* algebra/vector.spad.pamphlet (DualBasis): New.

	(LinearBasis): Likewise.
	(LinearElement): Use them.
	(LinearForm): New.

10 files changed, 27449 insertions, 27287 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index dbb4c351..39cb215e 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,10 @@
+2010-07-03  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
+	* algebra/vector.spad.pamphlet (DualBasis): New.
+	(LinearBasis): Likewise.
+	(LinearElement): Use them.
+	(LinearForm): New.
+
 2010-07-01  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
 	* interp/define.boot (registerInlinableDomain): New.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 5d04110f..690e7630 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -612,7 +612,6 @@ $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT)
 $(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT)
 $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT)
 $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT)
-$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
 
 axiom_algebra_layer_10 = \
   RESULT   BFUNCT   BPADIC   ANY      \
@@ -641,7 +640,7 @@ axiom_algebra_layer_10 = \
   FUNDESC  XPBWPOLY SMATCAT  SMATCAT- \
   RMATRIX  RMATCAT  RMATCAT- DIRPROD \
   DIRPCAT  DIRPCAT- IVECTOR  MATRIX  \
-  MATCAT   MATCAT-  IIARRAY2 LINELT
+  MATCAT   MATCAT-  IIARRAY2 
 
 
 axiom_algebra_layer_10_nrlibs = \
@@ -983,7 +982,8 @@ axiom_algebra_layer_user =  \
         ASP78    ASP9     ASP12    ASP55    ASP8     ASP19    \
         ASP20    ASP30    ASP31    ASP35    ASP41    ASP42    \
 	ASP74    ASP77    ASP80    ASP29    IRFORM   COMPILER \
-	ITFORM   ELABOR   TALGOP   YDIAGRAM
+	ITFORM   ELABOR   TALGOP   YDIAGRAM LINELT   DBASIS   \
+	LINFORM  LINBASIS
 
 axiom_algebra_layer_user_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -1064,6 +1064,13 @@ $(OUT)/ELABOR.$(FASLEXT): $(OUT)/ITFORM.$(FASLEXT) $(OUT)/ENV.$(FASLEXT) \
 	$(OUT)/IRFORM.$(FASLEXT)
 
 
+$(OUT)/LINBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/OVAR.$(FASLEXT)
+$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
+$(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT)
+$(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \
+	$(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT)
+
+
 .PHONY: all all-algebra mkdir-output-directory
 all: all-ax
 
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 2a600ccb..d0d6cc7e 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -619,7 +619,6 @@ $(OUT)/DIRPROD.$(FASLEXT): $(OUT)/DIRPCAT.$(FASLEXT)
 $(OUT)/DIRPCAT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/IVECTOR.$(FASLEXT)
 $(OUT)/MATRIX.$(FASLEXT): $(OUT)/MATCAT.$(FASLEXT)
 $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT)
-$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
 
 axiom_algebra_layer_10 = \
   RESULT   BFUNCT   BPADIC   ANY      \
@@ -648,7 +647,7 @@ axiom_algebra_layer_10 = \
   FUNDESC  XPBWPOLY SMATCAT  SMATCAT- \
   RMATRIX  RMATCAT  RMATCAT- DIRPROD \
   DIRPCAT  DIRPCAT- IVECTOR  MATRIX  \
-  MATCAT   MATCAT-  IIARRAY2 LINELT
+  MATCAT   MATCAT-  IIARRAY2 
 
 
 axiom_algebra_layer_10_nrlibs = \
@@ -1062,7 +1061,8 @@ axiom_algebra_layer_user =  \
         ASP78    ASP9     ASP12    ASP55    ASP8     ASP19    \
         ASP20    ASP30    ASP31    ASP35    ASP41    ASP42    \
 	ASP74    ASP77    ASP80    ASP29    IRFORM   COMPILER \
-	ITFORM   ELABOR   TALGOP   YDIAGRAM
+	ITFORM   ELABOR   TALGOP   YDIAGRAM LINELT   DBASIS   \
+	LINFORM  LINBASIS
 
 axiom_algebra_layer_user_nrlibs = \
 	$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -1142,6 +1142,13 @@ $(OUT)/ITFORM.$(FASLEXT): $(OUT)/IRFORM.$(FASLEXT)
 $(OUT)/ELABOR.$(FASLEXT): $(OUT)/ITFORM.$(FASLEXT) $(OUT)/ENV.$(FASLEXT) \
 	$(OUT)/IRFORM.$(FASLEXT)
 
+
+$(OUT)/LINBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/OVAR.$(FASLEXT)
+$(OUT)/LINELT.$(FASLEXT): $(OUT)/VSPACE.$(FASLEXT) $(OUT)/FM.$(FASLEXT)
+$(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT)
+$(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \
+	$(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT)
+
 @
 
 \section{Broken Files}
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index ba666e3a..3acfbcfe 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -126,6 +126,7 @@
   (|DrawComplex| . DRAWCX)
   (|DrawNumericHack| . DRAWHACK)
   (|DrawOption| . DROPT)
+  (|DualBasis| . DBASIS)
   (|EigenPackage| . EP)
   (|ElaboratedExpression| . ELABEXPR)
   (|ElementaryFunctionDefiniteIntegration| . DEFINTEF)
@@ -231,7 +232,9 @@
   (|LetAst| . LETAST)
   (|Library| . LIB)
   (|LieSquareMatrix| . LSQM)
+  (|LinearBasis| . LINBASIS)
   (|LinearElement| . LINELT)
+  (|LinearForm| . LINFORM)
   (|LinearOrdinaryDifferentialOperator| . LODO)
   (|LinearSystemMatrixPackage| . LSMP)
   (|LinearSystemMatrixPackage1| . LSMP1)
diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet
index 05474370..a708524a 100644
--- a/src/algebra/vector.spad.pamphlet
+++ b/src/algebra/vector.spad.pamphlet
@@ -450,11 +450,49 @@ DirectProductFunctions2(dim, A, B): Exports == Implementation where
 
 \section{Vector space of finite dimension given by a basis}
 
+
+<<domain LINBASIS LinearBasis>>=
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Descrption:
+++   Representation of a vector space basis, given by symbols.
+)abbrev domain LINBASIS LinearBasis
+LinearBasis(vars: List Symbol): Public == Private where
+  Public == Join(OrderedFinite,CoercibleFrom OrderedVariableList vars) with
+    dual: DualBasis vars -> %
+      ++ \spad{dual f} constructs the dual vector of a linear form
+      ++ which is part of a basis.
+  Private == OrderedVariableList vars add
+    coerce(s: Rep): % == per s
+    dual f == index(lookup f)@%
+
+@
+
+<<domain DBASIS DualBasis>>=
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Descrption:
+++   Representation of a dual vector space basis, given by symbols.
+)abbrev domain DBASIS DualBasis
+DualBasis(vars: List Symbol): Public == Private where
+  Public == Join(OrderedFinite) with
+    dual: LinearBasis vars -> %
+      ++ \spad{dual x} constructs the dual vector of a linear element
+      ++ which is part of a basis.
+  Private == OrderedVariableList vars add
+    dual v == index(lookup v)@%
+    coerce(x: %): OutputForm ==
+      superscript(convert(rep x)@Symbol,['_*::OutputForm])::OutputForm
+
+@
+
 <<domain LINELT LinearElement>>=
 )abbrev domain LINELT LinearElement
 ++ Author: Gabriel Dos Reis
 ++ Date Created: June 30, 2010
-++ Date Last Modified: June 30, 2010
+++ Date Last Modified: July 2, 2010
 ++ Description:
 ++   A simple data structure for elements that form a
 ++   vector space of finite dimension over a given field,
@@ -462,12 +500,13 @@ DirectProductFunctions2(dim, A, B): Exports == Implementation where
 LinearElement(K,B): Public == Private where
   K: Field
   B: List Symbol
-  macro Basis == OrderedVariableList B
-  Public == Join(VectorSpace K,CoercibleFrom Basis) with
-    linearElement: (List K,List Basis) -> %
-      ++ \spad{linearElement([x1,..,xn],[b1,..,bn]) constructs
-      ++ a linear element with coordinates \spad{[x1,..,xn]} with
-      ++ respect to the basis elements \spad{b1},...\spad{bn}.
+  macro Basis == LinearBasis B
+  Public == Join(VectorSpace K,CoercibleFrom Basis,_
+                 IndexedDirectProductCategory(K,Basis)) with
+    linearElement: List K -> %
+      ++ \spad{linearElement [x1,..,xn]} returns a linear element
+      ++  with coordinates \spad{[x1,..,xn]} with respect to
+      ++ the basis elements \spad{B}.
     coordinates: % -> Vector K
       ++ \spad{coordinates x} returns the coordinates of the linear
       ++ element with respect to the basis \spad{B}.
@@ -478,10 +517,9 @@ LinearElement(K,B): Public == Private where
     dimension() ==
       size()$Basis::CardinalNumber
 
