 344089 344980 345008 "D01AMFA" 345013 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 343157 344048 344076 "D01ALFA" 344081 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 342225 343116 343144 "D01AKFA" 343149 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 341293 342184 342212 "D01AJFA" 342217 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 334588 336141 337702 "D01AGNT" 339752 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 333925 334053 334205 "CYCLOTOM" 334456 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 330658 331373 332100 "CYCLES" 333218 T CYCLES (NIL) -7 NIL NIL NIL) (-191 329970 330104 330275 "CVMP" 330519 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 327811 328069 328438 "CTRIGMNP" 329698 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 327247 327605 327678 "CTOR" 327758 T CTOR (NIL) -8 NIL NIL NIL) (-188 326756 326978 327079 "CTORKIND" 327166 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 326047 326363 326391 "CTORCAT" 326573 T CTORCAT (NIL) -9 NIL 326686 NIL) (-186 325645 325756 325915 "CTORCAT-" 325920 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 325107 325319 325427 "CTORCALL" 325569 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 324481 324580 324733 "CSTTOOLS" 325004 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 320280 320937 321695 "CRFP" 323793 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 319755 320001 320093 "CRCEAST" 320208 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 318802 318987 319215 "CRAPACK" 319559 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 318186 318287 318491 "CPMATCH" 318678 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 317911 317939 318045 "CPIMA" 318152 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 314259 314931 315650 "COORDSYS" 317246 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 313671 313792 313934 "CONTOUR" 314137 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 309562 311674 312166 "CONTFRAC" 313211 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 309442 309463 309491 "CONDUIT" 309528 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 308530 309084 309112 "COMRING" 309117 T COMRING (NIL) -9 NIL 309169 NIL) (-173 307584 307888 308072 "COMPPROP" 308366 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 307245 307280 307408 "COMPLPAT" 307543 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 296735 307054 307163 "COMPLEX" 307168 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 296371 296428 296535 "COMPLEX2" 296672 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 295710 295831 295991 "COMPILER" 296231 T COMPILER (NIL) -8 NIL NIL NIL) (-168 295428 295463 295561 "COMPFACT" 295669 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 277894 289132 289172 "COMPCAT" 290176 NIL COMPCAT (NIL T) -9 NIL 291524 NIL) (-166 267184 270173 273880 "COMPCAT-" 274236 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 266913 266941 267044 "COMMUPC" 267150 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 266707 266741 266800 "COMMONOP" 266874 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 266263 266458 266545 "COMM" 266640 T COMM (NIL) -8 NIL NIL NIL) (-162 265839 266067 266142 "COMMAAST" 266208 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 265088 265282 265310 "COMBOPC" 265648 T COMBOPC (NIL) -9 NIL 265823 NIL) (-160 263984 264194 264436 "COMBINAT" 264878 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 260441 261015 261642 "COMBF" 263406 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 259199 259557 259792 "COLOR" 260226 T COLOR (NIL) -8 NIL NIL NIL) (-157 258675 258920 259012 "COLONAST" 259127 T COLONAST (NIL) -8 NIL NIL NIL) (-156 258315 258362 258487 "CMPLXRT" 258622 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 257763 258015 258114 "CLLCTAST" 258236 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 253265 254293 255373 "CLIP" 256703 T CLIP (NIL) -7 NIL NIL NIL) (-153 251606 252366 252606 "CLIF" 253092 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 247781 249752 249793 "CLAGG" 250722 NIL CLAGG (NIL T) -9 NIL 251258 NIL) (-151 246203 246660 247243 "CLAGG-" 247248 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 245747 245832 245972 "CINTSLPE" 246112 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 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T) ((-628 $) -3739 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -3739 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-576))))) ((-234 $) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1131)) ((-300) -3739 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1196) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1196) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -3739 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -3739 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -3739 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-862) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1196)) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-915 (-1196)) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-917 #4#) -3739 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1196))))) ((-899 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576)))) ((-897 |#2|) |has| |#1| (-374)) ((-926) -12 (|has| |#1| (-374)) (|has| |#2| (-926))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1196)))) ((-1057 |#2|) . T) ((-1070 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -3739 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -3739 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -3739 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1222) |has| |#1| (-38 (-419 (-576)))) ((-1225) |has| |#1| (-38 (-419 (-576)))) ((-1237) . T) ((-1241) |has| |#1| (-374)) ((-1247 |#1|) . T) ((-1265 |#1| #0#) . T)) 
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+NIL 
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+NIL 
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+NIL 
+NIL 
+NIL 
+NIL 
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T T) -9 NIL 3229449 NIL) (-1307 3224001 3226142 3226530 "XPBWPOLY" 3227283 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1306 3219696 3221991 3222033 "XF" 3222654 NIL XF (NIL T) -9 NIL 3223054 NIL) (-1305 3219317 3219405 3219574 "XF-" 3219579 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1304 3214513 3215802 3215857 "XFALG" 3218029 NIL XFALG (NIL T T) -9 NIL 3218818 NIL) (-1303 3213646 3213750 3213955 "XEXPPKG" 3214405 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1302 3211755 3213496 3213592 "XDPOLY" 3213597 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1301 3210562 3211162 3211205 "XALG" 3211210 NIL XALG (NIL T) -9 NIL 3211321 NIL) (-1300 3204004 3208539 3209033 "WUTSET" 3210154 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1299 3202260 3203056 3203379 "WP" 3203815 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1298 3201862 3202082 3202152 "WHILEAST" 3202212 T WHILEAST (NIL) -8 NIL NIL NIL) (-1297 3201334 3201579 3201673 "WHEREAST" 3201790 T WHEREAST (NIL) -8 NIL NIL NIL) (-1296 3200220 3200418 3200713 "WFFINTBS" 3201131 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1295 3198124 3198551 3199013 "WEIER" 3199792 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1294 3197170 3197620 3197662 "VSPACE" 3197798 NIL VSPACE (NIL T) -9 NIL 3197872 NIL) (-1293 3197008 3197035 3197126 "VSPACE-" 3197131 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1292 3196817 3196859 3196927 "VOID" 3196962 T VOID (NIL) -8 NIL NIL NIL) (-1291 3194953 3195312 3195718 "VIEW" 3196433 T VIEW (NIL) -7 NIL NIL NIL) (-1290 3191377 3192016 3192753 "VIEWDEF" 3194238 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1289 3180681 3182925 3185098 "VIEW3D" 3189226 T VIEW3D (NIL) -8 NIL NIL NIL) (-1288 3172932 3174592 3176171 "VIEW2D" 3179124 T VIEW2D (NIL) -8 NIL NIL NIL) (-1287 3168285 3172702 3172794 "VECTOR" 3172875 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1286 3166862 3167121 3167439 "VECTOR2" 3168015 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1285 3160304 3164613 3164656 "VECTCAT" 3165651 NIL VECTCAT (NIL T) -9 NIL 3166238 NIL) (-1284 3159318 3159572 3159962 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(NIL T T) -8 NIL NIL NIL) (-1249 2988248 3000373 3000435 "ULSCCAT" 3001073 NIL ULSCCAT (NIL T T) -9 NIL 3001362 NIL) (-1248 2987298 2987543 2987931 "ULSCCAT-" 2987936 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1247 2976362 2982845 2982888 "ULSCAT" 2983751 NIL ULSCAT (NIL T) -9 NIL 2984482 NIL) (-1246 2975792 2975871 2976050 "ULS2" 2976277 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1245 2974911 2975421 2975528 "UINT8" 2975639 T UINT8 (NIL) -8 NIL NIL 2975724) (-1244 2974029 2974539 2974646 "UINT64" 2974757 T UINT64 (NIL) -8 NIL NIL 2974842) (-1243 2973147 2973657 2973764 "UINT32" 2973875 T UINT32 (NIL) -8 NIL NIL 2973960) (-1242 2972265 2972775 2972882 "UINT16" 2972993 T UINT16 (NIL) -8 NIL NIL 2973078) (-1241 2970568 2971525 2971555 "UFD" 2971767 T UFD (NIL) -9 NIL 2971881 NIL) (-1240 2970362 2970408 2970503 "UFD-" 2970508 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1239 2969444 2969627 2969843 "UDVO" 2970168 T UDVO (NIL) -7 NIL NIL NIL) (-1238 2967260 2967669 2968140 "UDPO" 2969008 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1237 2967193 2967198 2967228 "TYPE" 2967233 T TYPE (NIL) -9 NIL NIL NIL) (-1236 2966953 2967148 2967179 "TYPEAST" 2967184 T TYPEAST (NIL) -8 NIL NIL NIL) (-1235 2965924 2966126 2966366 "TWOFACT" 2966747 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1234 2964947 2965333 2965568 "TUPLE" 2965724 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1233 2962638 2963157 2963696 "TUBETOOL" 2964430 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1232 2961487 2961692 2961933 "TUBE" 2962431 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1231 2956216 2960459 2960742 "TS" 2961239 NIL TS (NIL T) -8 NIL NIL NIL) (-1230 2944856 2948975 2949072 "TSETCAT" 2954341 NIL TSETCAT (NIL T T T T) -9 NIL 2955872 NIL) (-1229 2939588 2941188 2943079 "TSETCAT-" 2943084 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1228 2934227 2935074 2936003 "TRMANIP" 2938724 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1227 2933668 2933731 2933894 "TRIMAT" 2934159 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1226 2931534 2931771 2932128 "TRIGMNIP" 2933417 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1225 2931054 2931167 2931197 "TRIGCAT" 2931410 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1224 2930723 2930802 2930943 "TRIGCAT-" 2930948 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1223 2927568 2929581 2929862 "TREE" 2930477 NIL TREE (NIL T) -8 NIL NIL NIL) (-1222 2926842 2927370 2927400 "TRANFUN" 2927435 T TRANFUN (NIL) -9 NIL 2927501 NIL) (-1221 2926121 2926312 2926592 "TRANFUN-" 2926597 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1220 2925925 2925957 2926018 "TOPSP" 2926082 T TOPSP (NIL) -7 NIL NIL NIL) (-1219 2925273 2925388 2925542 "TOOLSIGN" 2925806 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1218 2923907 2924450 2924689 "TEXTFILE" 2925056 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1217 2921819 2922360 2922789 "TEX" 2923500 T TEX (NIL) -8 NIL NIL NIL) (-1216 2921600 2921631 2921703 "TEX1" 2921782 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1215 2921248 2921311 2921401 "TEMUTL" 2921532 T TEMUTL (NIL) -7 NIL NIL NIL) (-1214 2919402 2919682 2920007 "TBCMPPK" 2920971 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1213 2911179 2917562 2917618 "TBAGG" 2918018 NIL TBAGG (NIL T T) -9 NIL 2918229 NIL) (-1212 2906249 2907737 2909491 "TBAGG-" 2909496 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1211 2905633 2905740 2905885 "TANEXP" 2906138 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1210 2905144 2905408 2905498 "TALGOP" 2905578 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1209 2898534 2905001 2905094 "TABLE" 2905099 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1208 2897946 2898045 2898183 "TABLEAU" 2898431 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1207 2892554 2893774 2895022 "TABLBUMP" 2896732 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1206 2891776 2891923 2892104 "SYSTEM" 2892395 T SYSTEM (NIL) -8 NIL NIL NIL) (-1205 2888235 2888934 2889717 "SYSSOLP" 2891027 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1204 2888033 2888190 2888221 "SYSPTR" 2888226 T SYSPTR (NIL) -8 NIL NIL NIL) (-1203 2887069 2887574 2887693 "SYSNNI" 2887879 NIL SYSNNI (NIL NIL) -8 NIL NIL 2887964) (-1202 2886368 2886827 2886906 "SYSINT" 2886966 NIL SYSINT (NIL NIL) -8 NIL NIL 2887011) (-1201 2882700 2883646 2884356 "SYNTAX" 2885680 T SYNTAX (NIL) -8 NIL NIL NIL) (-1200 2879858 2880460 2881092 "SYMTAB" 2882090 T SYMTAB (NIL) -8 NIL NIL NIL) (-1199 2875107 2876009 2876992 "SYMS" 2878897 T SYMS (NIL) -8 NIL NIL NIL) (-1198 2872342 2874565 2874795 "SYMPOLY" 2874912 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1197 2871859 2871934 2872057 "SYMFUNC" 2872254 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1196 2867879 2869171 2869984 "SYMBOL" 2871068 T SYMBOL (NIL) -8 NIL NIL NIL) (-1195 2861418 2863107 2864827 "SWITCH" 2866181 T SWITCH (NIL) -8 NIL NIL NIL) (-1194 2854762 2860374 2860668 "SUTS" 2861182 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2846938 2854144 2854408 "SUPXS" 2854556 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2838608 2846556 2846682 "SUP" 2846847 NIL SUP (NIL T) -8 NIL NIL NIL) (-1191 2837767 2837894 2838111 "SUPFRACF" 2838476 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1190 2837388 2837447 2837560 "SUP2" 2837702 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1189 2835836 2836110 2836466 "SUMRF" 2837087 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1188 2835171 2835237 2835429 "SUMFS" 2835757 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1187 2818245 2834483 2834725 "SULS" 2834987 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1186 2817847 2818067 2818137 "SUCHTAST" 2818197 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1185 2817142 2817372 2817512 "SUCH" 2817755 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1184 2811009 2812048 2813007 "SUBSPACE" 2816230 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1183 2810439 2810529 2810693 "SUBRESP" 2810897 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1182 2803807 2805104 2806415 "STTF" 2809175 NIL STTF (NIL T) -7 NIL NIL NIL) (-1181 2797980 2799100 2800247 "STTFNC" 2802707 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1180 2789293 2791162 2792956 "STTAYLOR" 2796221 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1179 2782423 2789157 2789240 "STRTBL" 2789245 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1178 2777787 2782378 2782409 "STRING" 2782414 T STRING (NIL) -8 NIL NIL NIL) (-1177 2772616 2777130 2777160 "STRICAT" 2777219 T STRICAT (NIL) -9 NIL 2777281 NIL) (-1176 2765369 2770235 2770846 "STREAM" 2772040 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2764879 2764956 2765100 "STREAM3" 2765286 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2763861 2764044 2764279 "STREAM2" 2764692 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2763549 2763601 2763694 "STREAM1" 2763803 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2762565 2762746 2762977 "STINPROD" 2763365 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2762117 2762327 2762357 "STEP" 2762437 T STEP (NIL) -9 NIL 2762515 NIL) (-1170 2761304 2761606 2761754 "STEPAST" 2761991 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2754736 2761203 2761280 "STBL" 2761285 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2749831 2753927 2753970 "STAGG" 2754123 NIL STAGG (NIL T) -9 NIL 2754212 NIL) (-1167 2747533 2748135 2749007 "STAGG-" 2749012 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2745680 2747303 2747395 "STACK" 2747476 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2738375 2743821 2744277 "SREGSET" 2745310 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2730800 2732169 2733682 "SRDCMPK" 2736981 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2723685 2728210 2728240 "SRAGG" 2729543 T SRAGG (NIL) -9 NIL 2730151 NIL) (-1162 2722702 2722957 2723336 "SRAGG-" 2723341 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2717073 2721649 2722070 "SQMATRIX" 2722328 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2710758 2713791 2714518 "SPLTREE" 2716418 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2706721 2707414 2708060 "SPLNODE" 2710184 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2705768 2706001 2706031 "SPFCAT" 2706475 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2704505 2704715 2704979 "SPECOUT" 2705526 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2695615 2697487 2697517 "SPADXPT" 2702193 T SPADXPT (NIL) -9 NIL 2704357 NIL) (-1155 2695376 2695416 2695485 "SPADPRSR" 2695568 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2693425 2695331 2695362 "SPADAST" 2695367 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2685370 2687143 2687186 "SPACEC" 2691559 NIL SPACEC (NIL T) -9 NIL 2693375 NIL) (-1152 2683500 2685302 2685351 "SPACE3" 2685356 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2682252 2682423 2682714 "SORTPAK" 2683305 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2680344 2680647 2681059 "SOLVETRA" 2681916 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2679394 2679616 2679877 "SOLVESER" 2680117 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2674698 2675586 2676581 "SOLVERAD" 2678446 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2670513 2671122 2671851 "SOLVEFOR" 2674065 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2664783 2669862 2669959 "SNTSCAT" 2669964 NIL SNTSCAT (NIL T T T T) -9 NIL 2670034 NIL) (-1145 2658889 2663106 2663497 "SMTS" 2664473 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2653485 2658777 2658854 "SMP" 2658859 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2651644 2651945 2652343 "SMITH" 2653182 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2643935 2648223 2648326 "SMATCAT" 2649677 NIL SMATCAT (NIL NIL T T T) -9 NIL 2650227 NIL) (-1141 2640653 2641538 2642796 "SMATCAT-" 2642801 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2638319 2639889 2639932 "SKAGG" 2640193 NIL SKAGG (NIL T) -9 NIL 2640328 NIL) (-1139 2634595 2637792 2637976 "SINT" 2638128 T SINT (NIL) -8 NIL NIL 2638290) (-1138 2634367 2634405 2634471 "SIMPAN" 2634551 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2633646 2633902 2634042 "SIG" 2634249 T SIG (NIL) -8 NIL NIL NIL) (-1136 2632484 2632705 2632980 "SIGNRF" 2633405 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2631317 2631468 2631752 "SIGNEF" 2632313 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2630623 2630900 2631024 "SIGAST" 2631215 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2628313 2628767 2629273 "SHP" 2630164 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2622318 2628214 2628290 "SHDP" 2628295 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2621891 2622083 2622113 "SGROUP" 2622206 T SGROUP (NIL) -9 NIL 2622268 NIL) (-1130 2621749 2621775 2621848 "SGROUP-" 2621853 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2618540 2619238 2619961 "SGCF" 2621048 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2612908 2617987 2618084 "SFRTCAT" 2618089 NIL SFRTCAT (NIL T T T T) -9 NIL 2618128 NIL) (-1127 2606329 2607347 2608483 "SFRGCD" 2611891 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2599455 2600528 2601714 "SFQCMPK" 2605262 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2599075 2599164 2599275 "SFORT" 2599396 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2598193 2598915 2599036 "SEXOF" 2599041 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2597300 2598074 2598142 "SEX" 2598147 T SEX (NIL) -8 NIL NIL NIL) (-1122 2593081 2593796 2593891 "SEXCAT" 2596513 NIL SEXCAT (NIL T T T T T) -9 NIL 2597073 NIL) (-1121 2590234 2593015 2593063 "SET" 2593068 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2588458 2588947 2589252 "SETMN" 2589975 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2587954 2588106 2588136 "SETCAT" 2588312 T SETCAT (NIL) -9 NIL 2588422 NIL) (-1118 2587646 2587724 2587854 "SETCAT-" 2587859 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2584007 2586107 2586150 "SETAGG" 2587020 NIL SETAGG (NIL T) -9 NIL 2587360 NIL) (-1116 2583465 2583581 2583818 "SETAGG-" 2583823 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2582908 2583161 2583262 "SEQAST" 2583386 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2582107 2582401 2582462 "SEGXCAT" 2582748 NIL SEGXCAT (NIL T T) -9 NIL 2582868 NIL) (-1113 2581113 2581773 2581955 "SEG" 2581960 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2580092 2580306 2580349 "SEGCAT" 2580871 NIL SEGCAT (NIL T) -9 NIL 2581092 NIL) (-1111 2579024 2579455 2579663 "SEGBIND" 2579919 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2578645 2578704 2578817 "SEGBIND2" 2578959 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2578218 2578446 2578523 "SEGAST" 2578590 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2577437 2577563 2577767 "SEG2" 2578062 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2576808 2577372 2577419 "SDVAR" 2577424 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2569246 2576578 2576708 "SDPOL" 2576713 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2567839 2568105 2568424 "SCPKG" 2568961 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2567003 2567175 2567367 "SCOPE" 2567669 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2566223 2566357 2566536 "SCACHE" 2566858 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2565869 2566055 2566085 "SASTCAT" 2566090 T SASTCAT (NIL) -9 NIL 2566103 NIL) (-1101 2565356 2565704 2565780 "SAOS" 2565815 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2564921 2564956 2565129 "SAERFFC" 2565315 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2558771 2564818 2564898 "SAE" 2564903 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2558364 2558399 2558558 "SAEFACT" 2558730 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2556685 2556999 2557400 "RURPK" 2558030 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2555322 2555628 2555933 "RULESET" 2556519 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2552545 2553075 2553533 "RULE" 2555003 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2552157 2552339 2552422 "RULECOLD" 2552497 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2551947 2551975 2552046 "RTVALUE" 2552108 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2551418 2551664 2551758 "RSTRCAST" 2551875 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2546266 2547061 2547981 "RSETGCD" 2550617 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2535496 2540575 2540672 "RSETCAT" 2544791 NIL RSETCAT (NIL T T T T) -9 NIL 2545888 NIL) (-1089 2533423 2533962 2534786 "RSETCAT-" 2534791 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2525809 2527185 2528705 "RSDCMPK" 2532022 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2523788 2524255 2524329 "RRCC" 2525415 NIL RRCC (NIL T T) -9 NIL 2525759 NIL) (-1086 2523139 2523313 2523592 "RRCC-" 2523597 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2522582 2522835 2522936 "RPTAST" 2523060 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2496245 2505694 2505761 "RPOLCAT" 2516427 NIL RPOLCAT (NIL T T T) -9 NIL 2519587 NIL) (-1083 2487743 2490083 2493205 "RPOLCAT-" 2493210 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2478674 2485954 2486436 "ROUTINE" 2487283 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2475421 2478300 2478440 "ROMAN" 2478556 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2473665 2474281 2474541 "ROIRC" 2475226 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2469897 2472181 2472211 "RNS" 2472515 T RNS (NIL) -9 NIL 2472789 NIL) (-1078 2468406 2468789 2469323 "RNS-" 2469398 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2467809 2468217 2468247 "RNG" 2468252 T RNG (NIL) -9 NIL 2468273 NIL) (-1076 2466812 2467174 2467376 "RNGBIND" 2467660 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2466211 2466599 2466642 "RMODULE" 2466647 NIL RMODULE (NIL T) -9 NIL 2466674 NIL) (-1074 2465047 2465141 2465477 "RMCAT2" 2466112 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2461897 2464393 2464690 "RMATRIX" 2464809 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2454724 2456984 2457099 "RMATCAT" 2460458 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2461440 NIL) (-1071 2454099 2454246 2454553 "RMATCAT-" 2454558 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2453500 2453721 2453764 "RLINSET" 2453958 NIL RLINSET (NIL T) -9 NIL 2454049 NIL) (-1069 2453067 2453142 2453270 "RINTERP" 2453419 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2452125 2452679 2452709 "RING" 2452765 T RING (NIL) -9 NIL 2452857 NIL) (-1067 2451917 2451961 2452058 "RING-" 2452063 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2450758 2450995 2451253 "RIDIST" 2451681 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2442047 2450226 2450432 "RGCHAIN" 2450606 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2441397 2441803 2441844 "RGBCSPC" 2441902 NIL RGBCSPC (NIL T) -9 NIL 2441954 NIL) (-1063 2440555 2440936 2440977 "RGBCMDL" 2441209 NIL RGBCMDL (NIL T) -9 NIL 2441323 NIL) (-1062 2437549 2438163 2438833 "RF" 2439919 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2437195 2437258 2437361 "RFFACTOR" 2437480 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2436920 2436955 2437052 "RFFACT" 2437154 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2435037 2435401 2435783 "RFDIST" 2436560 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2434490 2434582 2434745 "RETSOL" 2434939 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2434126 2434206 2434249 "RETRACT" 2434382 NIL RETRACT (NIL T) -9 NIL 2434469 NIL) (-1056 2433975 2434000 2434087 "RETRACT-" 2434092 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2433577 2433797 2433867 "RETAST" 2433927 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2426315 2433230 2433357 "RESULT" 2433472 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2424906 2425584 2425783 "RESRING" 2426218 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2424542 2424591 2424689 "RESLATC" 2424843 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2424247 2424282 2424389 "REPSQ" 2424501 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2421669 2422249 2422851 "REP" 2423667 T REP (NIL) -7 NIL NIL NIL) (-1049 2421366 2421401 2421512 "REPDB" 2421628 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2415266 2416655 2417878 "REP2" 2420178 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2411643 2412324 2413132 "REP1" 2414493 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2404339 2409784 2410240 "REGSET" 2411273 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2403104 2403487 2403737 "REF" 2404124 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2402481 2402584 2402751 "REDORDER" 2402988 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2398449 2401694 2401921 "RECLOS" 2402309 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2397501 2397682 2397897 "REALSOLV" 2398256 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2397347 2397388 2397418 "REAL" 2397423 T REAL (NIL) -9 NIL 2397458 NIL) (-1040 2393830 2394632 2395516 "REAL0Q" 2396512 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2389431 2390419 2391480 "REAL0" 2392811 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2388902 2389148 2389242 "RDUCEAST" 2389359 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2388307 2388379 2388586 "RDIV" 2388824 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2387375 2387549 2387762 "RDIST" 2388129 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2385972 2386259 2386631 "RDETRS" 2387083 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2383784 2384238 2384776 "RDETR" 2385514 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2382409 2382687 2383084 "RDEEFS" 2383500 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2380918 2381224 2381649 "RDEEF" 2382097 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2374979 2377899 2377929 "RCFIELD" 2379224 T RCFIELD (NIL) -9 NIL 2379955 NIL) (-1030 2373043 2373547 2374243 "RCFIELD-" 2374318 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2369312 2371144 2371187 "RCAGG" 2372271 NIL RCAGG (NIL T) -9 NIL 2372736 NIL) (-1028 2368940 2369034 2369197 "RCAGG-" 2369202 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2368275 2368387 2368552 "RATRET" 2368824 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2367828 2367895 2368016 "RATFACT" 2368203 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2367136 2367256 2367408 "RANDSRC" 2367698 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2366870 2366914 2366987 "RADUTIL" 2367085 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2359891 2365701 2366012 "RADIX" 2366593 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2350559 2359733 2359863 "RADFF" 2359868 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2350206 2350281 2350311 "RADCAT" 2350471 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2349988 2350036 2350136 "RADCAT-" 2350141 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2348086 2349758 2349850 "QUEUE" 2349931 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2344534 2348019 2348067 "QUAT" 2348072 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2344165 2344208 2344339 "QUATCT2" 2344485 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2337178 2340615 2340657 "QUATCAT" 2341448 NIL QUATCAT (NIL T) -9 NIL 2342214 NIL) (-1015 2333317 2334354 2335744 "QUATCAT-" 2335840 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2330782 2332393 2332436 "QUAGG" 2332817 NIL QUAGG (NIL T) -9 NIL 2332992 NIL) (-1013 2330384 2330604 2330674 "QQUTAST" 2330734 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2329397 2329897 2330062 "QFORM" 2330265 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2319971 2325299 2325341 "QFCAT" 2326009 NIL QFCAT (NIL T) -9 NIL 2327010 NIL) (-1010 2315316 2316579 2318253 "QFCAT-" 2318349 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2314947 2314990 2315121 "QFCAT2" 2315267 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2314402 2314512 2314644 "QEQUAT" 2314837 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2307528 2308601 2309787 "QCMPACK" 2313335 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2305066 2305514 2305944 "QALGSET" 2307183 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2304301 2304477 2304713 "QALGSET2" 2304884 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2302986 2303210 2303529 "PWFFINTB" 2304074 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2301161 2301329 2301685 "PUSHVAR" 2302800 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2297050 2298104 2298147 "PTRANFN" 2300058 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2295441 2295732 2296056 "PTPACK" 2296761 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2295070 2295127 2295238 "PTFUNC2" 2295378 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2289515 2293912 2293953 "PTCAT" 2294249 NIL PTCAT (NIL T) -9 NIL 2294402 NIL) (-998 2289173 2289208 2289332 "PSQFR" 2289474 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2287768 2288066 2288400 "PSEUDLIN" 2288871 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2274531 2276902 2279226 "PSETPK" 2285528 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2267549 2270289 2270385 "PSETCAT" 2273406 NIL PSETCAT (NIL T T T T) -9 NIL 2274220 NIL) (-994 2265385 2266019 2266840 "PSETCAT-" 2266845 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2264734 2264899 2264927 "PSCURVE" 2265195 T PSCURVE (NIL) -9 NIL 2265362 NIL) (-992 2260732 2262248 2262313 "PSCAT" 2263157 NIL PSCAT (NIL T T T) -9 NIL 2263397 NIL) (-991 2259795 2260011 2260411 "PSCAT-" 2260416 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2258154 2258864 2259127 "PRTITION" 2259552 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2257629 2257875 2257967 "PRTDAST" 2258082 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2246719 2248933 2251121 "PRS" 2255491 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2244530 2246069 2246109 "PRQAGG" 2246292 NIL PRQAGG (NIL T) -9 NIL 2246394 NIL) (-986 2243866 2244171 2244199 "PROPLOG" 2244338 T PROPLOG (NIL) -9 NIL 2244453 NIL) (-985 2243470 2243527 2243650 "PROPFUN2" 2243789 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2242785 2242906 2243078 "PROPFUN1" 2243331 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2240966 2241532 2241829 "PROPFRML" 2242521 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2240435 2240542 2240670 "PROPERTY" 2240858 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2234493 2238601 2239421 "PRODUCT" 2239661 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2231771 2233951 2234185 "PR" 2234304 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2231567 2231599 2231658 "PRINT" 2231732 T PRINT (NIL) -7 NIL NIL NIL) (-978 2230907 2231024 2231176 "PRIMES" 2231447 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2228972 2229373 2229839 "PRIMELT" 2230486 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2228701 2228750 2228778 "PRIMCAT" 2228902 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2224816 2228639 2228684 "PRIMARR" 2228689 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2223823 2224001 2224229 "PRIMARR2" 2224634 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2223466 2223522 2223633 "PREASSOC" 2223761 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2222941 2223074 2223102 "PPCURVE" 2223307 T PPCURVE (NIL) -9 NIL 2223443 NIL) (-971 2222536 2222736 2222819 "PORTNUM" 2222878 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2219895 2220294 2220886 "POLYROOT" 2222117 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2213988 2219499 2219659 "POLY" 2219768 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2213371 2213429 2213663 "POLYLIFT" 2213924 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2209646 2210095 2210724 "POLYCATQ" 2212916 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2196175 2201393 2201458 "POLYCAT" 2204972 NIL POLYCAT (NIL T T T) -9 