-    linearElement(cs,bs) ==
-      null cs or null bs => per 0$Rep
+    linearElement cs ==
       reduce(_+@(%,%)->%,
-         [per monomial(c,b) for c in cs for b in bs])
+         [per monomial(c,index(i)$Basis) for c in cs for i in 1..],0)
 
     coordinates x ==
       n := #B
@@ -496,7 +534,53 @@ LinearElement(K,B): Public == Private where
 @
 
 
+<<domain LINFORM LinearForm>>=
+)abbrev domain LINFORM LinearForm
+++ Author: Gabriel Dos Reis
+++ Date Created: July 2, 2010
+++ Date Last Modified: July 2, 2010
+++ Description:
+++   A simple data structure for linear forms on a vector space of
+++   finite dimension over a given field, with a given symbolic basis.
+LinearForm(K,B): Public == Private where
+  K: Field
+  B: List Symbol
+  macro Basis == DualBasis B
+  Public == Join(VectorSpace K,Eltable(LinearElement(K,B),K)) with
+    linearForm: List K -> %
+      ++ \spad{linearForm [x1,..,xn]} constructs
+      ++ a linear form with coordinates \spad{[x1,..,xn]} with
+      ++ respect to the basis elements \spad{DualBasis B}.
+    coordinates: % -> Vector K
+      ++ \spad{coordinates x} returns the coordinates of the linear
+      ++ form with respect to the basis \spad{DualBasis B}.
+  Private == FreeModule(K,Basis) add
+    dimension() ==
+      size()$Basis::CardinalNumber
+
+    linearForm cs ==
+      reduce(_+@(%,%)->%,
+         [per monomial(c,index(i)$Basis) for c in cs for i in 1..],0)
+
+    coordinates f ==
+      n := #B
+      v: Vector K := new(n,0$K)
+      ts := terms rep f
+      for i in 1..n repeat
+        t := first ts
+        lookup first t = i => 
+          v.i := second t
+          ts := rest ts
+      v
+
+    elt(f,x) ==
+      dot(coordinates f, coordinates x)$Vector(K)
+
+@
+
+
 \section{License}
+
 <<license>>=
 --Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
 --All rights reserved.
@@ -541,7 +625,12 @@ LinearElement(K,B): Public == Private where
 <<category DIRPCAT DirectProductCategory>>
 <<domain DIRPROD DirectProduct>>
 <<package DIRPROD2 DirectProductFunctions2>>
+
+<<domain LINBASIS LinearBasis>>
+<<domain DBASIS DualBasis>>
+
 <<domain LINELT LinearElement>>
+<<domain LINFORM LinearForm>>
  
 @
 \eject
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index f00b171a..1a7910e9 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2294960 . 3486967787)       
+(2296269 . 3487133927)       
 (-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."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . 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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4463 . T) (-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4459 . T) (-4464 . T) (-4458 . T)) 
+((-4467 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4463 . T) (-4468 . T) (-4462 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -2022) 
+(-32 R -2051) 
 ((|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 -1060) (QUOTE (-576))))) 
+((|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) 
 (-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 -4466))) 
+((|HasAttribute| |#1| (QUOTE -4470))) 
 (-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}."))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . 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"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . 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 -2022 UP UPUP -2948) 
+(-40 -2051 UP UPUP -2587) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2802 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-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)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (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 -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) 
-(-41 R -2022) 
+((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2839 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2839 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2839 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2839 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2839 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-2839 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) 
+(-41 R -2051) 
 ((|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 (-464))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -443) (|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 (-317)))) 
+((|HasCategory| |#1| (QUOTE (-318)))) 
 (-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."))) 
-((-4463 |has| |#1| (-568)) (-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) 
+((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) 
 (-45 |Key| |Entry|) 
 ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) 
-((-4466 . T) (-4467 . T)) 
-((-2802 (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) 
+((-4470 . T) (-4471 . T)) 
+((-2839 (-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|))))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-865))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-375)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| $ (QUOTE (-1071))) (|HasCategory| $ (LIST (QUOTE -1060) (QUOTE (-576))))) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) 
 (-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}."))) 
-((-4463 . T)) 
+((-4467 . 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 -2022) 
+(-54 |Base| R -2051) 
 ((|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"))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . 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}"))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-61 -2676) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-61 -2713) 
 ((|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 -2676) 
+(-62 -2713) 
 ((|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 -2676) 
+(-63 -2713) 
 ((|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 -2676) 
+(-64 -2713) 
 ((|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 -2676) 
+(-65 -2713) 
 ((|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 -2676) 
+(-66 -2713) 
 ((|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 -2676) 
+(-67 -2713) 
 ((|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 -2676) 
+(-68 -2713) 
 ((|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 -2676) 
+(-69 -2713) 
 ((|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 -2676) 
+(-70 -2713) 
 ((|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 -2676) 
+(-71 -2713) 
 ((|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 -2676) 
+(-72 -2713) 
 ((|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 -2676) 
+(-73 -2713) 
 ((|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 -2676) 
+(-74 -2713) 
 ((|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 -2676) 
+(-77 -2713) 
 ((|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 -2676) 
+(-78 -2713) 
 ((|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 -2676) 
+(-79 -2713) 
 ((|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 -2676) 
+(-80 -2713) 
 ((|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 -2676) 
+(-81 -2713) 
 ((|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 -2676) 
+(-82 -2713) 
 ((|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 -2676) 
+(-83 -2713) 
 ((|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 -2676) 
+(-84 -2713) 
 ((|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 -2676) 
+(-85 -2713) 
 ((|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 -2676) 
+(-86 -2713) 
 ((|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 -2676) 
+(-87 -2713) 
 ((|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 -2676) 
+(-88 -2713) 
 ((|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 -2676) 
+(-89 -2713) 
 ((|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 (-374)))) 
+((|HasCategory| |#1| (QUOTE (-375)))) 
 (-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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -318,15 +318,15 @@ NIL
 NIL 
 (-97) 
 ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) 
-((-4466 . T)) 
+((-4470 . 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."))) 
-((-4466 . T) ((-4468 "*") . T) (-4467 . T) (-4463 . T) (-4461 . T) (-4460 . T) (-4459 . T) (-4464 . T) (-4458 . T) (-4457 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4462 . T) (-4465 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4453 . T)) 
+((-4470 . T) ((-4472 "*") . T) (-4471 . T) (-4467 . T) (-4465 . T) (-4464 . T) (-4463 . T) (-4468 . T) (-4462 . T) (-4461 . T) (-4460 . T) (-4459 . T) (-4458 . T) (-4466 . T) (-4469 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4457 . 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}."))) 
-((-4463 . T)) 
+((-4467 . 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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-104 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4468 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4472 "*")))) 
 (-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"))) 
-((-4466 . T)) 
+((-4470 . 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."))) 
-((-4467 . T)) 
+((-4471 . 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (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) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2839 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (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}"))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1122))) (|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 (-1122))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-112) (QUOTE (-102)))) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-112) (QUOTE (-102)))) 
 (-111 R S) 
 ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . 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 -2022 UP) 
+(-116 -2051 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}."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-117 |#1|) (QUOTE (-929))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1044))) (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-2802 (|HasCategory| (-117 |#1|) (QUOTE (-833))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1174))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (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))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-929)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-117 |#1|) (QUOTE (-932))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-117 |#1|) (QUOTE (-1047))) (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865))) (-2839 (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-1177))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-318))) (|HasCategory| (-117 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4467))) 
+((|HasAttribute| |#1| (QUOTE -4471))) 
 (-120 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-123 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-124) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
 (-125 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-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."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2802 (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-130) (QUOTE (-862))) (-2802 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-2839 (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-130) (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-130) (QUOTE (-865))) (-2839 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4468 "*") . T)) 
+(((-4472 "*") . T)) 
 NIL 
-(-136 |minix| -2755 S T$) 
+(-136 |minix| -2791 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -2755 R) 
+(-137 |minix| -2791 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) 
-((-4466 . T) (-4456 . T) (-4467 . T)) 
-((-2802 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|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 (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) 
+((-4470 . T) (-4460 . T) (-4471 . T)) 
+((-2839 (-12 (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (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."))) 
-((-4463 . T)) 
+((-4467 . 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."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-149 -2022 UP UPUP) 
+(-149 -2051 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 -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasAttribute| |#1| (QUOTE -4466))) 
+((|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasAttribute| |#1| (QUOTE -4470))) 
 (-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."))) 
-((-4461 . T) (-4460 . T) (-4463 . T)) 
+((-4465 . T) (-4464 . T) (-4467 . 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 -2022) 
+(-159 R -2051) 
 ((|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 (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasAttribute| |#2| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) 
+((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4466)) (|HasAttribute| |#2| (QUOTE -4469)) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569)))) 
 (-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})"))) 
-((-4459 -2802 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4155 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 -2839 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-4159 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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}."))) 
-((-4459 -2802 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4465 |has| |#1| (-6 -4465)) (-4155 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2802 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-929))))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4465)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-360))))) 
+((-4463 -2839 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-4159 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-2839 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-361)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-932))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-932)))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-932))))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1085))) (-12 (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasAttribute| |#1| (QUOTE -4466)) (|HasAttribute| |#1| (QUOTE -4469)) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-361))))) 
 (-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."))) 
-(((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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}."))) 
-(((-4468 "*") . T) (-4459 . T) (-4464 . T) (-4458 . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") . T) (-4463 . T) (-4468 . T) (-4462 . T) (-4464 . T) (-4465 . T) (-4467 . 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| (-972 |#2|) (LIST (QUOTE -902) (|devaluate| |#1|)))) 
+((|HasCategory| (-975 |#2|) (LIST (QUOTE -905) (|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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-190 R -2022) 
+(-190 R -2051) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -796,4413 +796,4425 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2022 UP UPUP R) 
+(-217 |vars|) 
+((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
+NIL 
+NIL 
+(-218 -2051 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 -2022 FP) 
+(-219 -2051 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (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) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) 
 (-220) 
+((|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."))) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2839 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) 
+(-221) 
 ((|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 -2022) 
+(-222 R -2051) 
 ((|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 
-(-222 R) 
+(-223 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
-(-223 R1 R2) 
+(-224 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-224 S) 
+(-225 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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-225 |CoefRing| |listIndVar|) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-226 |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}."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-226 R -2022) 
+(-227 R -2051) 
 ((|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) 
+(-228) 