NIL 2206850 NIL) (-965 2189402 2191326 2193790 "POLYCAT-" 2193795 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2188989 2189057 2189177 "POLY2UP" 2189328 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2188621 2188678 2188787 "POLY2" 2188926 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2187306 2187545 2187821 "POLUTIL" 2188395 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2185661 2185938 2186269 "POLTOPOL" 2187028 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2181126 2185597 2185643 "POINT" 2185648 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2179313 2179670 2180045 "PNTHEORY" 2180771 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2177771 2178068 2178467 "PMTOOLS" 2179011 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2177364 2177442 2177559 "PMSYM" 2177687 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2176872 2176941 2177116 "PMQFCAT" 2177289 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2176227 2176337 2176493 "PMPRED" 2176749 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2175620 2175706 2175868 "PMPREDFS" 2176128 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2174284 2174492 2174870 "PMPLCAT" 2175382 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2173816 2173895 2174047 "PMLSAGG" 2174199 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2173289 2173365 2173547 "PMKERNEL" 2173734 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2172906 2172981 2173094 "PMINS" 2173208 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2172348 2172417 2172626 "PMFS" 2172831 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2171576 2171694 2171899 "PMDOWN" 2172225 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2170743 2170901 2171082 "PMASS" 2171415 T PMASS (NIL) -7 NIL NIL NIL) (-946 2170016 2170126 2170289 "PMASSFS" 2170630 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2169671 2169739 2169833 "PLOTTOOL" 2169942 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2164278 2165482 2166630 "PLOT" 2168543 T PLOT (NIL) -8 NIL NIL NIL) (-943 2160082 2161126 2162047 "PLOT3D" 2163377 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2158994 2159171 2159406 "PLOT1" 2159886 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2134385 2139060 2143911 "PLEQN" 2154260 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2133703 2133825 2134005 "PINTERP" 2134250 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2133396 2133443 2133546 "PINTERPA" 2133650 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2132612 2133160 2133247 "PI" 2133287 T PI (NIL) -8 NIL NIL 2133354) (-937 2130909 2131884 2131912 "PID" 2132094 T PID (NIL) -9 NIL 2132228 NIL) (-936 2130660 2130697 2130772 "PICOERCE" 2130866 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2129980 2130119 2130295 "PGROEB" 2130516 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2125567 2126381 2127286 "PGE" 2129095 T PGE (NIL) -7 NIL NIL NIL) (-933 2123690 2123937 2124303 "PGCD" 2125284 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2123028 2123131 2123292 "PFRPAC" 2123574 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2119668 2121576 2121929 "PFR" 2122707 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2118057 2118301 2118626 "PFOTOOLS" 2119415 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2116590 2116829 2117180 "PFOQ" 2117814 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2115091 2115303 2115659 "PFO" 2116374 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2111644 2114980 2115049 "PF" 2115054 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2108978 2110249 2110277 "PFECAT" 2110862 T PFECAT (NIL) -9 NIL 2111246 NIL) (-925 2108423 2108577 2108791 "PFECAT-" 2108796 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2107026 2107278 2107579 "PFBRU" 2108172 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2104892 2105244 2105676 "PFBR" 2106677 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2100938 2102404 2103051 "PERM" 2104278 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2096172 2097145 2098015 "PERMGRP" 2100101 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2094291 2095251 2095292 "PERMCAT" 2095692 NIL PERMCAT (NIL T) -9 NIL 2095990 NIL) (-919 2093944 2093985 2094109 "PERMAN" 2094244 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2091432 2093609 2093731 "PENDTREE" 2093855 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2090361 2090576 2090617 "PDSPC" 2091150 NIL PDSPC (NIL T) -9 NIL 2091395 NIL) (-916 2089464 2089682 2090044 "PDSPC-" 2090049 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2088346 2089114 2089155 "PDRING" 2089160 NIL PDRING (NIL T) -9 NIL 2089188 NIL) (-914 2087233 2087851 2087905 "PDMOD" 2087910 NIL PDMOD (NIL T T) -9 NIL 2088014 NIL) (-913 2084448 2085226 2085894 "PDEPROB" 2086585 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2081993 2082497 2083052 "PDEPACK" 2083913 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2080905 2081095 2081346 "PDECOMP" 2081792 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2078484 2079327 2079355 "PDECAT" 2080142 T PDECAT (NIL) -9 NIL 2080855 NIL) (-909 2078113 2078168 2078222 "PDDOM" 2078387 NIL PDDOM (NIL T T) -9 NIL 2078467 NIL) (-908 2077932 2077962 2078069 "PDDOM-" 2078074 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2077683 2077716 2077806 "PCOMP" 2077893 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2075861 2076484 2076781 "PBWLB" 2077412 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2068334 2069934 2071272 "PATTERN" 2074544 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2067966 2068023 2068132 "PATTERN2" 2068271 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2065723 2066111 2066568 "PATTERN1" 2067555 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2063091 2063672 2064153 "PATRES" 2065288 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2062655 2062722 2062854 "PATRES2" 2063018 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2060538 2060943 2061350 "PATMATCH" 2062322 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2060048 2060257 2060298 "PATMAB" 2060405 NIL PATMAB (NIL T) -9 NIL 2060488 NIL) (-898 2058566 2058902 2059160 "PATLRES" 2059853 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2058112 2058235 2058276 "PATAB" 2058281 NIL PATAB (NIL T) -9 NIL 2058453 NIL) (-896 2056294 2056689 2057112 "PARTPERM" 2057709 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2055915 2055978 2056080 "PARSURF" 2056225 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2055547 2055604 2055713 "PARSU2" 2055852 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2055311 2055351 2055418 "PARSER" 2055500 T PARSER (NIL) -7 NIL NIL NIL) (-892 2054932 2054995 2055097 "PARSCURV" 2055242 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2054564 2054621 2054730 "PARSC2" 2054869 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2054203 2054261 2054358 "PARPCURV" 2054500 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2053835 2053892 2054001 "PARPC2" 2054140 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2052896 2053208 2053390 "PARAMAST" 2053673 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2052416 2052502 2052621 "PAN2EXPR" 2052797 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2051193 2051537 2051765 "PALETTE" 2052208 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2049586 2050198 2050558 "PAIR" 2050879 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2043365 2048843 2049038 "PADICRC" 2049440 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2036489 2042709 2042894 "PADICRAT" 2043212 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2034804 2036426 2036471 "PADIC" 2036476 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2031914 2033478 2033518 "PADICCT" 2034099 NIL PADICCT (NIL NIL) -9 NIL 2034381 NIL) (-880 2030871 2031071 2031339 "PADEPAC" 2031701 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2030083 2030216 2030422 "PADE" 2030733 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2028470 2029291 2029571 "OWP" 2029887 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2027963 2028176 2028273 "OVERSET" 2028393 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2027009 2027568 2027740 "OVAR" 2027831 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2026273 2026394 2026555 "OUT" 2026868 T OUT (NIL) -7 NIL NIL NIL) (-874 2015145 2017382 2019582 "OUTFORM" 2024093 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2014481 2014742 2014869 "OUTBFILE" 2015038 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2013788 2013953 2013981 "OUTBCON" 2014299 T OUTBCON (NIL) -9 NIL 2014465 NIL) (-871 2013389 2013501 2013658 "OUTBCON-" 2013663 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2012769 2013118 2013207 "OSI" 2013320 T OSI (NIL) -8 NIL NIL NIL) (-869 2012299 2012637 2012665 "OSGROUP" 2012670 T OSGROUP (NIL) -9 NIL 2012692 NIL) (-868 2011044 2011271 2011556 "ORTHPOL" 2012046 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2008595 2010879 2011000 "OREUP" 2011005 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2005998 2008286 2008413 "ORESUP" 2008537 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2003526 2004026 2004587 "OREPCTO" 2005487 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 1997212 1999413 1999454 "OREPCAT" 2001802 NIL OREPCAT (NIL T) -9 NIL 2002906 NIL) (-863 1994359 1995141 1996199 "OREPCAT-" 1996204 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 1993510 1993808 1993836 "ORDSET" 1994145 T ORDSET (NIL) -9 NIL 1994309 NIL) (-861 1992941 1993089 1993313 "ORDSET-" 1993318 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 1991506 1992297 1992325 "ORDRING" 1992527 T ORDRING (NIL) -9 NIL 1992652 NIL) (-859 1991151 1991245 1991389 "ORDRING-" 1991394 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1990531 1990994 1991022 "ORDMON" 1991027 T ORDMON (NIL) -9 NIL 1991048 NIL) (-857 1989693 1989840 1990035 "ORDFUNS" 1990380 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1989031 1989450 1989478 "ORDFIN" 1989543 T ORDFIN (NIL) -9 NIL 1989617 NIL) (-855 1985590 1987617 1988026 "ORDCOMP" 1988655 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1984856 1984983 1985169 "ORDCOMP2" 1985450 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1981437 1982347 1983161 "OPTPROB" 1984062 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1978239 1978878 1979582 "OPTPACK" 1980753 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1975926 1976692 1976720 "OPTCAT" 1977539 T OPTCAT (NIL) -9 NIL 1978189 NIL) (-850 1975310 1975603 1975708 "OPSIG" 1975841 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1975078 1975117 1975183 "OPQUERY" 1975264 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1972209 1973389 1973893 "OP" 1974607 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1971583 1971809 1971850 "OPERCAT" 1972062 NIL OPERCAT (NIL T) -9 NIL 1972159 NIL) (-846 1971338 1971394 1971511 "OPERCAT-" 1971516 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1968151 1970135 1970504 "ONECOMP" 1971002 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1967456 1967571 1967745 "ONECOMP2" 1968023 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1966875 1966981 1967111 "OMSERVER" 1967346 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1963737 1966315 1966355 "OMSAGG" 1966416 NIL OMSAGG (NIL T) -9 NIL 1966480 NIL) (-841 1962360 1962623 1962905 "OMPKG" 1963475 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1961790 1961893 1961921 "OM" 1962220 T OM (NIL) -9 NIL NIL NIL) (-839 1960337 1961339 1961508 "OMLO" 1961671 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1959297 1959444 1959664 "OMEXPR" 1960163 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1958588 1958843 1958979 "OMERR" 1959181 T OMERR (NIL) -8 NIL NIL NIL) (-836 1957739 1958009 1958169 "OMERRK" 1958448 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1957190 1957416 1957524 "OMENC" 1957651 T OMENC (NIL) -8 NIL NIL NIL) (-834 1951085 1952270 1953441 "OMDEV" 1956039 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1950154 1950325 1950519 "OMCONN" 1950911 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1948675 1949651 1949679 "OINTDOM" 1949684 T OINTDOM (NIL) -9 NIL 1949705 NIL) (-831 1946013 1947363 1947700 "OFMONOID" 1948370 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1945385 1945950 1945995 "ODVAR" 1946000 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1942808 1945130 1945285 "ODR" 1945290 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1935300 1942584 1942710 "ODPOL" 1942715 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1929275 1935172 1935277 "ODP" 1935282 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1928041 1928256 1928531 "ODETOOLS" 1929049 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1925008 1925666 1926382 "ODESYS" 1927374 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1919890 1920798 1921823 "ODERTRIC" 1924083 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1919316 1919398 1919592 "ODERED" 1919802 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1916204 1916752 1917429 "ODERAT" 1918739 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1913163 1913628 1914225 "ODEPRRIC" 1915733 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1911106 1911702 1912188 "ODEPROB" 1912697 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1907626 1908111 1908758 "ODEPRIM" 1910585 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1906875 1906977 1907237 "ODEPAL" 1907518 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1903037 1903828 1904692 "ODEPACK" 1906031 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1902098 1902205 1902427 "ODEINT" 1902926 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1896199 1897624 1899071 "ODEIFTBL" 1900671 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1891597 1892383 1893335 "ODEEF" 1895358 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1890946 1891035 1891258 "ODECONST" 1891502 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1889071 1889732 1889760 "ODECAT" 1890365 T ODECAT (NIL) -9 NIL 1890896 NIL) (-811 1885926 1888776 1888898 "OCT" 1888981 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1885564 1885607 1885734 "OCTCT2" 1885877 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1880175 1882610 1882650 "OC" 1883747 NIL OC (NIL T) -9 NIL 1884605 NIL) (-808 1877402 1878150 1879140 "OC-" 1879234 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1876754 1877222 1877250 "OCAMON" 1877255 T OCAMON (NIL) -9 NIL 1877276 NIL) (-806 1876285 1876626 1876654 "OASGP" 1876659 T OASGP (NIL) -9 NIL 1876679 NIL) (-805 1875546 1876035 1876063 "OAMONS" 1876103 T OAMONS (NIL) -9 NIL 1876146 NIL) (-804 1874960 1875393 1875421 "OAMON" 1875426 T OAMON (NIL) -9 NIL 1875446 NIL) (-803 1874218 1874736 1874764 "OAGROUP" 1874769 T OAGROUP (NIL) -9 NIL 1874789 NIL) (-802 1873908 1873958 1874046 "NUMTUBE" 1874162 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1867481 1868999 1870535 "NUMQUAD" 1872392 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1863237 1864225 1865250 "NUMODE" 1866476 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1860592 1861472 1861500 "NUMINT" 1862423 T NUMINT (NIL) -9 NIL 1863187 NIL) (-798 1859540 1859737 1859955 "NUMFMT" 1860394 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1845899 1848844 1851376 "NUMERIC" 1857047 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1840269 1845348 1845443 "NTSCAT" 1845448 NIL NTSCAT (NIL T T T T) -9 NIL 1845487 NIL) (-795 1839463 1839628 1839821 "NTPOLFN" 1840108 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1827451 1836288 1837100 "NSUP" 1838684 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1827083 1827140 1827249 "NSUP2" 1827388 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1817220 1826857 1826990 "NSMP" 1826995 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1815652 1815953 1816310 "NREP" 1816908 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1814243 1814495 1814853 "NPCOEF" 1815395 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1813309 1813424 1813640 "NORMRETR" 1814124 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1811350 1811640 1812049 "NORMPK" 1813017 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1811035 1811063 1811187 "NORMMA" 1811316 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1810835 1810992 1811021 "NONE" 1811026 T NONE (NIL) -8 NIL NIL NIL) (-785 1810624 1810653 1810722 "NONE1" 1810799 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1810121 1810183 1810362 "NODE1" 1810556 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1808402 1809253 1809508 "NNI" 1809855 T NNI (NIL) -8 NIL NIL 1810090) (-782 1806822 1807135 1807499 "NLINSOL" 1808070 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1803063 1804058 1804957 "NIPROB" 1805943 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1801820 1802054 1802356 "NFINTBAS" 1802825 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1800994 1801470 1801511 "NETCLT" 1801683 NIL NETCLT (NIL T) -9 NIL 1801765 NIL) (-778 1799702 1799933 1800214 "NCODIV" 1800762 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1799464 1799501 1799576 "NCNTFRAC" 1799659 