 ((|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}."))) 
-((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4148 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-228) 
+(-229) 
 ((|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)}.}"))) 
 NIL 
 NIL 
-(-229 R) 
+(-230 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}"))) 
-((-4466 . T) (-4467 . T)) 
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-(-230 A S) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-231 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
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+(-232 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."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-232 R) 
+(-233 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-233 S T$) 
+(-234 S T$) 
 ((|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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-234 T$) 
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 ((|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 ((|#1| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#1| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-235 R) 
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 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-236 S) 
+(-237 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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}."))) 
 NIL 
 NIL 
-(-237) 
+(-238) 
 ((|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}."))) 
 NIL 
 NIL 
-(-238) 
+(-239) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-239 A S) 
+(-240 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 -4466))) 
-(-240 S) 
+((|HasAttribute| |#1| (QUOTE -4470))) 
+(-241 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}."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-241) 
+(-242) 
 ((|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 -2755 R) 
+(-243 S -2791 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 (-374))) (|HasCategory| |#3| (QUOTE (-806))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4463)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-739))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1071))) (|HasCategory| |#3| (QUOTE (-1122)))) 
-(-243 -2755 R) 
+((|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (QUOTE (-865))) (|HasAttribute| |#3| (QUOTE -4467)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (QUOTE (-1125)))) 
+(-244 -2791 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"))) 
-((-4460 |has| |#2| (-1071)) (-4461 |has| |#2| (-1071)) (-4463 |has| |#2| (-6 -4463)) (-4466 . T)) 
+((-4464 |has| |#2| (-1074)) (-4465 |has| |#2| (-1074)) (-4467 |has| |#2| (-6 -4467)) (-4470 . T)) 
 NIL 
-(-244 -2755 A B) 
+(-245 -2791 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 -2755 R) 
+(-246 -2791 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."))) 
-((-4460 |has| |#2| (-1071)) (-4461 |has| |#2| (-1071)) (-4463 |has| |#2| (-6 -4463)) (-4466 . T)) 
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+(-247) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
 NIL 
-(-247 S) 
+(-248 S) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
 NIL 
 NIL 
-(-248) 
+(-249) 
 ((|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}."))) 
-((-4459 . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-249 S) 
+(-250 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."))) 
 NIL 
 NIL 
-(-250 S) 
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 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-4467 . T) (-4466 . T)) 
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-(-251 M) 
+((-4471 . T) (-4470 . T)) 
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+(-252 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 R) 
+(-253 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-253 |vl| R) 
+(-254 |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"))) 
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-(-254) 
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+(-255) 
 ((|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 
-(-255) 
+(-256) 
 ((|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 
-(-256) 
+(-257) 
 ((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
 NIL 
 NIL 
-(-257 |n| R M S) 
+(-258 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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-(-259 A R S V E) 
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+(-260 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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)))) 
-(-260 R S V E) 
+((|HasCategory| |#2| (QUOTE (-239)))) 
+(-261 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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-261 S) 
+(-262 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}."))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
-(-262) 
+(-263) 
 ((|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 
-(-263 R |Ex|) 
+(-264 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 
-(-264) 
+(-265) 
 ((|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 
-(-265 R) 
+(-266 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 
-(-266 |Ex|) 
+(-267 |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 
-(-267) 
+(-268) 
 ((|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 
-(-268) 
+(-269) 
 ((|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 
-(-269 S) 
+(-270 S) 
 ((|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 
-(-270) 
+(-271) 
 ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) 
 NIL 
 NIL 
-(-271 S R) 
+(-272 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-237)))) 
-(-272 R) 
+((|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-238)))) 
+(-273 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
-(-273 R S V) 
+(-274 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
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+(-275 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 
-(-275 S) 
+(-276 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 
-(-276) 
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 ((|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\axiom{\\spad{l}}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}."))) 
 NIL 
 NIL 
-(-277) 
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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 
-(-278) 
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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 
-(-279) 
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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 
-(-280) 
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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 
-(-281) 
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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 
-(-282) 
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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 
-(-283) 
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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 
-(-284) 
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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 
-(-285 R -2022) 
+(-286 R -2051) 
 ((|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 
-(-286 R -2022) 
+(-287 R -2051) 
 ((|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 
-(-287 |Coef| UTS ULS) 
+(-288 |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 (-374)))) 
-(-288 |Coef| ULS UPXS EFULS) 
+((|HasCategory| |#1| (QUOTE (-375)))) 
+(-289 |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 (-374)))) 
-(-289) 
+((|HasCategory| |#1| (QUOTE (-375)))) 
+(-290) 
 ((|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 
-(-290) 
+(-291) 
 ((|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 
-(-291 A S) 
+(-292 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 (-862))) (|HasCategory| |#2| (QUOTE (-1122)))) 
-(-292 S) 
+((|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125)))) 
+(-293 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}."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-293 S) 
+(-294 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-294) 
+(-295) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-295 |Coef| UTS) 
+(-296 |Coef| UTS) 
 ((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) 
 NIL 
 NIL 
-(-296 S T$) 
+(-297 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 
-(-297 S |Dom| |Im|) 
+(-298 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 -4467))) 
-(-298 |Dom| |Im|) 
+((|HasAttribute| |#1| (QUOTE -4471))) 
+(-299 |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 
-(-299 S R |Mod| -2921 -3073 |exactQuo|) 
+(-300 S R |Mod| -3062 -3283 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-300) 
+(-301) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4459 . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-301) 
+(-302) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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 
-(-302 R) 
+(-303 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 
-(-303 S R) 
+(-304 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 
-(-304 S) 
+(-305 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) 
-((-4463 -2802 (|has| |#1| (-1071)) (|has| |#1| (-485))) (-4460 |has| |#1| (-1071)) (-4461 |has| |#1| (-1071))) 
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-(-305 |Key| |Entry|) 
+((-4467 -2839 (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4464 |has| |#1| (-1074)) (-4465 |has| |#1| (-1074))) 
+((|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2839 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-742)))) (|HasCategory| |#1| (QUOTE (-486))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1137)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-313))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-486)))) (-2839 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742)))) (-2839 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-742)))) 
+(-306 |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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) 
-(-306) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102)))) 
+(-307) 
 ((|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 
-(-307 -2022 S) 
+(-308 -2051 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 
-(-308 E -2022) 
+(-309 E -2051) 
 ((|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 
-(-309 A B) 
+(-310 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 
-(-310) 
+(-311) 
 ((|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 
-(-311 S) 
+(-312 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 -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1071)))) 
-(-312) 
+((|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1074)))) 
+(-313) 
 ((|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 
-(-313 R1) 
+(-314 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 
-(-314 R1 R2) 
+(-315 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 
-(-315) 
+(-316) 
 ((|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 
-(-316 S) 
+(-317 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 
-(-317) 
+(-318) 
 ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-318 S R) 
+(-319 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 
-(-319 R) 
+(-320 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 
-(-320 -2022) 
+(-321 -2051) 
 ((|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 
-(-321) 
+(-322) 
 ((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) 
 NIL 
 NIL 
-(-322) 
+(-323) 
 ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) 
 NIL 
 NIL 
-(-323 R FE |var| |cen|) 
+(-324 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
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-(-324 R S) 
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+(-325 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 
-(-325 R FE) 
+(-326 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 
-(-326 R) 
+(-327 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
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-(-327 R -2022) 
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+(-328 R -2051) 
 ((|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 
-(-328) 
+(-329) 
 ((|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 
-(-329 FE |var| |cen|) 
+(-330 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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+(-331 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 
-(-332 S) 
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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."))) 
-((-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-805)))) 
-(-333 S E) 
+((-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-808)))) 
+(-334 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) 
 NIL 
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+((|HasCategory| (-787) (QUOTE (-808)))) 
+(-336 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-336 R E) 
+((|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-337 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-337 S) 
+(-338 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-338 S -2022) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-339 S -2051) 
 ((|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 (-379)))) 
-(-339 -2022) 
+((|HasCategory| |#2| (QUOTE (-380)))) 
+(-340 -2051) 
 ((|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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-340) 
+(-341) 
 ((|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 
-(-341 E) 
+(-342 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 
-(-342) 
+(-343) 
 ((|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 
-(-343) 
+(-344) 
 ((|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 
-(-344 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+(-345 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 
-(-345 S -2022 UP UPUP R) 
+(-346 S -2051 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 
-(-346 -2022 UP UPUP R) 
+(-347 -2051 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 
-(-347 -2022 UP UPUP R) 
+(-348 -2051 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
-(-348 S R) 
+(-349 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) 