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1797644 1798008 1798428 "NCEP" 1799089 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1796495 1797268 1797296 "NASRING" 1797406 T NASRING (NIL) -9 NIL 1797486 NIL) (-774 1796290 1796334 1796428 "NASRING-" 1796433 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1795397 1795922 1795950 "NARNG" 1796067 T NARNG (NIL) -9 NIL 1796158 NIL) (-772 1795089 1795156 1795290 "NARNG-" 1795295 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1793968 1794175 1794410 "NAGSP" 1794874 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1785240 1786924 1788597 "NAGS" 1792315 T NAGS (NIL) -7 NIL NIL NIL) (-769 1783788 1784096 1784427 "NAGF07" 1784929 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1778326 1779617 1780924 "NAGF04" 1782501 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1771294 1772908 1774541 "NAGF02" 1776713 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1766518 1767618 1768735 "NAGF01" 1770197 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1760146 1761712 1763297 "NAGE04" 1764953 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1751315 1753436 1755566 "NAGE02" 1758036 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1747268 1748215 1749179 "NAGE01" 1750371 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1745063 1745597 1746155 "NAGD03" 1746730 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1736813 1738741 1740695 "NAGD02" 1743129 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1730624 1732049 1733489 "NAGD01" 1735393 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1726833 1727655 1728492 "NAGC06" 1729807 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1725298 1725630 1725986 "NAGC05" 1726497 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1724674 1724793 1724937 "NAGC02" 1725174 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1723633 1724216 1724256 "NAALG" 1724335 NIL NAALG (NIL T) -9 NIL 1724396 NIL) (-755 1723468 1723497 1723587 "NAALG-" 1723592 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1717418 1718526 1719713 "MULTSQFR" 1722364 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1716737 1716812 1716996 "MULTFACT" 1717330 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1709408 1713322 1713375 "MTSCAT" 1714445 NIL MTSCAT (NIL T T) -9 NIL 1714960 NIL) (-751 1709120 1709174 1709266 "MTHING" 1709348 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1708912 1708945 1709005 "MSYSCMD" 1709080 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1704994 1707667 1707987 "MSET" 1708625 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1702063 1704555 1704596 "MSETAGG" 1704601 NIL MSETAGG (NIL T) -9 NIL 1704635 NIL) (-747 1697905 1699442 1700187 "MRING" 1701363 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1697471 1697538 1697669 "MRF2" 1697832 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1697089 1697124 1697268 "MRATFAC" 1697430 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1694701 1694996 1695427 "MPRFF" 1696794 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1688909 1694555 1694652 "MPOLY" 1694657 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1688399 1688434 1688642 "MPCPF" 1688868 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1687913 1687956 1688140 "MPC3" 1688350 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1687108 1687189 1687410 "MPC2" 1687828 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1685409 1685746 1686136 "MONOTOOL" 1686768 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1684634 1684951 1684979 "MONOID" 1685198 T MONOID (NIL) -9 NIL 1685345 NIL) (-737 1684180 1684299 1684480 "MONOID-" 1684485 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1673915 1679958 1680017 "MONOGEN" 1680691 NIL MONOGEN (NIL T T) -9 NIL 1681147 NIL) (-735 1671133 1671868 1672868 "MONOGEN-" 1672987 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1669966 1670412 1670440 "MONADWU" 1670832 T MONADWU (NIL) -9 NIL 1671070 NIL) (-733 1669338 1669497 1669745 "MONADWU-" 1669750 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1668697 1668941 1668969 "MONAD" 1669176 T MONAD (NIL) -9 NIL 1669288 NIL) (-731 1668382 1668460 1668592 "MONAD-" 1668597 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1666671 1667295 1667574 "MOEBIUS" 1668135 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1665949 1666353 1666393 "MODULE" 1666398 NIL MODULE (NIL T) -9 NIL 1666437 NIL) (-728 1665517 1665613 1665803 "MODULE-" 1665808 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1663197 1663881 1664208 "MODRING" 1665341 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1660141 1661302 1661823 "MODOP" 1662726 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1658729 1659208 1659485 "MODMONOM" 1660004 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1648684 1657020 1657434 "MODMON" 1658366 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1645840 1647528 1647804 "MODFIELD" 1648559 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1644817 1645121 1645311 "MMLFORM" 1645670 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1644343 1644386 1644565 "MMAP" 1644768 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1642422 1643189 1643230 "MLO" 1643653 NIL MLO (NIL T) -9 NIL 1643895 NIL) (-719 1639788 1640304 1640906 "MLIFT" 1641903 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1639179 1639263 1639417 "MKUCFUNC" 1639699 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1638778 1638848 1638971 "MKRECORD" 1639102 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1637825 1637987 1638215 "MKFUNC" 1638589 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1637213 1637317 1637473 "MKFLCFN" 1637708 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1636490 1636592 1636777 "MKBCFUNC" 1637106 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1633165 1636044 1636180 "MINT" 1636374 T MINT (NIL) -8 NIL NIL NIL) (-712 1631977 1632220 1632497 "MHROWRED" 1632920 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1627357 1630512 1630917 "MFLOAT" 1631592 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1626714 1626790 1626961 "MFINFACT" 1627269 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1623029 1623877 1624761 "MESH" 1625850 T MESH (NIL) -7 NIL NIL NIL) (-708 1621419 1621731 1622084 "MDDFACT" 1622716 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1618214 1620578 1620619 "MDAGG" 1620874 NIL MDAGG (NIL T) -9 NIL 1621017 NIL) (-706 1607101 1617507 1617714 "MCMPLX" 1618027 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1606238 1606384 1606585 "MCDEN" 1606950 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1604128 1604398 1604778 "MCALCFN" 1605968 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1603053 1603293 1603526 "MAYBE" 1603934 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1600665 1601188 1601750 "MATSTOR" 1602524 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1596622 1600037 1600285 "MATRIX" 1600450 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1592388 1593095 1593831 "MATLIN" 1595979 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1582494 1585680 1585757 "MATCAT" 1590637 NIL MATCAT (NIL T T T) -9 NIL 1592054 NIL) (-698 1578850 1579871 1581227 "MATCAT-" 1581232 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1577444 1577597 1577930 "MATCAT2" 1578685 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1575556 1575880 1576264 "MAPPKG3" 1577119 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1574537 1574710 1574932 "MAPPKG2" 1575380 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1573036 1573320 1573647 "MAPPKG1" 1574243 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1572115 1572442 1572619 "MAPPAST" 1572879 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1571726 1571784 1571907 "MAPHACK3" 1572051 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1571318 1571379 1571493 "MAPHACK2" 1571658 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1570756 1570859 1571001 "MAPHACK1" 1571209 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1568835 1569456 1569760 "MAGMA" 1570484 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1568314 1568559 1568650 "MACROAST" 1568764 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1564732 1566553 1567014 "M3D" 1567886 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1558807 1563071 1563112 "LZSTAGG" 1563894 NIL LZSTAGG (NIL T) -9 NIL 1564189 NIL) (-685 1554765 1555938 1557395 "LZSTAGG-" 1557400 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1551852 1552656 1553143 "LWORD" 1554310 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1551428 1551656 1551731 "LSTAST" 1551797 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1544505 1551199 1551333 "LSQM" 1551338 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1543729 1543868 1544096 "LSPP" 1544360 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1541541 1541842 1542298 "LSMP" 1543418 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1538320 1538994 1539724 "LSMP1" 1540843 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1532166 1537457 1537498 "LSAGG" 1537560 NIL LSAGG (NIL T) -9 NIL 1537638 NIL) (-677 1528861 1529785 1530998 "LSAGG-" 1531003 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1526460 1528005 1528254 "LPOLY" 1528656 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1526042 1526127 1526250 "LPEFRAC" 1526369 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1524363 1525136 1525389 "LO" 1525874 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1524015 1524127 1524155 "LOGIC" 1524266 T LOGIC (NIL) -9 NIL 1524347 NIL) (-672 1523877 1523900 1523971 "LOGIC-" 1523976 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1523070 1523210 1523403 "LODOOPS" 1523733 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1520493 1522986 1523052 "LODO" 1523057 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1519031 1519266 1519619 "LODOF" 1520240 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1515235 1517666 1517707 "LODOCAT" 1518145 NIL LODOCAT (NIL T) -9 NIL 1518356 NIL) (-667 1514968 1515026 1515153 "LODOCAT-" 1515158 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1512288 1514809 1514927 "LODO2" 1514932 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1509723 1512225 1512270 "LODO1" 1512275 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1508604 1508769 1509074 "LODEEF" 1509546 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1503907 1506798 1506839 "LNAGG" 1507701 NIL LNAGG (NIL T) -9 NIL 1508136 NIL) (-662 1503054 1503268 1503610 "LNAGG-" 1503615 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1499190 1499979 1500618 "LMOPS" 1502469 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1498593 1498981 1499022 "LMODULE" 1499027 NIL LMODULE (NIL T) -9 NIL 1499053 NIL) (-659 1495791 1498238 1498361 "LMDICT" 1498503 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1495197 1495418 1495459 "LLINSET" 1495650 NIL LLINSET (NIL T) -9 NIL 1495741 NIL) (-657 1494896 1495105 1495165 "LITERAL" 1495170 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1488059 1493830 1494134 "LIST" 1494625 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1487584 1487658 1487797 "LIST3" 1487979 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1486591 1486769 1486997 "LIST2" 1487402 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1484725 1485037 1485436 "LIST2MAP" 1486238 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1484321 1484558 1484599 "LINSET" 1484604 NIL LINSET (NIL T) -9 NIL 1484638 NIL) (-651 1483050 1483583 1483624 "LINEXP" 1483975 NIL LINEXP (NIL T) -9 NIL 1484166 NIL) (-650 1481627 1481887 1482198 "LINDEP" 1482802 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1478394 1479113 1479890 "LIMITRF" 1480882 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1476697 1476993 1477402 "LIMITPS" 1478089 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1471125 1476208 1476436 "LIE" 1476518 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1470073 1470542 1470582 "LIECAT" 1470722 NIL LIECAT (NIL T) -9 NIL 1470873 NIL) (-645 1469914 1469941 1470029 "LIECAT-" 1470034 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1462501 1469454 1469610 "LIB" 1469778 T LIB (NIL) -8 NIL NIL NIL) (-643 1458136 1459019 1459954 "LGROBP" 1461618 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1456134 1456408 1456758 "LF" 1457857 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1454974 1455666 1455694 "LFCAT" 1455901 T LFCAT (NIL) -9 NIL 1456040 NIL) (-640 1451876 1452506 1453194 "LEXTRIPK" 1454338 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1448620 1449446 1449949 "LEXP" 1451456 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1448096 1448341 1448433 "LETAST" 1448548 T LETAST (NIL) -8 NIL NIL NIL) (-637 1446494 1446807 1447208 "LEADCDET" 1447778 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1445684 1445758 1445987 "LAZM3PK" 1446415 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1440601 1443761 1444299 "LAUPOL" 1445196 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1440180 1440224 1440385 "LAPLACE" 1440551 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1438119 1439281 1439532 "LA" 1440013 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1437113 1437697 1437738 "LALG" 1437800 NIL LALG (NIL T) -9 NIL 1437859 NIL) (-631 1436827 1436886 1437022 "LALG-" 1437027 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1436662 1436686 1436727 "KVTFROM" 1436789 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1435585 1436029 1436214 "KTVLOGIC" 1436497 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1435420 1435444 1435485 "KRCFROM" 1435547 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1434324 1434511 1434810 "KOVACIC" 1435220 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1434159 1434183 1434224 "KONVERT" 1434286 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1433994 1434018 1434059 "KOERCE" 1434121 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1431825 1432587 1432964 "KERNEL" 1433650 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1431321 1431402 1431534 "KERNEL2" 1431739 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1425091 1429860 1429914 "KDAGG" 1430291 NIL KDAGG (NIL T T) -9 NIL 1430497 NIL) (-621 1424620 1424744 1424949 "KDAGG-" 1424954 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1417768 1424281 1424436 "KAFILE" 1424498 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1412196 1417279 1417507 "JORDAN" 1417589 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1411575 1411845 1411966 "JOINAST" 1412095 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1411421 1411480 1411535 "JAVACODE" 1411540 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1407673 1409626 1409680 "IXAGG" 1410609 NIL IXAGG (NIL T T) -9 NIL 1411068 NIL) (-615 1406592 1406898 1407317 "IXAGG-" 1407322 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1402122 1406514 1406573 "IVECTOR" 1406578 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1400888 1401125 1401391 "ITUPLE" 1401889 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1399390 1399567 1399862 "ITRIGMNP" 1400710 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1398135 1398339 1398622 "ITFUN3" 1399166 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1397767 1397824 1397933 "ITFUN2" 1398072 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1396926 1397247 1397421 "ITFORM" 1397613 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1394887 1395946 1396224 "ITAYLOR" 1396681 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1383832 1389024 1390187 "ISUPS" 1393757 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1382936 1383076 1383312 "ISUMP" 1383679 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1378311 1382881 1382922 "ISTRING" 1382927 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1377787 1378032 1378124 "ISAST" 1378239 T ISAST (NIL) -8 NIL NIL NIL) (-603 1376996 1377078 1377294 "IRURPK" 1377701 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1375932 1376133 1376373 "IRSN" 1376776 T IRSN (NIL) -7 NIL NIL NIL) (-601 1374003 1374358 1374787 "IRRF2F" 1375570 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1373750 1373788 1373864 "IRREDFFX" 1373959 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1372365 1372624 1372923 "IROOT" 1373483 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1368969 1370049 1370741 "IR" 1371705 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1368174 1368462 1368613 "IRFORM" 1368838 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1365787 1366282 1366848 "IR2" 1367652 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1364887 1365000 1365214 "IR2F" 1365670 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1364678 1364712 1364772 "IPRNTPK" 1364847 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1361259 1364567 1364636 "IPF" 1364641 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1359586 1361184 1361241 "IPADIC" 1361246 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1358898 1359146 1359276 "IP4ADDR" 1359476 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1358272 1358527 1358659 "IOMODE" 1358786 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1357345 