-(-349 R) 
+((|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+(-350 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
-(-350 |basicSymbols| |subscriptedSymbols| R) 
+(-351 |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.}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1060) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1071))) (|HasCategory| $ (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-351 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-352 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 
-(-352 S -2022 UP UPUP) 
+(-353 S -2051 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 (-379))) (|HasCategory| |#2| (QUOTE (-374)))) 
-(-353 -2022 UP UPUP) 
+((|HasCategory| |#2| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-375)))) 
+(-354 -2051 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."))) 
-((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-354 |p| |extdeg|) 
+(-355 |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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) 
-(-355 GF |defpol|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) 
+(-356 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-356 GF |extdeg|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-357 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-357 GF) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-358 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 
-(-358 F1 GF F2) 
+(-359 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 
-(-359 S) 
+(-360 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 
-(-360) 
+(-361) 
 ((|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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-361 R UP -2022) 
+(-362 R UP -2051) 
 ((|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 
-(-362 |p| |extdeg|) 
+(-363 |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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) 
-(-363 GF |uni|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) 
+(-364 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-364 GF |extdeg|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-365 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-365 |p| |n|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-366 |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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| (-930 |#1|) (QUOTE (-146))) (|HasCategory| (-930 |#1|) (QUOTE (-379)))) (|HasCategory| (-930 |#1|) (QUOTE (-148))) (|HasCategory| (-930 |#1|) (QUOTE (-379))) (|HasCategory| (-930 |#1|) (QUOTE (-146)))) 
-(-366 GF |defpol|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) 
+(-367 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-367 -2022 GF) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-368 -2051 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 
-(-368 GF) 
+(-369 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\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 
-(-369 -2022 FP FPP) 
+(-370 -2051 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 
-(-370 GF |n|) 
+(-371 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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-371 R |ls|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-372 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 
-(-372 S) 
+(-373 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-373 S) 
+(-374 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
 NIL 
 NIL 
-(-374) 
+(-375) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-375 |Name| S) 
+(-376 |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 
-(-376 S) 
+(-377 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
 NIL 
 NIL 
-(-377 S R) 
+(-378 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 (-568)))) 
-(-378 R) 
+((|HasCategory| |#2| (QUOTE (-569)))) 
+(-379 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4463 |has| |#1| (-568)) (-4461 . T) (-4460 . T)) 
+((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) 
 NIL 
-(-379) 
+(-380) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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 
-(-380 S R UP) 
+(-381 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 (-374)))) 
-(-381 R UP) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-375)))) 
+(-382 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-382 S A R B) 
+(-383 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-383 A S) 
+(-384 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4467)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122)))) 
-(-384 S) 
+((|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125)))) 
+(-385 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4466 . T)) 
+((-4470 . T)) 
 NIL 
-(-385 |VarSet| R) 
+(-386 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4461 . T) (-4460 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4465 . T) (-4464 . T)) 
 NIL 
-(-386 S V) 
+(-387 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 
-(-387 S R) 
+(-388 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 -652) (QUOTE (-576))))) 
-(-388 R) 
+((|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) 
+(-389 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 
-(-389 |Par|) 
+(-390 |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 
-(-390) 
+(-391) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4449 . T) (-4457 . T) (-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4453 . T) (-4461 . T) (-4148 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-391 |Par|) 
+(-392 |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 
-(-392 R S) 
+(-393 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}"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174)))) 
-(-393 R |Basis|) 
+(-394 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}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-394) 
+(-395) 
 ((|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 
-(-395) 
+(-396) 
 ((|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 
-(-396 R S) 
+(-397 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."))) 
-((-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-397 S) 
+((-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-398 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
 NIL 
-(-398 S) 
+(-399 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-862)))) 
-(-399) 
+((|HasCategory| |#1| (QUOTE (-865)))) 
+(-400) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-400) 
+(-401) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
 NIL 
-(-401) 
+(-402) 
 ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|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 
-(-402 |n| |class| R) 
+(-403 |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"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-403) 
+(-404) 
 ((|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 
-(-404 -2022 UP UPUP R) 
+(-405 -2051 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 
-(-405 S) 
+(-406 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 
-(-406) 
+(-407) 
 ((|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 
-(-407) 
+(-408) 
 ((|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 
-(-408) 
+(-409) 
 ((|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 
-(-409) 
+(-410) 
 ((|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 
-(-410 -2676 |returnType| -1373 |symbols|) 
+(-411 -2713 |returnType| -1376 |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-411 -2022 UP) 
+(-412 -2051 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
-(-412 R) 
+(-413 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
 NIL 
 NIL 
-(-413 S) 
+(-414 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
 NIL 
 NIL 
-(-414) 
+(-415) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-415 S) 
+(-416 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 
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-(-416) 
+((|HasAttribute| |#1| (QUOTE -4453)) (|HasAttribute| |#1| (QUOTE -4461))) 
+(-417) 
 ((|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\"."))) 
-((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4148 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-417 R S) 
+(-418 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
 NIL 
 NIL 
-(-418 A B) 
+(-419 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 
-(-419 S) 
+(-420 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."))) 
-((-4453 -12 (|has| |#1| (-6 -4464)) (|has| |#1| (-464)) (|has| |#1| (-6 -4453))) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
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-(-420 S R UP) 
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+(-421 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 
-(-421 R UP) 
+(-422 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-422 A S) 
+(-423 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-423 S) 
+((|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-424 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-424 R1 F1 U1 A1 R2 F2 U2 A2) 
+(-425 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 
-(-425 R -2022 UP A) 
+(-426 R -2051 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)}."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-426 R -2022 UP A |ibasis|) 
+(-427 R -2051 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (LIST (QUOTE -1060) (|devaluate| |#2|)))) 
-(-427 AR R AS S) 
+((|HasCategory| |#4| (LIST (QUOTE -1063) (|devaluate| |#2|)))) 
+(-428 AR R AS S) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
 NIL 
-(-428 S R) 
+(-429 S R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-374)))) 
-(-429 R) 
+((|HasCategory| |#2| (QUOTE (-375)))) 
+(-430 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\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."))) 
-((-4463 |has| |#1| (-568)) (-4461 . T) (-4460 . T)) 
+((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) 
 NIL 
-(-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."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1243))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1243)))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|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 -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) 
 (-431 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."))) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -320) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -297) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1246))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1246)))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-465)))) 
+(-432 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 
-(-432 R FE |x| |cen|) 
+(-433 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 
-(-433 R A S B) 
+(-434 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 
-(-434 R FE |Expon| UPS TRAN |x|) 
+(-435 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| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) 
 NIL 
 NIL 
-(-435 S A R B) 
+(-436 S A R B) 
 ((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-436 A S) 
+(-437 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) 
-(-437 S) 
+((|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-380)))) 
+(-438 S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4466 . T) (-4456 . T) (-4467 . T)) 
+((-4470 . T) (-4460 . T) (-4471 . T)) 
 NIL 
-(-438 R -2022) 
+(-439 R -2051) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
-(-439 R E) 
+(-440 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) 
-((-4453 -12 (|has| |#1| (-6 -4453)) (|has| |#2| (-6 -4453))) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4453)) (|HasAttribute| |#2| (QUOTE -4453)))) 
-(-440 R -2022) 
+((-4457 -12 (|has| |#1| (-6 -4457)) (|has| |#2| (-6 -4457))) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#2| (QUOTE -4457)))) 
+(-441 R -2051) 
 ((|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 
-(-441 S R) 
+(-442 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 -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1134))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) 
-(-442 R) 
+((|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-1137))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) 
+(-443 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}."))) 
-((-4463 -2802 (|has| |#1| (-1071)) (|has| |#1| (-485))) (-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) ((-4468 "*") |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-568)) (-4458 |has| |#1| (-568))) 
+((-4467 -2839 (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) 
 NIL 
-(-443 R -2022) 
+(-444 R -2051) 
 ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) 
 NIL 
 NIL 
-(-444 R -2022) 
+(-445 R -2051) 
 ((|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)))) 
-(-445 R -2022) 
+(-446 R -2051) 
 ((|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 
-(-446) 
+(-447) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-447 R -2022 UP) 
+(-448 R -2051 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 -1060) (QUOTE (-48))))) 
-(-448) 
+((|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-48))))) 
+(-449) 
 ((|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 
-(-449) 
+(-450) 
 ((|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 
-(-450 |f|) 
+(-451 |f|) 
 ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-451) 
+(-452) 
 ((|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|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) 
 NIL 
 NIL 
-(-452) 
+(-453) 
 ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|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 
-(-453) 
+(-454) 
 ((|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 
-(-454 UP) 
+(-455 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."))) 
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-(-455 R UP -2022) 
+(-456 R UP -2051) 
 ((|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 
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-(-456 R UP) 
+(-457 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)."))) 
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-(-457 R) 
+(-458 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."))) 