1357869 1357996 "IOBFILE" 1358165 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1356833 1357249 1357277 "IOBCON" 1357282 T IOBCON (NIL) -9 NIL 1357303 NIL) (-587 1356344 1356402 1356585 "INVLAPLA" 1356769 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1345992 1348346 1350732 "INTTR" 1354008 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1342327 1343069 1343934 "INTTOOLS" 1345177 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1341913 1342004 1342121 "INTSLPE" 1342230 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1339866 1341836 1341895 "INTRVL" 1341900 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1337468 1337980 1338555 "INTRF" 1339351 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1336879 1336976 1337118 "INTRET" 1337366 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1334876 1335265 1335735 "INTRAT" 1336487 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1332139 1332722 1333341 "INTPM" 1334361 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1328884 1329483 1330221 "INTPAF" 1331525 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1324063 1325025 1326076 "INTPACK" 1327853 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1320961 1323860 1323969 "INT" 1323974 T INT (NIL) -8 NIL NIL NIL) (-575 1320213 1320365 1320573 "INTHERTR" 1320803 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1319652 1319732 1319920 "INTHERAL" 1320127 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1317498 1317941 1318398 "INTHEORY" 1319215 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1308904 1310525 1312297 "INTG0" 1315850 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1289477 1294267 1299077 "INTFTBL" 1304114 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1288726 1288864 1289037 "INTFACT" 1289336 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1286153 1286599 1287156 "INTEF" 1288280 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1284520 1285259 1285287 "INTDOM" 1285588 T INTDOM (NIL) -9 NIL 1285795 NIL) (-567 1283889 1284063 1284305 "INTDOM-" 1284310 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1280277 1282205 1282259 "INTCAT" 1283058 NIL INTCAT (NIL T) -9 NIL 1283379 NIL) (-565 1279749 1279852 1279980 "INTBIT" 1280169 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1278448 1278602 1278909 "INTALG" 1279594 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1277931 1278021 1278178 "INTAF" 1278352 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1271274 1277741 1277881 "INTABL" 1277886 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1270607 1271073 1271138 "INT8" 1271172 T INT8 (NIL) -8 NIL NIL 1271217) (-560 1269939 1270405 1270470 "INT64" 1270504 T INT64 (NIL) -8 NIL NIL 1270549) (-559 1269271 1269737 1269802 "INT32" 1269836 T INT32 (NIL) -8 NIL NIL 1269881) (-558 1268603 1269069 1269134 "INT16" 1269168 T INT16 (NIL) -8 NIL NIL 1269213) (-557 1263398 1266164 1266192 "INS" 1267126 T INS (NIL) -9 NIL 1267791 NIL) (-556 1260638 1261409 1262383 "INS-" 1262456 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1259413 1259640 1259938 "INPSIGN" 1260391 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1258531 1258648 1258845 "INPRODPF" 1259293 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1257425 1257542 1257779 "INPRODFF" 1258411 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1256425 1256577 1256837 "INNMFACT" 1257261 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1255622 1255719 1255907 "INMODGCD" 1256324 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1254130 1254375 1254699 "INFSP" 1255367 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1253314 1253431 1253614 "INFPROD0" 1254010 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1250169 1251379 1251894 "INFORM" 1252807 T INFORM (NIL) -8 NIL NIL NIL) (-547 1249779 1249839 1249937 "INFORM1" 1250104 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1249302 1249391 1249505 "INFINITY" 1249685 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1248478 1249022 1249123 "INETCLTS" 1249221 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1247094 1247344 1247665 "INEP" 1248226 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1246343 1246991 1247056 "INDE" 1247061 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1245907 1245975 1246092 "INCRMAPS" 1246270 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1244725 1245176 1245382 "INBFILE" 1245721 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1240024 1240961 1241905 "INBFF" 1243813 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1238932 1239201 1239229 "INBCON" 1239742 T INBCON (NIL) -9 NIL 1240008 NIL) (-538 1238184 1238407 1238683 "INBCON-" 1238688 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1237663 1237908 1237999 "INAST" 1238113 T INAST (NIL) -8 NIL NIL NIL) (-536 1237090 1237342 1237448 "IMPTAST" 1237577 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1233536 1236934 1237038 "IMATRIX" 1237043 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1232244 1232367 1232683 "IMATQF" 1233392 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1230464 1230691 1231028 "IMATLIN" 1232000 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1225042 1230388 1230446 "ILIST" 1230451 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1222947 1224902 1225015 "IIARRAY2" 1225020 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1218345 1222858 1222922 "IFF" 1222927 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1217692 1217962 1218078 "IFAST" 1218249 T IFAST (NIL) -8 NIL NIL NIL) (-528 1212687 1216984 1217172 "IFARRAY" 1217549 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1211867 1212591 1212664 "IFAMON" 1212669 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1211451 1211516 1211570 "IEVALAB" 1211777 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1211126 1211194 1211354 "IEVALAB-" 1211359 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1210757 1211040 1211103 "IDPO" 1211108 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1210007 1210646 1210721 "IDPOAMS" 1210726 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1209314 1209896 1209971 "IDPOAM" 1209976 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1208373 1208649 1208702 "IDPC" 1209115 NIL IDPC (NIL T T) -9 NIL 1209264 NIL) (-520 1207842 1208265 1208338 "IDPAM" 1208343 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1207218 1207734 1207807 "IDPAG" 1207812 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1206863 1207054 1207129 "IDENT" 1207163 T IDENT (NIL) -8 NIL NIL NIL) (-517 1203118 1203966 1204861 "IDECOMP" 1206020 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1195955 1197041 1198088 "IDEAL" 1202154 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1195115 1195227 1195427 "ICDEN" 1195839 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1194186 1194595 1194742 "ICARD" 1194988 T ICARD (NIL) -8 NIL NIL NIL) (-513 1192246 1192559 1192964 "IBPTOOLS" 1193863 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1187853 1191866 1191979 "IBITS" 1192165 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1184576 1185152 1185847 "IBATOOL" 1187270 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1182355 1182817 1183350 "IBACHIN" 1184111 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1180184 1182201 1182304 "IARRAY2" 1182309 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1176290 1180110 1180167 "IARRAY1" 1180172 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1170328 1174702 1175183 "IAN" 1175829 T IAN (NIL) -8 NIL NIL NIL) (-506 1169839 1169896 1170069 "IALGFACT" 1170265 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1169367 1169480 1169508 "HYPCAT" 1169715 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1168905 1169022 1169208 "HYPCAT-" 1169213 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1168500 1168700 1168783 "HOSTNAME" 1168842 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1168345 1168382 1168423 "HOMOTOP" 1168428 NIL HOMOTOP (NIL T) -9 NIL 1168461 NIL) (-501 1164977 1166355 1166396 "HOAGG" 1167377 NIL HOAGG (NIL T) -9 NIL 1168056 NIL) (-500 1163571 1163970 1164496 "HOAGG-" 1164501 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1157480 1163164 1163314 "HEXADEC" 1163441 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1156228 1156450 1156713 "HEUGCD" 1157257 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1155304 1156065 1156195 "HELLFDIV" 1156200 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1153483 1155081 1155169 "HEAP" 1155248 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1152746 1153035 1153169 "HEADAST" 1153369 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1146765 1152661 1152723 "HDP" 1152728 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1140664 1146400 1146552 "HDMP" 1146666 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1139988 1140128 1140292 "HB" 1140520 T HB (NIL) -7 NIL NIL NIL) (-491 1133374 1139834 1139938 "HASHTBL" 1139943 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1132850 1133095 1133187 "HASAST" 1133302 T HASAST (NIL) -8 NIL NIL NIL) (-489 1130628 1132472 1132654 "HACKPI" 1132688 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1126296 1130481 1130594 "GTSET" 1130599 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1119711 1126174 1126272 "GSTBL" 1126277 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1112098 1118876 1119132 "GSERIES" 1119511 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1111239 1111656 1111684 "GROUP" 1111887 T GROUP (NIL) -9 NIL 1112021 NIL) (-484 1110605 1110764 1111015 "GROUP-" 1111020 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1108972 1109293 1109680 "GROEBSOL" 1110282 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1107886 1108174 1108225 "GRMOD" 1108754 NIL GRMOD (NIL T T) -9 NIL 1108922 NIL) (-481 1107654 1107690 1107818 "GRMOD-" 1107823 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1102944 1104008 1105008 "GRIMAGE" 1106674 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1101410 1101671 1101995 "GRDEF" 1102640 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1100854 1100970 1101111 "GRAY" 1101289 T GRAY (NIL) -7 NIL NIL NIL) (-477 1100041 1100447 1100498 "GRALG" 1100651 NIL GRALG (NIL T T) -9 NIL 1100744 NIL) (-476 1099702 1099775 1099938 "GRALG-" 1099943 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1096479 1099287 1099465 "GPOLSET" 1099609 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1095833 1095890 1096148 "GOSPER" 1096416 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1091565 1092271 1092797 "GMODPOL" 1095532 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1090570 1090754 1090992 "GHENSEL" 1091377 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1084726 1085569 1086589 "GENUPS" 1089654 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1084423 1084474 1084563 "GENUFACT" 1084669 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1083835 1083912 1084077 "GENPGCD" 1084341 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1083309 1083344 1083557 "GENMFACT" 1083794 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1081875 1082132 1082439 "GENEEZ" 1083052 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1075934 1081486 1081648 "GDMP" 1081798 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1065277 1069705 1070811 "GCNAALG" 1074917 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1063604 1064466 1064494 "GCDDOM" 1064749 T GCDDOM (NIL) -9 NIL 1064906 NIL) (-463 1063074 1063201 1063416 "GCDDOM-" 1063421 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1061746 1061931 1062235 "GB" 1062853 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1050362 1052692 1055084 "GBINTERN" 1059437 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1048199 1048491 1048912 "GBF" 1050037 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1046980 1047145 1047412 "GBEUCLID" 1048015 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1046329 1046454 1046603 "GAUSSFAC" 1046851 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1044696 1044998 1045312 "GALUTIL" 1046048 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1043004 1043278 1043602 "GALPOLYU" 1044423 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1040369 1040659 1041066 "GALFACTU" 1042701 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1032175 1033674 1035282 "GALFACT" 1038801 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1029563 1030221 1030249 "FVFUN" 1031405 T FVFUN (NIL) -9 NIL 1032125 NIL) (-452 1028829 1029011 1029039 "FVC" 1029330 T FVC (NIL) -9 NIL 1029513 NIL) (-451 1028472 1028654 1028722 "FUNDESC" 1028781 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1028087 1028269 1028350 "FUNCTION" 1028424 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1025831 1026409 1026875 "FT" 1027641 T FT (NIL) -8 NIL NIL NIL) (-448 1024622 1025132 1025335 "FTEM" 1025648 T FTEM (NIL) -8 NIL NIL NIL) (-447 1022913 1023202 1023599 "FSUPFACT" 1024313 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1021310 1021599 1021931 "FST" 1022601 T FST (NIL) -8 NIL NIL NIL) (-445 1020509 1020615 1020803 "FSRED" 1021192 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1019208 1019464 1019811 "FSPRMELT" 1020224 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1016514 1016952 1017438 "FSPECF" 1018771 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 997816 1006288 1006329 "FS" 1010213 NIL FS (NIL T) -9 NIL 1012502 NIL) (-441 986459 989452 993509 "FS-" 993809 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 985987 986041 986211 "FSINT" 986400 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 984279 984980 985283 "FSERIES" 985766 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 983321 983437 983661 "FSCINT" 984159 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 979529 982265 982306 "FSAGG" 982676 NIL FSAGG (NIL T) -9 NIL 982935 NIL) (-436 977291 977892 978688 "FSAGG-" 978783 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 976333 976476 976703 "FSAGG2" 977144 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 974011 974291 974839 "FS2UPS" 976051 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 973645 973688 973817 "FS2" 973962 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 972523 972694 972996 "FS2EXPXP" 973470 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 971949 972064 972216 "FRUTIL" 972403 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 963362 967444 968802 "FR" 970623 NIL FR (NIL T) -8 NIL NIL NIL) (-429 958376 961051 961091 "FRNAALG" 962411 NIL FRNAALG (NIL T) -9 NIL 963009 NIL) (-428 954049 955125 956400 "FRNAALG-" 957150 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 953687 953730 953857 "FRNAAF2" 954000 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 952062 952536 952832 "FRMOD" 953499 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 949805 950437 950755 "FRIDEAL" 951853 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 948996 949083 949374 "FRIDEAL2" 949712 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 948129 948543 948584 "FRETRCT" 948589 NIL FRETRCT (NIL T) -9 NIL 948765 NIL) (-422 947241 947472 947823 "FRETRCT-" 947828 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 944329 945539 945598 "FRAMALG" 946480 NIL FRAMALG (NIL T T) -9 NIL 946772 NIL) (-420 942463 942918 943548 "FRAMALG-" 943771 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 936293 941936 942213 "FRAC" 942218 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 935929 935986 936093 "FRAC2" 936230 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 935565 935622 935729 "FR2" 935866 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 930078 932971 932999 "FPS" 934118 T FPS (NIL) -9 NIL 934675 NIL) (-415 929527 929636 929800 "FPS-" 929946 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 926829 928498 928526 "FPC" 928751 T FPC (NIL) -9 NIL 928893 NIL) (-413 926622 926662 926759 "FPC-" 926764 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 925412 926110 926151 "FPATMAB" 926156 NIL FPATMAB (NIL T) -9 NIL 926308 NIL) (-411 923651 924154 924501 "FPARFRAC" 925128 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 919045 919543 920225 "FORTRAN" 923083 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 916761 917261 917800 "FORT" 918526 T FORT (NIL) -7 NIL NIL NIL) (-408 914437 914999 915027 "FORTFN" 916087 T FORTFN (NIL) -9 NIL 916711 NIL) (-407 914201 914251 914279 "FORTCAT" 914338 T FORTCAT (NIL) -9 NIL 914400 NIL) (-406 912307 912817 913207 "FORMULA" 913831 T FORMULA (NIL) -8 NIL NIL NIL) (-405 912095 912125 912194 "FORMULA1" 912271 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 911618 911670 911843 "FORDER" 912037 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 910714 910878 911071 "FOP" 911445 T FOP (NIL) -7 NIL NIL NIL) (-402 909295 909994 910168 "FNLA" 910596 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 908024 908439 908467 "FNCAT" 908927 T FNCAT (NIL) -9 NIL 909187 NIL) (-400 907563 907983 908011 "FNAME" 908016 T FNAME (NIL) -8 NIL NIL NIL) (-399 906126 907089 907117 "FMTC" 907122 T FMTC (NIL) -9 NIL 907158 NIL) (-398 904872 906062 906108 "FMONOID" 906113 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 