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-((|HasCategory| |#1| (QUOTE (-416)))) 
-(-458) 
+((|HasCategory| |#1| (QUOTE (-417)))) 
+(-459) 
 ((|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}."))) 
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-(-459 |Dom| |Expon| |VarSet| |Dpol|) 
+(-460 |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."))) 
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-(-460 |Dom| |Expon| |VarSet| |Dpol|) 
+(-461 |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 
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-(-461 |Dom| |Expon| |VarSet| |Dpol|) 
+(-462 |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 
-(-462 |Dom| |Expon| |VarSet| |Dpol|) 
+(-463 |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 (-374)))) 
-(-463 S) 
+((|HasCategory| |#1| (QUOTE (-375)))) 
+(-464 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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-464) 
+(-465) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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}."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-465 R |n| |ls| |gamma|) 
+(-466 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"))) 
-((-4463 |has| (-419 (-972 |#1|)) (-568)) (-4461 . T) (-4460 . T)) 
-((|HasCategory| (-419 (-972 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-972 |#1|)) (QUOTE (-568)))) 
-(-466 |vl| R E) 
+((-4467 |has| (-420 (-975 |#1|)) (-569)) (-4465 . T) (-4464 . T)) 
+((|HasCategory| (-420 (-975 |#1|)) (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-420 (-975 |#1|)) (QUOTE (-569)))) 
+(-467 |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"))) 
-(((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
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-(-467 R BP) 
+(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
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+(-468 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 
-(-468 OV E S R P) 
+(-469 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 
-(-469 E OV R P) 
+(-470 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 
-(-470 R) 
+(-471 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 
-(-471 R FE) 
+(-472 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 
-(-472 RP TP) 
+(-473 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 
-(-473 |vl| R IS E |ff| P) 
+(-474 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-474 E V R P Q) 
+(-475 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
 NIL 
 NIL 
-(-475 R E |VarSet| P) 
+(-476 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-476 S R E) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-477 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 
-(-477 R E) 
+(-478 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 
-(-478) 
+(-479) 
 ((|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 
-(-479) 
+(-480) 
 ((|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 
-(-480) 
+(-481) 
 ((|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 
-(-481 S R E) 
+(-482 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-482 R E) 
+(-483 R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-483 |lv| -2022 R) 
+(-484 |lv| -2051 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
-(-484 S) 
+(-485 S) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
 NIL 
 NIL 
-(-485) 
+(-486) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-486 |Coef| |var| |cen|) 
+(-487 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|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 (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|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 -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|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 -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
-(-487 |Key| |Entry| |Tbl| |dent|) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) 
+(-488 |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."))) 
-((-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122)))) 
-(-488 R E V P) 
+((-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125)))) 
+(-489 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)}"))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-489) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-490) 
 ((|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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-490) 
+(-491) 
 ((|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 
-(-491 |Key| |Entry| |hashfn|) 
+(-492 |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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) 
-(-492) 
+((-4470 . T) (-4471 . T)) 
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+(-493) 
 ((|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 
-(-493 |vl| R) 
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 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is 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 "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 
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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}."))) 
-((-4466 . T) (-4467 . T)) 
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-(-497 -2022 UP UPUP R) 
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 ((|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 
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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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (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) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) 
-(-500 A S) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2839 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) 
+(-501 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 -4466)) (|HasAttribute| |#1| (QUOTE -4467)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) 
-(-501 S) 
+((|HasAttribute| |#1| (QUOTE -4470)) (|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) 
+(-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
 NIL 
-(-502 S) 
+(-503 S) 
 ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) 
 NIL 
 NIL 
-(-503) 
+(-504) 
 ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) 
 NIL 
 NIL 
-(-504 S) 
+(-505 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-505) 
+(-506) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-506 -2022 UP |AlExt| |AlPol|) 
+(-507 -2051 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
-(-507) 
+(-508) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| $ (QUOTE (-1071))) (|HasCategory| $ (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-508 S |mn|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-509 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-509 R |mnRow| |mnCol|) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-510 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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-510 K R UP) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-511 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) 
 NIL 
 NIL 
-(-511 R UP -2022) 
+(-512 R UP -2051) 
 ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-512 |mn|) 
+(-513 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1122))) (|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 (-1122))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-112) (QUOTE (-102)))) 
-(-513 K R UP L) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-112) (QUOTE (-102)))) 
+(-514 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 
-(-514) 
+(-515) 
 ((|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 
-(-515 R Q A B) 
+(-516 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 
-(-516 -2022 |Expon| |VarSet| |DPoly|) 
+(-517 -2051 |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 -626) (QUOTE (-1198))))) 
-(-517 |vl| |nv|) 
+((|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-1201))))) 
+(-518 |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 
-(-518) 
+(-519) 
 ((|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 
-(-519 A S) 
+(-520 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-520 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-521 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-521 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-522 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-522 A S) 
+(-523 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-523 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-524 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-524 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-525 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
-(-525 S A B) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) 
+(-526 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|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 
-(-526 A B) 
+(-527 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 
-(-527 S E |un|) 
+(-528 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-805)))) 
-(-528 S |mn|) 
+((|HasCategory| |#2| (QUOTE (-808)))) 
+(-529 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}"))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-529) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-530) 
 ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) 
 NIL 
 NIL 
-(-530 |p| |n|) 
+(-531 |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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (|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|) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((-2839 (|HasCategory| (-594 |#1|) (QUOTE (-146))) (|HasCategory| (-594 |#1|) (QUOTE (-380)))) (|HasCategory| (-594 |#1|) (QUOTE (-148))) (|HasCategory| (-594 |#1|) (QUOTE (-380))) (|HasCategory| (-594 |#1|) (QUOTE (-146)))) 
+(-532 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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-532 S |mn|) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-533 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."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-533 R |Row| |Col| M) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-534 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 -4467))) 
-(-534 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasAttribute| |#3| (QUOTE -4471))) 
+(-535 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 -4467))) 
-(-535 R |mnRow| |mnCol|) 
+((|HasAttribute| |#7| (QUOTE -4471))) 
+(-536 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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-536) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-537) 
 ((|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 
-(-537) 
+(-538) 
 ((|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 
-(-538 S) 
+(-539 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 
-(-539) 
+(-540) 
 ((|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 
-(-540 GF) 
+(-541 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 
-(-541) 
+(-542) 
 ((|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 
-(-542 R) 
+(-543 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 
-(-543 |Varset|) 
+(-544 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
-((-12 (|HasCategory| (-784) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-1122))))) 
-(-544 K -2022 |Par|) 
+((-12 (|HasCategory| (-787) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125))))) 
+(-545 K -2051 |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 
-(-545) 
+(-546) 
 NIL 
 NIL 
 NIL 
-(-546) 
+(-547) 
 ((|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 
-(-547 R) 
+(-548 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 
-(-548) 
+(-549) 
 ((|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 
-(-549 |Coef| UTS) 
+(-550 |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 
-(-550 K -2022 |Par|) 
+(-551 K -2051 |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 
-(-551 R BP |pMod| |nextMod|) 
+(-552 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 
-(-552 OV E R P) 
+(-553 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 
-(-553 K UP |Coef| UTS) 
+(-554 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 
-(-554 |Coef| UTS) 
+(-555 |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 
-(-555 R UP) 
+(-556 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 
-(-556 S) 
+(-557 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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-557) 
+(-558) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-4464 . T) (-4465 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-558) 
+(-559) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-559) 
+(-560) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-560) 
+(-561) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-561) 
+(-562) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-562 |Key| |Entry| |addDom|) 
+(-563 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) 
-(-563 R -2022) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102)))) 
+(-564 R -2051) 
 ((|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 
-(-564 R0 -2022 UP UPUP R) 
+(-565 R0 -2051 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 
-(-565) 
+(-566) 
 ((|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 
-(-566 R) 
+(-567 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-4144 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4148 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-567 S) 
+(-568 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
 NIL 
 NIL 
-(-568) 
+(-569) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-569 R -2022) 
+(-570 R -2051) 
 ((|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 
-(-570 I) 
+(-571 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 
-(-571) 
+(-572) 
 ((|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 
-(-572 R -2022 L) 
+(-573 R -2051 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 -669) (|devaluate| |#2|)))) 
-(-573) 
+((|HasCategory| |#3| (LIST (QUOTE -672) (|devaluate| |#2|)))) 
+(-574) 
 ((|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 
-(-574 -2022 UP UPUP R) 
+(-575 -2051 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 
-(-575 -2022 UP) 
+(-576 -2051 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 
-(-576) 
+(-577) 
 ((|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."))) 
-((-4448 . T) (-4454 . T) (-4458 . T) (-4453 . T) (-4464 . T) (-4465 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4452 . T) (-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-577) 
+(-578) 
 ((|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 
-(-578 R -2022 L) 
+(-579 R -2051 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 -669) (|devaluate| |#2|)))) 
-(-579 R -2022) 
+((|HasCategory| |#3| (LIST (QUOTE -672) (|devaluate| |#2|)))) 
+(-580 R -2051) 
 ((|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 -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) 
-(-580 -2022 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1164)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-642))))) 
+(-581 -2051 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 
-(-581 S) 
+(-582 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 
-(-582 -2022) 
+(-583 -2051) 
 ((|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 
-(-583 R) 
+(-584 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."))) 
-((-4144 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4148 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-584) 
+(-585) 
 ((|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 
-(-585 R -2022) 
+(-586 R -2051) 
 ((|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 -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) 
-(-586 -2022 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-295))) (|HasCategory| |#2| (QUOTE (-642))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-295)))) (|HasCategory| |#1| (QUOTE (-569)))) 
+(-587 -2051 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 
-(-587 R -2022) 
+(-588 R -2051) 
 ((|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 
-(-588) 
+(-589) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-589) 
+(-590) 
 ((|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 
-(-590) 
+(-591) 
 ((|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 
-(-591) 
+(-592) 
 ((|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 
-(-592 |p| |unBalanced?|) 
+(-593 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-593 |p|) 
+(-594 |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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) 
-(-594) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-380)))) 
+(-595) 
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-595 R -2022) 
+(-596 R -2051) 
 ((|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 
-(-596 E -2022) 
+(-597 E -2051) 
 ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) 
 NIL 
 NIL 
-(-597) 
+(-598) 
 ((|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 
-(-598 -2022) 
+(-599 -2051) 
 ((|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}."))) 
-((-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-1198))))) 
-(-599 I) 
+((-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201))))) 
+(-600 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 
-(-600 GF) 
+(-601 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 
-(-601 R) 
+(-602 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)))) 
-(-602) 
+(-603) 
 ((|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 
-(-603 R E V P TS) 
+(-604 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 
-(-604) 
+(-605) 
 ((|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 
-(-605 |mn|) 
+(-606 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2802 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-145) (QUOTE (-862))) (-2802 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1122))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) 
-(-606 E V R P) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2839 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-2839 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) 
+(-607 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-607 |Coef|) 
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|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 -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) 
 (-608 |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}."))) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
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+(-609 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
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 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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 
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 ((|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 
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 ((|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 
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 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{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 
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 ((|constructor| (NIL "\\indented{1}{This package implements 'infinite tuples' for the interpreter.} The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
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 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
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-(-616 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (QUOTE (-865))) (|HasAttribute| |#1| (QUOTE -4470)) (|HasCategory| |#3| (QUOTE (-1125)))) 
+(-617 |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 
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 ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join \\spad{`x'}.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4463 -2802 (-2724 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) 
-((-2802 (|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|)))) (-2802 (-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|) 
+((-4467 -2839 (-2761 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) 
+((-2839 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) 
+(-621 |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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1180))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1180)) (|:| -4440 |#1|)) (QUOTE (-102)))) 
-(-621 S |Key| |Entry|) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-102)))) 
+(-622 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 
-(-622 |Key| |Entry|) 
+(-623 |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}."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-623 R S) 
+(-624 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-624 S) 
+(-625 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 -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) 
-(-625 S) 
+((|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) 
+(-626 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 
-(-626 S) 
+(-627 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-627 -2022 UP) 
+(-628 -2051 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-628 S) 
+(-629 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 
-(-629) 
+(-630) 
 ((|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| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-630 S) 
+(-631 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) 
 NIL 
 NIL 
-(-631 S R) 
+(-632 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 
-(-632 R) 
+(-633 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."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-633 A R S) 
+(-634 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}."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-861)))) 
-(-634 R -2022) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-864)))) 
+(-635 R -2051) 
 ((|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 
-(-635 R UP) 
+(-636 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"))) 
-((-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4459 . T) (-4463 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-636 R E V P TS ST) 
+((-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4463 . T) (-4467 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-637 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 
-(-637 OV E Z P) 
+(-638 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 
-(-638) 
+(-639) 
 ((|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 
-(-639 |VarSet| R |Order|) 
+(-640 |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}}."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-640 R |ls|) 
+(-641 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 
-(-641) 
+(-642) 
 ((|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 
-(-642 R -2022) 
+(-643 R -2051) 
 ((|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 
-(-643 |lv| -2022) 
+(-644 |lv| -2051) 
 ((|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 
-(-644) 
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 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|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."))) 
-((-4467 . T)) 
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-(-645 S R) 
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+(-646 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-374)))) 
-(-646 R) 
+((|HasCategory| |#2| (QUOTE (-375)))) 
+(-647 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4461 . T) (-4460 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4465 . T) (-4464 . T)) 
 NIL 
-(-647 R A) 
+(-648 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4463 -2802 (-2724 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4461 . T) (-4460 . T)) 
-((-2802 (|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|)))) (-2802 (-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) 
+((-4467 -2839 (-2761 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) 
+((-2839 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) 
+(-649 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 
-(-649 R) 
+(-650 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 
-(-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."))) 
+(-651 |vars|) 
+((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) 
+NIL 
 NIL 
-((-2712 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-651 K B) 
-((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|) (|List| (|OrderedVariableList| |#2|))) "\\spad{linearElement([x1,..,xn],[b1,..,bn]) constructs a linear element with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{b1},{}...\\spad{bn}."))) 
-((-4461 . T) (-4460 . T)) 
+(-652 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 
-(-652 R) 
+((-2749 (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-653 K B) 
+((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) 
+((-4465 . T) (-4464 . T)) 
+((-12 (|HasCategory| (-651 |#2|) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125))))) 
+(-654 R) 
 ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
-(-653 S) 
+(-655 K B) 
+((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) 
+((-4465 . T) (-4464 . T)) 
+NIL 
+(-656 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 
-(-654 A B) 
+(-657 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 
-(-655 A B) 
+(-658 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 
-(-656 A B C) 
+(-659 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 
-(-657 S) 
+(-660 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."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-658 T$) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-661 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-659 S) 
+(-662 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| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-660 S) 
+(-663 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-661 R) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-664 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-662 S E |un|) 
+(-665 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 
-(-663 A S) 
+(-666 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 -4467))) 
-(-664 S) 
+((|HasAttribute| |#1| (QUOTE -4471))) 
+(-667 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 
-(-665 R -2022 L) 
+(-668 R -2051 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 
-(-666 A) 
+(-669 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}}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-667 A M) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-670 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-668 S A) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-671 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-374)))) 
-(-669 A) 
+((|HasCategory| |#2| (QUOTE (-375)))) 
+(-672 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}."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-670 -2022 UP) 
+(-673 -2051 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)))) 
-(-671 A -1411) 
+(-674 A -4382) 
 ((|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}}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-672 A L) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-675 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 
-(-673 S) 
+(-676 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-674) 
+(-677) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-675 M R S) 
+(-678 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}."))) 
-((-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (QUOTE (-804)))) 
-(-676 R) 
+((-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (QUOTE (-807)))) 
+(-679 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 
-(-677 |VarSet| R) 
+(-680 |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) (-4461 . T) (-4460 . T)) 
-((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-678 A S) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4465 . T) (-4464 . T)) 
+((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-681 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 
-(-679 S) 
+(-682 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}."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-680 -2022) 
+(-683 -2051) 
 ((|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 
-(-681 -2022 |Row| |Col| M) 
+(-684 -2051 |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 
-(-682 R E OV P) 
+(-685 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 