901700 902868 902909 "FMONCAT" 904126 NIL FMONCAT (NIL T) -9 NIL 904731 NIL) (-396 900892 901442 901591 "FM" 901596 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 898316 898962 898990 "FMFUN" 900134 T FMFUN (NIL) -9 NIL 900842 NIL) (-394 897585 897766 897794 "FMC" 898084 T FMC (NIL) -9 NIL 898266 NIL) (-393 894664 895524 895578 "FMCAT" 896773 NIL FMCAT (NIL T T) -9 NIL 897268 NIL) (-392 893530 894430 894530 "FM1" 894609 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 891304 891720 892214 "FLOATRP" 893081 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 884882 889033 889654 "FLOAT" 890703 T FLOAT (NIL) -8 NIL NIL NIL) (-389 882320 882820 883398 "FLOATCP" 884349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 881167 881926 881967 "FLINEXP" 881972 NIL FLINEXP (NIL T) -9 NIL 882065 NIL) (-387 880099 880396 880804 "FLINEXP-" 880809 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 879175 879319 879543 "FLASORT" 879951 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 876291 877159 877211 "FLALG" 878438 NIL FLALG (NIL T T) -9 NIL 878905 NIL) (-384 869995 873747 873788 "FLAGG" 875050 NIL FLAGG (NIL T) -9 NIL 875702 NIL) (-383 868721 869060 869550 "FLAGG-" 869555 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 867763 867906 868133 "FLAGG2" 868574 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 864614 865622 865681 "FINRALG" 866809 NIL FINRALG (NIL T T) -9 NIL 867317 NIL) (-380 863774 864003 864342 "FINRALG-" 864347 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 863154 863393 863421 "FINITE" 863617 T FINITE (NIL) -9 NIL 863724 NIL) (-378 855511 857698 857738 "FINAALG" 861405 NIL FINAALG (NIL T) -9 NIL 862858 NIL) (-377 850843 851893 853037 "FINAALG-" 854416 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 850211 850598 850701 "FILE" 850773 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 848869 849207 849261 "FILECAT" 849945 NIL FILECAT (NIL T T) -9 NIL 850161 NIL) (-374 846585 848113 848141 "FIELD" 848181 T FIELD (NIL) -9 NIL 848261 NIL) (-373 845205 845590 846101 "FIELD-" 846106 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 843055 843840 844187 "FGROUP" 844891 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 842145 842309 842529 "FGLMICPK" 842887 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 837977 842070 842127 "FFX" 842132 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 837578 837639 837774 "FFSLPE" 837910 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 833568 834350 835146 "FFPOLY" 836814 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 833072 833108 833317 "FFPOLY2" 833526 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 828918 832991 833054 "FFP" 833059 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 824316 828829 828893 "FF" 828898 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 819442 823659 823849 "FFNBX" 824170 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 814370 818577 818835 "FFNBP" 819296 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 809003 813654 813865 "FFNB" 814203 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 807835 808033 808348 "FFINTBAS" 808800 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 803861 806082 806110 "FFIELDC" 806730 T FFIELDC (NIL) -9 NIL 807106 NIL) (-359 802523 802894 803391 "FFIELDC-" 803396 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 802092 802138 802262 "FFHOM" 802465 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 799787 800274 800791 "FFF" 801607 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 795405 799529 799630 "FFCGX" 799730 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 791027 795137 795244 "FFCGP" 795348 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 786210 790754 790862 "FFCG" 790963 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 765891 775886 775972 "FFCAT" 781137 NIL FFCAT (NIL T T T) -9 NIL 782588 NIL) (-352 761088 762136 763450 "FFCAT-" 764680 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 760499 760542 760777 "FFCAT2" 761039 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 749822 753471 754691 "FEXPR" 759351 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 748784 749219 749260 "FEVALAB" 749344 NIL FEVALAB (NIL T) -9 NIL 749605 NIL) (-348 747943 748153 748491 "FEVALAB-" 748496 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 746509 747326 747529 "FDIV" 747842 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 743529 744270 744385 "FDIVCAT" 745953 NIL FDIVCAT (NIL T T T T) -9 NIL 746390 NIL) (-345 743291 743318 743488 "FDIVCAT-" 743493 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 742511 742598 742875 "FDIV2" 743198 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 741485 741806 742008 "FCTRDATA" 742329 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 740171 740430 740719 "FCPAK1" 741216 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 739270 739671 739812 "FCOMP" 740062 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 722975 726420 729958 "FC" 735752 T FC (NIL) -8 NIL NIL NIL) (-339 715254 719282 719322 "FAXF" 721124 NIL FAXF (NIL T) -9 NIL 721816 NIL) (-338 712531 713188 714013 "FAXF-" 714478 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 707583 711907 712083 "FARRAY" 712388 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 702477 704544 704597 "FAMR" 705620 NIL FAMR (NIL T T) -9 NIL 706080 NIL) (-335 701367 701669 702104 "FAMR-" 702109 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 700536 701289 701342 "FAMONOID" 701347 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 698322 699032 699085 "FAMONC" 700026 NIL FAMONC (NIL T T) -9 NIL 700412 NIL) (-332 696986 698076 698213 "FAGROUP" 698218 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 694781 695100 695503 "FACUTIL" 696667 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 693880 694065 694287 "FACTFUNC" 694591 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 686302 693183 693382 "EXPUPXS" 693736 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 683785 684325 684911 "EXPRTUBE" 685736 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 680056 680648 681378 "EXPRODE" 683124 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 665775 678705 679134 "EXPR" 679660 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 660329 660916 661722 "EXPR2UPS" 665073 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 659961 660018 660127 "EXPR2" 660266 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 651214 659112 659403 "EXPEXPAN" 659797 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 651014 651171 651200 "EXIT" 651205 T EXIT (NIL) -8 NIL NIL NIL) (-321 650494 650738 650829 "EXITAST" 650943 T EXITAST (NIL) -8 NIL NIL NIL) (-320 650121 650183 650296 "EVALCYC" 650426 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 649662 649780 649821 "EVALAB" 649991 NIL EVALAB (NIL T) -9 NIL 650095 NIL) (-318 649143 649265 649486 "EVALAB-" 649491 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 646511 647813 647841 "EUCDOM" 648396 T EUCDOM (NIL) -9 NIL 648746 NIL) (-316 644916 645358 645948 "EUCDOM-" 645953 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 632455 635214 637964 "ESTOOLS" 642186 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 632087 632144 632253 "ESTOOLS2" 632392 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 631838 631880 631960 "ESTOOLS1" 632039 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 625875 627483 627511 "ES" 630279 T ES (NIL) -9 NIL 631689 NIL) (-311 620822 622109 623926 "ES-" 624090 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 617196 617957 618737 "ESCONT" 620062 T ESCONT (NIL) -7 NIL NIL NIL) (-309 616941 616973 617055 "ESCONT1" 617158 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 616616 616666 616766 "ES2" 616885 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 616246 616304 616413 "ES1" 616552 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 615462 615591 615767 "ERROR" 616090 T ERROR (NIL) -7 NIL NIL NIL) (-305 608854 615321 615412 "EQTBL" 615417 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 601357 604168 605617 "EQ" 607438 NIL -3066 (NIL T) -8 NIL NIL NIL) (-303 600989 601046 601155 "EQ2" 601294 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 596280 597327 598420 "EP" 599928 NIL EP (NIL T) -7 NIL NIL NIL) (-301 594880 595171 595477 "ENV" 595994 T ENV (NIL) -8 NIL NIL NIL) (-300 593974 594528 594556 "ENTIRER" 594561 T ENTIRER (NIL) -9 NIL 594607 NIL) (-299 590668 592156 592517 "EMR" 593782 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 589798 589983 590037 "ELTAGG" 590417 NIL ELTAGG (NIL T T) -9 NIL 590628 NIL) (-297 589517 589579 589720 "ELTAGG-" 589725 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 589281 589310 589364 "ELTAB" 589448 NIL ELTAB (NIL T T) -9 NIL 589500 NIL) (-295 588407 588553 588752 "ELFUTS" 589132 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 588149 588205 588233 "ELEMFUN" 588338 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 588019 588040 588108 "ELEMFUN-" 588113 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 582833 586089 586130 "ELAGG" 587070 NIL ELAGG (NIL T) -9 NIL 587533 NIL) (-291 581118 581552 582215 "ELAGG-" 582220 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 580430 580567 580723 "ELABOR" 580982 T ELABOR (NIL) -8 NIL NIL NIL) (-289 579091 579370 579664 "ELABEXPR" 580156 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 571925 573728 574557 "EFUPXS" 578366 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 565373 567174 567985 "EFULS" 571200 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 562858 563216 563688 "EFSTRUC" 565005 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 552649 554215 555763 "EF" 561373 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 551723 552134 552283 "EAB" 552520 T EAB (NIL) -8 NIL NIL NIL) (-283 550905 551682 551710 "E04UCFA" 551715 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 550087 550864 550892 "E04NAFA" 550897 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 549269 550046 550074 "E04MBFA" 550079 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 548451 549228 549256 "E04JAFA" 549261 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 547635 548410 548438 "E04GCFA" 548443 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 546819 547594 547622 "E04FDFA" 547627 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 546001 546778 546806 "E04DGFA" 546811 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 540174 541526 542890 "E04AGNT" 544657 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 538945 539488 539528 "DVARCAT" 539869 NIL DVARCAT (NIL T) -9 NIL 540032 NIL) (-274 538149 538361 538675 "DVARCAT-" 538680 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 531197 537948 538077 "DSMP" 538082 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 529620 530339 530380 "DSEXT" 530743 NIL DSEXT (NIL T) -9 NIL 531037 NIL) (-271 527905 528333 528999 "DSEXT-" 529004 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 522686 523850 524918 "DROPT" 526857 T DROPT (NIL) -8 NIL NIL NIL) (-269 522351 522410 522508 "DROPT1" 522621 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 517466 518592 519729 "DROPT0" 521234 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 515811 516136 516522 "DRAWPT" 517100 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 510398 511321 512400 "DRAW" 514785 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 510031 510084 510202 "DRAWHACK" 510339 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 508762 509031 509322 "DRAWCX" 509760 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 508277 508346 508497 "DRAWCURV" 508688 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 498745 500707 502822 "DRAWCFUN" 506182 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 495509 497438 497479 "DQAGG" 498108 NIL DQAGG (NIL T) -9 NIL 498382 NIL) (-260 483161 489720 489803 "DPOLCAT" 491655 NIL DPOLCAT (NIL T T T T) -9 NIL 492200 NIL) (-259 477998 479346 481304 "DPOLCAT-" 481309 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 471580 477859 477957 "DPMO" 477962 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 465065 471360 471527 "DPMM" 471532 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 464635 464849 464938 "DOMTMPLT" 464996 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 464068 464437 464517 "DOMCTOR" 464575 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 463280 463548 463699 "DOMAIN" 463937 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 457179 462915 463067 "DMP" 463181 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 455124 456246 456287 "DMEXT" 456292 NIL DMEXT (NIL T) -9 NIL 456468 NIL) (-251 454724 454780 454924 "DLP" 455062 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 448546 454051 454241 "DLIST" 454566 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 445343 447399 447440 "DLAGG" 447990 NIL DLAGG (NIL T) -9 NIL 448220 NIL) (-248 444019 444683 444711 "DIVRING" 444803 T DIVRING (NIL) -9 NIL 444886 NIL) (-247 443256 443446 443746 "DIVRING-" 443751 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 441358 441715 442121 "DISPLAY" 442870 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 435397 441272 441335 "DIRPROD" 441340 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 434245 434448 434713 "DIRPROD2" 435190 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 423173 429031 429084 "DIRPCAT" 429342 NIL DIRPCAT (NIL NIL T) -9 NIL 430217 NIL) (-242 420277 420981 421942 "DIRPCAT-" 422279 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 419564 419724 419910 "DIOSP" 420111 T DIOSP (NIL) -7 NIL NIL NIL) (-240 416219 418476 418517 "DIOPS" 418951 NIL DIOPS (NIL T) -9 NIL 419180 NIL) (-239 415768 415882 416073 "DIOPS-" 416078 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 414819 415447 415475 "DIFRING" 415480 T DIFRING (NIL) -9 NIL 415502 NIL) (-237 414491 414565 414593 "DIFFSPC" 414712 T DIFFSPC (NIL) -9 NIL 414787 NIL) (-236 414136 414214 414366 "DIFFSPC-" 414371 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 413192 413670 413711 "DIFFMOD" 413716 NIL DIFFMOD (NIL T) -9 NIL 413814 NIL) (-234 412900 412945 412986 "DIFFDOM" 413107 NIL DIFFDOM (NIL T) -9 NIL 413175 NIL) (-233 412753 412777 412861 "DIFFDOM-" 412866 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 410685 411957 411998 "DIFEXT" 412003 NIL DIFEXT (NIL T) -9 NIL 412156 NIL) (-231 407960 410217 410258 "DIAGG" 410263 NIL DIAGG (NIL T) -9 NIL 410283 NIL) (-230 407344 407501 407753 "DIAGG-" 407758 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 402761 406303 406580 "DHMATRIX" 407113 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 398373 399282 400292 "DFSFUN" 401771 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 393453 397304 397616 "DFLOAT" 398081 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 391716 391997 392386 "DFINTTLS" 393161 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 388745 389737 390137 "DERHAM" 391382 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 386546 388520 388609 "DEQUEUE" 388689 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 385800 385933 386116 "DEGRED" 386408 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 382230 382975 383821 "DEFINTRF" 385028 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 379785 380254 380846 "DEFINTEF" 381749 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 379135 379405 379520 "DEFAST" 379690 T DEFAST (NIL) -8 NIL NIL NIL) (-219 373044 378728 378878 "DECIMAL" 379005 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 370556 371014 371520 "DDFACT" 372588 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 370152 370195 370346 "DBLRESP" 370507 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 368020 368382 368743 "DBASE" 369918 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 367262 367500 367646 "DATAARY" 367919 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 366368 367221 367249 "D03FAFA" 367254 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 365475 366327 366355 "D03EEFA" 366360 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 363425 363891 364380 "D03AGNT" 365006 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 362714 363384 363412 "D02EJFA" 363417 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 362003 362673 362701 "D02CJFA" 362706 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 361292 361962 361990 "D02BHFA" 361995 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 360581 361251 361279 "D02BBFA" 361284 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 353778 355367 356973 "D02AGNT" 358995 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 351546 352069 352615 "D01WGTS" 353252 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 350613 351505 351533 "D01TRNS" 351538 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 349681 350572 350600 "D01GBFA" 350605 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 348749 349640 349668 "D01FCFA" 349673 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 347817 348708 348736 "D01ASFA" 348741 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 346885 347776 347804 "D01AQFA" 347809 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 345953 346844 346872 "D01APFA" 346877 T D01APFA (NIL) -8 NIL NIL NIL) (-199 345021 345912 345940 "D01ANFA" 345945 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 344089 344980 345008 "D01AMFA" 345013 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 343157 344048 344076 "D01ALFA" 344081 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 342225 343116 343144 "D01AKFA" 343149 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 341293 342184 342212 "D01AJFA" 342217 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 334588 336141 337702 "D01AGNT" 339752 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 333925 334053 334205 "CYCLOTOM" 334456 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 330658 331373 332100 "CYCLES" 333218 T CYCLES (NIL) -7 NIL NIL NIL) (-191 329970 330104 330275 "CVMP" 330519 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 327811 328069 328438 "CTRIGMNP" 329698 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 327247 327605 327678 "CTOR" 327758 T CTOR (NIL) -8 NIL NIL NIL) (-188 326756 326978 327079 "CTORKIND" 327166 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 326047 326363 326391 "CTORCAT" 326573 T CTORCAT (NIL) -9 NIL 326686 NIL) (-186 325645 325756 325915 "CTORCAT-" 325920 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 325107 325319 325427 "CTORCALL" 325569 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 324481 324580 324733 "CSTTOOLS" 325004 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 320280 320937 321695 "CRFP" 323793 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 319755 320001 320093 "CRCEAST" 320208 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 318802 318987 319215 "CRAPACK" 319559 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 318186 318287 318491 "CPMATCH" 318678 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 317911 317939 318045 "CPIMA" 318152 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 314259 314931 315650 "COORDSYS" 317246 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 313671 313792 313934 "CONTOUR" 314137 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 309562 311674 312166 "CONTFRAC" 313211 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 309442 309463 309491 "CONDUIT" 309528 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 308530 309084 309112 "COMRING" 309117 T COMRING (NIL) -9 NIL 309169 NIL) (-173 307584 307888 308072 "COMPPROP" 308366 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 307245 307280 307408 "COMPLPAT" 307543 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 296735 307054 307163 "COMPLEX" 307168 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 296371 296428 296535 "COMPLEX2" 296672 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 295710 295831 295991 "COMPILER" 296231 T COMPILER (NIL) -8 NIL NIL NIL) (-168 295428 295463 295561 "COMPFACT" 295669 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 277894 289132 289172 "COMPCAT" 290176 NIL COMPCAT (NIL T) -9 NIL 291524 NIL) (-166 267184 270173 273880 "COMPCAT-" 274236 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 266913 266941 267044 "COMMUPC" 267150 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 266707 266741 266800 "COMMONOP" 266874 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 266263 266458 266545 "COMM" 266640 T COMM (NIL) -8 NIL NIL NIL) (-162 265839 266067 266142 "COMMAAST" 266208 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 265088 265282 265310 "COMBOPC" 265648 T COMBOPC (NIL) -9 NIL 265823 NIL) (-160 263984 264194 264436 "COMBINAT" 264878 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 260441 261015 261642 "COMBF" 263406 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 259199 259557 259792 "COLOR" 260226 T COLOR (NIL) -8 NIL NIL NIL) (-157 258675 258920 259012 "COLONAST" 259127 T COLONAST (NIL) -8 NIL NIL NIL) (-156 258315 258362 258487 "CMPLXRT" 258622 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 257763 258015 258114 "CLLCTAST" 258236 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 253265 254293 255373 "CLIP" 256703 T CLIP (NIL) -7 NIL NIL NIL) (-153 251606 252366 252606 "CLIF" 253092 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 247781 249752 249793 "CLAGG" 250722 NIL CLAGG (NIL T) -9 NIL 251258 NIL) (-151 246203 246660 247243 "CLAGG-" 247248 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 245747 245832 245972 "CINTSLPE" 246112 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 243248 243719 244267 "CHVAR" 245275 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 242422 242976 243004 "CHARZ" 243009 T CHARZ (NIL) -9 NIL 243024 NIL) (-147 242176 242216 242294 "CHARPOL" 242376 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 241234 241821 241849 "CHARNZ" 241896 T CHARNZ (NIL) -9 NIL 241952 NIL) (-145 239140 239888 240241 "CHAR" 240901 T CHAR (NIL) -8 NIL NIL NIL) (-144 238866 238927 238955 "CFCAT" 239066 T CFCAT (NIL) -9 NIL NIL NIL) (-143 238107 238218 238401 "CDEN" 238750 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 234072 237260 237540 "CCLASS" 237847 T CCLASS (NIL) -8 NIL NIL NIL) (-141 233323 233480 233657 "CATEGORY" 233915 T -10 (NIL) -8 NIL NIL NIL) (-140 232896 233242 233290 "CATCTOR" 233295 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 232347 232599 232697 "CATAST" 232818 T CATAST (NIL) -8 NIL NIL NIL) (-138 231823 232068 232160 "CASEAST" 232275 T CASEAST (NIL) -8 NIL NIL NIL) (-137 226961 227980 228724 "CARTEN" 231135 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 226069 226217 226438 "CARTEN2" 226808 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 224385 225219 225476 "CARD" 225832 T CARD (NIL) -8 NIL NIL NIL) (-134 223961 224189 224264 "CAPSLAST" 224330 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 223465 223673 223701 "CACHSET" 223833 T CACHSET (NIL) -9 NIL 223911 NIL) (-132 222935 223257 223285 "CABMON" 223335 T CABMON (NIL) -9 NIL 223391 NIL) (-131 222408 222639 222749 "BYTEORD" 222845 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 221385 221937 222079 "BYTE" 222242 T BYTE (NIL) -8 NIL NIL 222364) (-129 216735 220890 221062 "BYTEBUF" 221233 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214244 216427 216534 "BTREE" 216661 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 211693 213892 214014 "BTOURN" 214154 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 209063 211163 211204 "BTCAT" 211272 NIL BTCAT (NIL T) -9 NIL 211349 NIL) (-125 208730 208810 208959 "BTCAT-" 208964 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 204109 207989 208017 "BTAGG" 208131 T BTAGG (NIL) -9 NIL 208241 NIL) (-123 203599 203724 203930 "BTAGG-" 203935 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 200594 202877 203092 "BSTREE" 203416 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 199732 199858 200042 "BRILL" 200450 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 196384 198458 198499 "BRAGG" 199148 NIL BRAGG (NIL T) -9 NIL 199406 NIL) (-119 194913 195319 195874 "BRAGG-" 195879 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 188037 194257 194442 "BPADICRT" 194760 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 186352 187974 188019 "BPADIC" 188024 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 186050 186080 186194 "BOUNDZRO" 186316 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 181278 182476 183388 "BOP" 185158 T BOP (NIL) -8 NIL NIL NIL) (-114 179059 179463 179938 "BOP1" 180836 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 178760 178821 178849 "BOOLE" 178960 T BOOLE (NIL) -9 NIL 179042 NIL) (-112 177585 178334 178483 "BOOLEAN" 178631 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 176864 177268 177322 "BMODULE" 177327 NIL BMODULE (NIL T T) -9 NIL 177392 NIL) (-110 172665 176662 176735 "BITS" 176811 T BITS (NIL) -8 NIL NIL NIL) (-109 172086 172205 172345 "BINDING" 172545 T BINDING (NIL) -8 NIL NIL NIL) (-108 165998 171681 171830 "BINARY" 171957 T BINARY (NIL) -8 NIL NIL NIL) (-107 163778 165253 165294 "BGAGG" 165554 NIL BGAGG (NIL T) -9 NIL 165691 NIL) (-106 163609 163641 163732 "BGAGG-" 163737 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 162680 162993 163198 "BFUNCT" 163424 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 161370 161548 161836 "BEZOUT" 162504 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 157839 160222 160552 "BBTREE" 161073 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 157573 157626 157654 "BASTYPE" 157773 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 157425 157454 157527 "BASTYPE-" 157532 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 156859 156935 157087 "BALFACT" 157336 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 155715 156274 156460 "AUTOMOR" 156704 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 155441 155446 155472 "ATTREG" 155477 T ATTREG (NIL) -9 NIL NIL NIL) (-97 153693 154138 154490 "ATTRBUT" 155107 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 153301 153521 153587 "ATTRAST" 153645 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 152837 152950 152976 "ATRIG" 153177 T ATRIG (NIL) -9 NIL NIL NIL) (-94 152646 152687 152774 "ATRIG-" 152779 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 152291 152477 152503 "ASTCAT" 152508 T ASTCAT (NIL) -9 NIL 152538 NIL) (-92 152018 152077 152196 "ASTCAT-" 152201 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 150167 151794 151882 "ASTACK" 151961 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 148672 148969 149334 "ASSOCEQ" 149849 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 147704 148331 148455 "ASP9" 148579 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 147467 147652 147691 "ASP8" 147696 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 146335 147072 147214 "ASP80" 147356 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 145233 145970 146102 "ASP7" 146234 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 144187 144910 145028 "ASP78" 145146 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 143156 143867 143984 "ASP77" 144101 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142068 142794 142925 "ASP74" 143056 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 140968 141703 141835 "ASP73" 141967 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140072 140794 140894 "ASP6" 140899 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139019 139749 139867 "ASP55" 139985 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 137968 138693 138812 "ASP50" 138931 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137056 137669 137779 "ASP4" 137889 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 136144 136757 136867 "ASP49" 136977 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 134928 135683 135851 "ASP42" 136033 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 133705 134461 134631 "ASP41" 134815 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 132655 133382 133500 "ASP35" 133618 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 132420 132603 132642 "ASP34" 132647 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 132157 132224 132300 "ASP33" 132375 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131051 131792 131924 "ASP31" 132056 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 130816 130999 131038 "ASP30" 131043 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 130551 130620 130696 "ASP29" 130771 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 130316 130499 130538 "ASP28" 130543 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130081 130264 130303 "ASP27" 130308 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 129165 129779 129890 "ASP24" 130001 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 128242 128967 129079 "ASP20" 129084 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 127330 127943 128053 "ASP1" 128163 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 126273 127004 127123 "ASP19" 127242 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126010 126077 126153 "ASP12" 126228 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 124862 125609 125753 "ASP10" 125897 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 122713 124706 124797 "ARRAY2" 124802 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 118478 122361 122475 "ARRAY1" 122630 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 117510 117683 117904 "ARRAY12" 118301 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 111822 113740 113815 "ARR2CAT" 116445 NIL ARR2CAT (NIL T T T) -9 NIL 117203 NIL) (-56 109256 110000 110954 "ARR2CAT-" 110959 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 108573 108883 109008 "ARITY" 109149 T ARITY (NIL) -8 NIL NIL NIL) (-54 107349 107501 107800 "APPRULE" 108409 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107000 107048 107167 "APPLYORE" 107295 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 106354 106593 106713 "ANY" 106898 T ANY (NIL) -8 NIL NIL NIL) (-51 105632 105755 105912 "ANY1" 106228 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 103162 104069 104396 "ANTISYM" 105356 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 102654 102869 102965 "ANON" 103084 T ANON (NIL) -8 NIL NIL NIL) (-48 96832 101193 101647 "AN" 102218 T AN (NIL) -8 NIL NIL NIL) (-47 92730 94118 94169 "AMR" 94917 NIL AMR (NIL T T) -9 NIL 95517 NIL) (-46 91842 92063 92426 "AMR-" 92431 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76281 91759 91820 "ALIST" 91825 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73086 75875 76044 "ALGSC" 76199 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 69642 70196 70803 "ALGPKG" 72526 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 68919 69020 69204 "ALGMFACT" 69528 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 64954 65533 66127 "ALGMANIP" 68503 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55373 64580 64730 "ALGFF" 64887 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54569 54700 54879 "ALGFACT" 55231 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53510 54110 54148 "ALGEBRA" 54153 NIL ALGEBRA (NIL T) -9 NIL 54194 NIL) (-37 53228 53287 53419 "ALGEBRA-" 53424 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35291 51200 51252 "ALAGG" 51388 NIL ALAGG (NIL T T) -9 NIL 51549 NIL) (-35 34827 34940 34966 "AHYP" 35167 T AHYP (NIL) -9 NIL NIL NIL) (-34 33758 34006 34032 "AGG" 34531 T AGG (NIL) -9 NIL 34810 NIL) (-33 33192 33354 33568 "AGG-" 33573 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30998 31421 31826 "AF" 32834 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30478 30723 30813 "ADDAST" 30926 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29746 30005 30161 "ACPLOT" 30340 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26678 26716 "ACFS" 27323 NIL ACFS (NIL T) -9 NIL 27562 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 1e83b5e7..1f2f3f68 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,6969 +1,6412 @@
 
-(731300 . 3485856134)        
-(((*1 *2 *1) (-12 (-5 *2 (-575)) (-5 *1 (-833))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-655 (-1194))) (-5 *2 (-1290)) (-5 *1 (-1197))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-655 (-1194))) (-5 *3 (-1194)) (-5 *2 (-1290))
-   (-5 *1 (-1197))))
- ((*1 *2 *3 *4 *1)
-  (-12 (-5 *4 (-655 (-1194))) (-5 *3 (-1194)) (-5 *2 (-1290))
-   (-5 *1 (-1197))))) 
-(((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-112)) (-4 *6 (-13 (-463) (-1055 (-575)) (-650 (-575))))
-   (-4 *3 (-13 (-27) (-1220) (-441 *6) (-10 -8 (-15 -2882 ($ *7)))))
-   (-4 *7 (-859))
-   (-4 *8
-    (-13 (-1263 *3 *7) (-373) (-1220)
-     (-10 -8 (-15 -2382 ($ $)) (-15 -4388 ($ $)))))
-   (-5 *2
-    (-3 (|:| |%series| *8)
-     (|:| |%problem| (-2 (|:| |func| (-1176)) (|:| |prob| (-1176))))))
-   (-5 *1 (-433 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1176)) (-4 *9 (-1000 *8))
-   (-14 *10 (-1194))))) 
-(((*1 *2 *2)
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-   (-4 *2 (-13 (-441 *3) (-1019)))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-1055 (-575))) (-4 *3 (-567)) (-5 *1 (-32 *3 *2))
-   (-4 *2 (-441 *3))))
- ((*1 *2)
-  (-12 (-4 *4 (-174)) (-5 *2 (-1190 *4)) (-5 *1 (-166 *3 *4))
-   (-4 *3 (-167 *4))))
- ((*1 *1 *1) (-12 (-4 *1 (-1066)) (-4 *1 (-311))))
- ((*1 *2) (-12 (-4 *1 (-338 *3)) (-4 *3 (-373)) (-5 *2 (-1190 *3))))
- ((*1 *2) (-12 (-4 *1 (-735 *3 *2)) (-4 *3 (-174)) (-4 *2 (-1261 *3))))
+(731328 . 3485863923)        
+(((*1 *1 *2)
+  (-12 (-5 *2 (-656 (-922 *3))) (-4 *3 (-1119)) (-5 *1 (-921 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) 
+(((*1 *1 *1 *1) (-5 *1 (-874)))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1292)) (-5 *1 (-834))))) 
+(((*1 *2 *3 *1)
+  (-12 (-4 *1 (-1090 *4 *5 *6 *3)) (-4 *4 (-464)) (-4 *5 (-805))
+   (-4 *6 (-862)) (-4 *3 (-1084 *4 *5 *6)) (-5 *2 (-112))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-1192 *1)) (-5 *3 (-1196)) (-4 *1 (-27))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1192 *1)) (-4 *1 (-27))))
+ ((*1 *1 *2) (-12 (-5 *2 (-969 *1)) (-4 *1 (-27))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1196)) (-4 *1 (-29 *3)) (-4 *3 (-568))))
+ ((*1 *1 *1) (-12 (-4 *1 (-29 *2)) (-4 *2 (-568))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-47 *3 *2)) (-4 *3 (-1068)) (-4 *2 (-804))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1085 *3 *2)) (-4 *3 (-13 (-859) (-373)))
-   (-4 *2 (-1261 *3))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-904 *3)) (-4 *3 (-1117))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-260 *2)) (-4 *2 (-1235))))) 
-(((*1 *2 *3 *4 *3 *5 *5 *3 *5 *4)
-  (-12 (-5 *4 (-700 (-227))) (-5 *5 (-700 (-575))) (-5 *3 (-575))
-   (-5 *2 (-1052)) (-5 *1 (-767))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1261 *5)) (-4 *5 (-373))
-   (-5 *2
-    (-2 (|:| |ir| (-597 (-418 *6))) (|:| |specpart| (-418 *6))
-     (|:| |polypart| *6)))
-   (-5 *1 (-585 *5 *6)) (-5 *3 (-418 *6))))) 
-(((*1 *2 *1 *1)
-  (-12 (-4 *3 (-373)) (-4 *3 (-1066))
-   (-5 *2 (-2 (|:| -3262 *1) (|:| -4041 *1))) (-4 *1 (-863 *3))))
- ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-99 *5)) (-4 *5 (-373)) (-4 *5 (-1066))
-   (-5 *2 (-2 (|:| -3262 *3) (|:| -4041 *3))) (-5 *1 (-864 *5 *3))
-   (-4 *3 (-863 *5))))) 
-(((*1 *1 *1)
-  (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804))
-   (-4 *4 (-861)) (-4 *2 (-567))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-655 (-575))) (-5 *2 (-919 (-575))) (-5 *1 (-932))))
- ((*1 *2) (-12 (-5 *2 (-919 (-575))) (-5 *1 (-932))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-1302 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1066))
-   (-5 *2 (-830 *3))))
+  (-12 (-5 *2 (-783)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1068))
+   (-14 *4 (-656 (-1196)))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-857)) (-5 *1 (-1308 *3 *2)) (-4 *3 (-1066))))) 
-(((*1 *2)
-  (-12 (-4 *3 (-463)) (-4 *4 (-804)) (-4 *5 (-861))
-   (-4 *6 (-1082 *3 *4 *5)) (-5 *2 (-1290))
-   (-5 *1 (-1089 *3 *4 *5 *6 *7)) (-4 *7 (-1088 *3 *4 *5 *6))))
- ((*1 *2)
-  (-12 (-4 *3 (-463)) (-4 *4 (-804)) (-4 *5 (-861))
-   (-4 *6 (-1082 *3 *4 *5)) (-5 *2 (-1290))
-   (-5 *1 (-1125 *3 *4 *5 *6 *7)) (-4 *7 (-1088 *3 *4 *5 *6))))) 
-(((*1 *2 *3)
-  (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-694 *4 *3)) (-4 *4 (-1117))
-   (-4 *3 (-1117))))) 
-(((*1 *2 *2 *3)
-  (-12 (-5 *2 (-655 (-655 (-958 (-227))))) (-5 *3 (-655 (-885)))
-   (-5 *1 (-479))))) 
-(((*1 *2 *3)
-  (-12 (-4 *4 (-38 (-418 (-575))))
-   (-5 *2 (-2 (|:| -3759 (-1174 *4)) (|:| -3772 (-1174 *4))))
-   (-5 *1 (-1180 *4)) (-5 *3 (-1174 *4))))) 
-(((*1 *2 *2)
-  (-12 (-5 *2 (-655 *6)) (-4 *6 (-1082 *3 *4 *5)) (-4 *3 (-567))
-   (-4 *4 (-804)) (-4 *5 (-861)) (-5 *1 (-994 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-576)) (-5 *1 (-225 *3 *4)) (-4 *3 (-13 (-1068) (-862)))
+   (-14 *4 (-656 (-1196)))))
+ ((*1 *2 *1 *3)
+  (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862))
+   (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783))))
+ ((*1 *2 *1) (-12 (-5 *2 (-783)) (-5 *1 (-284))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-1192 *8)) (-5 *4 (-656 *6)) (-4 *6 (-862))
+   (-4 *8 (-966 *7 *5 *6)) (-4 *5 (-805)) (-4 *7 (-1068))
+   (-5 *2 (-656 (-783))) (-5 *1 (-331 *5 *6 *7 *8))))
+ ((*1 *2 *1) (-12 (-4 *1 (-339 *3)) (-4 *3 (-374)) (-5 *2 (-938))))
+ ((*1 *2 *1)
+  (-12 (-4 *1 (-385 *3 *4)) (-4 *3 (-862)) (-4 *4 (-174))
+   (-5 *2 (-783))))
+ ((*1 *2 *1) (-12 (-4 *1 (-482 *3 *2)) (-4 *3 (-174)) (-4 *2 (-23))))
+ ((*1 *2 *1)
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-     (|:| |endPointContinuity|
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-           (|:| |upperSingular|
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-           (|:| |bothSingular|
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-           (|:| |notEvaluated|
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-           (|:| |notEvaluated| "Range not yet evaluated")))))
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+            (|:| |relerr| (-227))))
+      (|:| -3153
+           (-2
+            (|:| |endPointContinuity|
+                 (-3 (|:| |continuous| "Continuous at the end points")
+                  (|:| |lowerSingular|
+                       "There is a singularity at the lower end point")
+                  (|:| |upperSingular|
+                       "There is a singularity at the upper end point")
+                  (|:| |bothSingular|
+                       "There are singularities at both end points")
+                  (|:| |notEvaluated|
+                       "End point continuity not yet evaluated")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1176 (-227)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3672
+                 (-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)
-  (-12 (-5 *2 (-1159 *3 *4)) (-14 *3 (-936)) (-4 *4 (-373))
-   (-5 *1 (-1010 *3 *4))))) 
+  (-12 (-5 *2 (-783)) (-5 *1 (-687 *3)) (-4 *3 (-1068))
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+ ((*1 *1 *1) (-4 *1 (-1079)))) 
+(((*1 *1 *1)
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) 
+(((*1 *1 *1 *1)
+  (|partial| -12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227)))
-     (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227))
+    (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227)))
+     (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227))
      (|:| |relerr| (-227))))
    (-5 *2
     (-2
@@ -6978,3156 +6421,3527 @@
            (|:| |notEvaluated|
                 "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1174 (-227)))
+          (-3 (|:| |str| (-1176 (-227)))
            (|:| |notEvaluated|
                 "Internal singularities not yet evaluated")))
-     (|:| -1974
+     (|:| -3672
           (-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 (-570))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-655 (-967 (-575)))) (-5 *1 (-448))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1194)) (-5 *4 (-700 (-227))) (-5 *2 (-1121))
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-(((*1 *2 *2 *3)
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-(((*1 *1 *1)
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+  (-12 (-5 *2 (-2 (|:| -2857 *1) (|:| -4449 *1) (|:| |associate| *1)))
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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 *1 *3 *4)
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+    (-1 (-112) (-2 (|:| -4308 *3) (|:| -2273 *4))
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 (((*1 *2 *1)
-  (-12
-   (-5 *2
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-            (|:| |relerr| (-227))))
-      (|:| -3179
-           (-2
-            (|:| |endPointContinuity|
-                 (-3 (|:| |continuous| "Continuous at the end points")
-                  (|:| |lowerSingular|
-                       "There is a singularity at the lower end point")
-                  (|:| |upperSingular|
-                       "There is a singularity at the upper end point")
-                  (|:| |bothSingular|
-                       "There are singularities at both end points")
-                  (|:| |notEvaluated|
-                       "End point continuity not yet evaluated")))
-            (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1174 (-227)))
-                  (|:| |notEvaluated|
-                       "Internal singularities not yet evaluated")))
-            (|:| -1974
-                 (-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 (-570))))
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 (((*1 *2 *2)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *2)
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    (-5 *2
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 (((*1 *2 *1)
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+     (-2 (|:| |eqzro| (-656 *7)) (|:| |neqzro| (-656 *7))
+      (|:| |wcond| (-656 (-969 *4)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *4))))))))))
+   (-5 *1 (-941 *4 *5 *6 *7)) (-4 *7 (-966 *4 *6 *5))))) 
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+      (|:| |wcond| (-656 (-969 *5)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *5))))))))))
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+     (-2 (|:| |eqzro| (-656 *8)) (|:| |neqzro| (-656 *8))
+      (|:| |wcond| (-656 (-969 *5)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *5))))))))))
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+     (-2 (|:| |eqzro| (-656 *7)) (|:| |neqzro| (-656 *7))
+      (|:| |wcond| (-656 (-969 *4)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *4))))))))))
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+      (|:| |wcond| (-656 (-969 *6)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *6))))))))))
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+ ((*1 *2 *3 *4 *5)
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+   (-5 *2
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+      (|:| |wcond| (-656 (-969 *6)))
+      (|:| |bsoln|
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+            (|:| -4261 (-656 (-1287 (-419 (-969 *6))))))))))
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+ ((*1 *2 *3 *4)
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+   (-4 *5 (-13 (-317) (-148))) (-4 *6 (-13 (-862) (-626 (-1196))))
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+    (-656
+     (-2 (|:| |eqzro| (-656 *8)) (|:| |neqzro| (-656 *8))
+      (|:| |wcond| (-656 (-969 *5)))
+      (|:| |bsoln|
+           (-2 (|:| |partsol| (-1287 (-419 (-969 *5))))
+            (|:| -4261 (-656 (-1287 (-419 (-969 *5))))))))))
+   (-5 *1 (-941 *5 *6 *7 *8))))
+ ((*1 *2 *3 *4 *5)
+  (-12 (-5 *3 (-701 *9)) (-5 *4 (-656 *9)) (-5 *5 (-1178))
+   (-4 *9 (-966 *6 *8 *7)) (-4 *6 (-13 (-317) (-148)))
+   (-4 *7 (-13 (-862) (-626 (-1196)))) (-4 *8 (-805)) (-5 *2 (-576))
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+ ((*1 *2 *3 *4 *5)
+  (-12 (-5 *3 (-701 *9)) (-5 *4 (-656 (-1196))) (-5 *5 (-1178))
+   (-4 *9 (-966 *6 *8 *7)) (-4 *6 (-13 (-317) (-148)))
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+   (-5 *1 (-941 *6 *7 *8 *9))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-701 *8)) (-5 *4 (-1178)) (-4 *8 (-966 *5 *7 *6))
+   (-4 *5 (-13 (-317) (-148))) (-4 *6 (-13 (-862) (-626 (-1196))))
+   (-4 *7 (-805)) (-5 *2 (-576)) (-5 *1 (-941 *5 *6 *7 *8))))
+ ((*1 *2 *3 *4 *5 *6)
+  (-12 (-5 *3 (-701 *10)) (-5 *4 (-656 *10)) (-5 *5 (-938))
+   (-5 *6 (-1178)) (-4 *10 (-966 *7 *9 *8)) (-4 *7 (-13 (-317) (-148)))
+   (-4 *8 (-13 (-862) (-626 (-1196)))) (-4 *9 (-805)) (-5 *2 (-576))
+   (-5 *1 (-941 *7 *8 *9 *10))))
+ ((*1 *2 *3 *4 *5 *6)
+  (-12 (-5 *3 (-701 *10)) (-5 *4 (-656 (-1196))) (-5 *5 (-938))
+   (-5 *6 (-1178)) (-4 *10 (-966 *7 *9 *8)) (-4 *7 (-13 (-317) (-148)))
+   (-4 *8 (-13 (-862) (-626 (-1196)))) (-4 *9 (-805)) (-5 *2 (-576))
+   (-5 *1 (-941 *7 *8 *9 *10))))
+ ((*1 *2 *3 *4 *5)
+  (-12 (-5 *3 (-701 *9)) (-5 *4 (-938)) (-5 *5 (-1178))
+   (-4 *9 (-966 *6 *8 *7)) (-4 *6 (-13 (-317) (-148)))
+   (-4 *7 (-13 (-862) (-626 (-1196)))) (-4 *8 (-805)) (-5 *2 (-576))
+   (-5 *1 (-941 *6 *7 *8 *9))))) 
 (((*1 *2 *3)
   (|partial| -12
       (-5 *3
-       (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227)))
-        (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227))
+       (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227)))
+        (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227))
         (|:| |relerr| (-227))))
       (-5 *2
        (-2
@@ -10142,6391 +9956,6501 @@
               (|:| |notEvaluated|
                    "End point continuity not yet evaluated")))
         (|:| |singularitiesStream|
-             (-3 (|:| |str| (-1174 (-227)))
+             (-3 (|:| |str| (-1176 (-227)))
               (|:| |notEvaluated|
                    "Internal singularities not yet evaluated")))
-        (|:| -1974
+        (|:| -3672
              (-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 (-570))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-1151 *3)) (-4 *3 (-1066)) (-5 *2 (-1182 3 *3))))
- ((*1 *1) (-12 (-5 *1 (-1182 *2 *3)) (-14 *2 (-936)) (-4 *3 (-1066))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1150 (-227))) (-5 *1 (-1287))))
- ((*1 *2 *1) (-12 (-5 *2 (-1150 (-227))) (-5 *1 (-1287))))) 
-(((*1 *2 *3)
-  (-12
-   (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-782)) (|:| |poli| *7)
-     (|:| |polj| *7)))
-   (-4 *5 (-804)) (-4 *7 (-964 *4 *5 *6)) (-4 *4 (-463)) (-4 *6 (-861))
-   (-5 *2 (-112)) (-5 *1 (-460 *4 *5 *6 *7))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-359)) (-5 *2 (-782))))
- ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-413)) (-5 *2 (-782))))) 
-(((*1 *2 *3)
+      (-5 *1 (-571))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-1137)) (-5 *1 (-1134))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1292)) (-5 *1 (-834))))) 
+(((*1 *2 *1 *1)
+  (-12 (-5 *2 (-656 (-794 *3))) (-5 *1 (-794 *3)) (-4 *3 (-568))
+   (-4 *3 (-1068))))) 
+(((*1 *1 *1 *2 *2)
+  (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2)
+   (-14 *4 (-783)) (-4 *5 (-174))))
+ ((*1 *1 *1 *2 *1 *2)
+  (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2)
+   (-14 *4 (-783)) (-4 *5 (-174))))
+ ((*1 *2 *2 *3)
   (-12
-   (-5 *3
-    (-655 (-2 (|:| -2412 (-418 (-575))) (|:| -2429 (-418 (-575))))))
-   (-5 *2 (-655 (-418 (-575)))) (-5 *1 (-1037 *4))
-   (-4 *4 (-1261 (-575)))))) 
-(((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-575)) (|has| *1 (-6 -4461)) (-4 *1 (-383 *3))
-   (-4 *3 (-1235))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-942))))) 
-(((*1 *2 *3 *4)
-  (-12 (-4 *5 (-1117)) (-4 *3 (-913 *5)) (-5 *2 (-1285 *3))
-   (-5 *1 (-703 *5 *3 *6 *4)) (-4 *6 (-383 *3))
-   (-4 *4 (-13 (-383 *5) (-10 -7 (-6 -4460))))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1194)) (-5 *4 (-967 (-575))) (-5 *2 (-339))
-   (-5 *1 (-341))))) 
+   (-5 *2
+    (-516 (-419 (-576)) (-245 *5 (-783)) (-876 *4)
+     (-253 *4 (-419 (-576)))))
+   (-5 *3 (-656 (-876 *4))) (-14 *4 (-656 (-1196))) (-14 *5 (-783))
+   (-5 *1 (-517 *4 *5))))) 
+(((*1 *1 *1 *2 *3 *1)
+  (-12 (-4 *1 (-336 *2 *3)) (-4 *2 (-1068)) (-4 *3 (-804))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-625 *2) (-174))) (-5 *2 (-904 *4))
-   (-5 *1 (-172 *4 *5 *3)) (-4 *4 (-1117)) (-4 *3 (-167 *5))))
+  (-12 (-4 *5 (-13 (-626 *2) (-174))) (-5 *2 (-905 *4))
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+     (|:| -3153
+          (-2
+           (|:| |endPointContinuity|
+                (-3 (|:| |continuous| "Continuous at the end points")
+                 (|:| |lowerSingular|
+                      "There is a singularity at the lower end point")
+                 (|:| |upperSingular|
+                      "There is a singularity at the upper end point")
+                 (|:| |bothSingular|
+                      "There are singularities at both end points")
+                 (|:| |notEvaluated|
+                      "End point continuity not yet evaluated")))
+           (|:| |singularitiesStream|
+                (-3 (|:| |str| (-1176 (-227)))
+                 (|:| |notEvaluated|
+                      "Internal singularities not yet evaluated")))
+           (|:| -3672
+                (-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)
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+  (-12
+   (-5 *2
+    (-656
+     (-2
+      (|:| -4147
+           (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227)))
+            (|:| -3672 (-1113 (-855 (-227)))) (|:| |abserr| (-227))
+            (|:| |relerr| (-227))))
+      (|:| -3153
+           (-2
+            (|:| |endPointContinuity|
+                 (-3 (|:| |continuous| "Continuous at the end points")
+                  (|:| |lowerSingular|
+                       "There is a singularity at the lower end point")
+                  (|:| |upperSingular|
+                       "There is a singularity at the upper end point")
+                  (|:| |bothSingular|
+                       "There are singularities at both end points")
+                  (|:| |notEvaluated|
+                       "End point continuity not yet evaluated")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1176 (-227)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3672
+                 (-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 (-571))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1232 *3)) (-4 *3 (-993))))) 
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-      (-4 *3
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-         (-15 -1608 (*6 $)))))))
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+           (|:| |upperInfinite| "The top of range is infinite")
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   (-12
+   (-5 *3
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-(((*1 *2 *2)
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+    (-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")))
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 (((*1 *2 *3 *1)
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-(((*1 *2 *3)
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- ((*1 *2 *3 *4)
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- ((*1 *2 *3)
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\ No newline at end of file