-(-683 |n| R) 
+(-686 |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."))) 
-((-4463 . T) (-4466 . T) (-4460 . T) (-4461 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2802 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-684) 
+((-4467 . T) (-4470 . T) (-4464 . T) (-4465 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569))) (-2839 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-687) 
 ((|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 
-(-685 |VarSet|) 
+(-688 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-686 A S) 
+(-689 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-687 S) 
+(-690 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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 
-(-688 R) 
+(-691 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 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-689) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-692) 
 ((|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 
-(-690 |VarSet|) 
+(-693 |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 
-(-691 A) 
+(-694 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 
-(-692 A C) 
+(-695 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 
-(-693 A B C) 
+(-696 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 
-(-694) 
+(-697) 
 ((|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 
-(-695 A) 
+(-698 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 
-(-696 A C) 
+(-699 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 
-(-697 A B C) 
+(-700 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 
-(-698 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-701 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 
-(-699 S R |Row| |Col|) 
+(-702 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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) 
-(-700 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569)))) 
+(-703 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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
-(-701 R |Row| |Col| M) 
+(-704 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 (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) 
-(-702 R) 
+((|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569)))) 
+(-705 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."))) 
-((-4466 . T) (-4467 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4468 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-703 R) 
+((-4470 . T) (-4471 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-706 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 
-(-704 T$) 
+(-707 T$) 
 ((|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 
-(-705 S -2022 FLAF FLAS) 
+(-708 S -2051 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 
-(-706 R Q) 
+(-709 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 
-(-707) 
+(-710) 
 ((|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"))) 
-((-4459 . T) (-4464 |has| (-712) (-374)) (-4458 |has| (-712) (-374)) (-4155 . T) (-4465 |has| (-712) (-6 -4465)) (-4462 |has| (-712) (-6 -4462)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-712) (QUOTE (-148))) (|HasCategory| (-712) (QUOTE (-146))) (|HasCategory| (-712) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-712) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-712) (QUOTE (-379))) (|HasCategory| (-712) (QUOTE (-374))) (-2802 (|HasCategory| (-712) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-712) (QUOTE (-374)))) (|HasCategory| (-712) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-712) (QUOTE (-238))) (|HasCategory| (-712) (QUOTE (-237))) (-2802 (-12 (|HasCategory| (-712) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-712) (QUOTE (-374)))) (|HasCategory| (-712) (LIST (QUOTE -920) (QUOTE (-1198))))) (-2802 (|HasCategory| (-712) (QUOTE (-374))) (|HasCategory| (-712) (QUOTE (-360)))) (|HasCategory| (-712) (QUOTE (-360))) (|HasCategory| (-712) (LIST (QUOTE -296) (QUOTE (-712)) (QUOTE (-712)))) (|HasCategory| (-712) (LIST (QUOTE -319) (QUOTE (-712)))) (|HasCategory| (-712) (LIST (QUOTE -526) (QUOTE (-1198)) (QUOTE (-712)))) (|HasCategory| (-712) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-712) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-712) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-712) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (-2802 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-374))) (|HasCategory| (-712) (QUOTE (-360)))) (|HasCategory| (-712) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-712) (QUOTE (-1044))) (|HasCategory| (-712) (QUOTE (-1224))) (-12 (|HasCategory| (-712) (QUOTE (-1024))) (|HasCategory| (-712) (QUOTE (-1224)))) (-2802 (-12 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (QUOTE (-374))) (-12 (|HasCategory| (-712) (QUOTE (-360))) (|HasCategory| (-712) (QUOTE (-929))))) (-2802 (-12 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (-12 (|HasCategory| (-712) (QUOTE (-374))) (|HasCategory| (-712) (QUOTE (-929)))) (-12 (|HasCategory| (-712) (QUOTE (-360))) (|HasCategory| (-712) (QUOTE (-929))))) (|HasCategory| (-712) (QUOTE (-557))) (-12 (|HasCategory| (-712) (QUOTE (-1082))) (|HasCategory| (-712) (QUOTE (-1224)))) (|HasCategory| (-712) (QUOTE (-1082))) (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929))) (-2802 (-12 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (QUOTE (-374)))) (-2802 (-12 (|HasCategory| (-712) (QUOTE (-238))) (|HasCategory| (-712) (QUOTE (-374)))) (|HasCategory| (-712) (QUOTE (-237)))) (-2802 (-12 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (QUOTE (-568)))) (-12 (|HasCategory| (-712) (QUOTE (-237))) (|HasCategory| (-712) (QUOTE (-374)))) (-12 (|HasCategory| (-712) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-712) (QUOTE (-374)))) (-12 (|HasCategory| (-712) (QUOTE (-238))) (|HasCategory| (-712) (QUOTE (-374)))) (-12 (|HasCategory| (-712) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-712) (QUOTE (-374)))) (|HasCategory| (-712) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-712) (QUOTE (-568))) (|HasAttribute| (-712) (QUOTE -4465)) (|HasAttribute| (-712) (QUOTE -4462)) (-12 (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (LIST (QUOTE -920) (QUOTE (-1198)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (QUOTE (-146)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-712) (QUOTE (-317))) (|HasCategory| (-712) (QUOTE (-929)))) (|HasCategory| (-712) (QUOTE (-360))))) 
-(-708 S) 
+((-4463 . T) (-4468 |has| (-715) (-375)) (-4462 |has| (-715) (-375)) (-4159 . T) (-4469 |has| (-715) (-6 -4469)) (-4466 |has| (-715) (-6 -4466)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-715) (QUOTE (-148))) (|HasCategory| (-715) (QUOTE (-146))) (|HasCategory| (-715) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-715) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-715) (QUOTE (-380))) (|HasCategory| (-715) (QUOTE (-375))) (-2839 (|HasCategory| (-715) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-715) (QUOTE (-375)))) (|HasCategory| (-715) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-715) (QUOTE (-239))) (|HasCategory| (-715) (QUOTE (-238))) (-2839 (-12 (|HasCategory| (-715) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-715) (QUOTE (-375)))) (|HasCategory| (-715) (LIST (QUOTE -923) (QUOTE (-1201))))) (-2839 (|HasCategory| (-715) (QUOTE (-375))) (|HasCategory| (-715) (QUOTE (-361)))) (|HasCategory| (-715) (QUOTE (-361))) (|HasCategory| (-715) (LIST (QUOTE -297) (QUOTE (-715)) (QUOTE (-715)))) (|HasCategory| (-715) (LIST (QUOTE -320) (QUOTE (-715)))) (|HasCategory| (-715) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-715)))) (|HasCategory| (-715) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-715) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-715) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-715) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (-2839 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-375))) (|HasCategory| (-715) (QUOTE (-361)))) (|HasCategory| (-715) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-715) (QUOTE (-1047))) (|HasCategory| (-715) (QUOTE (-1227))) (-12 (|HasCategory| (-715) (QUOTE (-1027))) (|HasCategory| (-715) (QUOTE (-1227)))) (-2839 (-12 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (QUOTE (-375))) (-12 (|HasCategory| (-715) (QUOTE (-361))) (|HasCategory| (-715) (QUOTE (-932))))) (-2839 (-12 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (-12 (|HasCategory| (-715) (QUOTE (-375))) (|HasCategory| (-715) (QUOTE (-932)))) (-12 (|HasCategory| (-715) (QUOTE (-361))) (|HasCategory| (-715) (QUOTE (-932))))) (|HasCategory| (-715) (QUOTE (-558))) (-12 (|HasCategory| (-715) (QUOTE (-1085))) (|HasCategory| (-715) (QUOTE (-1227)))) (|HasCategory| (-715) (QUOTE (-1085))) (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932))) (-2839 (-12 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (QUOTE (-375)))) (-2839 (-12 (|HasCategory| (-715) (QUOTE (-239))) (|HasCategory| (-715) (QUOTE (-375)))) (|HasCategory| (-715) (QUOTE (-238)))) (-2839 (-12 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (QUOTE (-569)))) (-12 (|HasCategory| (-715) (QUOTE (-238))) (|HasCategory| (-715) (QUOTE (-375)))) (-12 (|HasCategory| (-715) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-715) (QUOTE (-375)))) (-12 (|HasCategory| (-715) (QUOTE (-239))) (|HasCategory| (-715) (QUOTE (-375)))) (-12 (|HasCategory| (-715) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-715) (QUOTE (-375)))) (|HasCategory| (-715) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-715) (QUOTE (-569))) (|HasAttribute| (-715) (QUOTE -4469)) (|HasAttribute| (-715) (QUOTE -4466)) (-12 (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (LIST (QUOTE -923) (QUOTE (-1201)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (QUOTE (-146)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-715) (QUOTE (-318))) (|HasCategory| (-715) (QUOTE (-932)))) (|HasCategory| (-715) (QUOTE (-361))))) 
+(-711 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}."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-709 U) 
+(-712 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 
-(-710) 
+(-713) 
 ((|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 
-(-711 OV E -2022 PG) 
+(-714 OV E -2051 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 
-(-712) 
+(-715) 
 ((|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}"))) 
-((-4144 . T) (-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4148 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-713 R) 
+(-716 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 
-(-714) 
+(-717) 
 ((|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}"))) 
-((-4465 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4469 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-715 S D1 D2 I) 
+(-718 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 
-(-716 S) 
+(-719 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 
-(-717 S) 
+(-720 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 
-(-718 S T$) 
+(-721 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 
-(-719 S -2097 I) 
+(-722 S -2132 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 
-(-720 E OV R P) 
+(-723 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 
-(-721 R) 
+(-724 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)}.}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-722 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-725 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 
-(-723) 
+(-726) 
 ((|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 
-(-724 R |Mod| -2921 -3073 |exactQuo|) 
+(-727 R |Mod| -3062 -3283 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-725 R |Rep|) 
+(-728 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
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-(-726 IS E |ff|) 
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+(-729 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-727 R M) 
+(-730 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . T)) 
+((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-728 R |Mod| -2921 -3073 |exactQuo|) 
+(-731 R |Mod| -3062 -3283 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-729 S R) 
+(-732 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-730 R) 
+(-733 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-731 -2022) 
+(-734 -2051) 
 ((|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]]}."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-732 S) 
+(-735 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-733) 
+(-736) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 
-(-734 S) 
+(-737 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 
-(-735) 
+(-738) 
 ((|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 
-(-736 S R UP) 
+(-739 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 (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) 
-(-737 R UP) 
+((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-380)))) 
+(-740 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."))) 
-((-4459 |has| |#1| (-374)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 |has| |#1| (-375)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-738 S) 
+(-741 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 
-(-739) 
+(-742) 
 ((|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 
-(-740 -2022 UP) 
+(-743 -2051 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 
-(-741 |VarSet| E1 E2 R S PR PS) 
+(-744 |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 
-(-742 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-745 |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 
-(-743 E OV R PPR) 
+(-746 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 
-(-744 |vl| R) 
+(-747 |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."))) 
-(((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-929))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-879 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-745 E OV R PRF) 
+(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-932))) (-2839 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2839 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-748 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 
-(-746 E OV R P) 
+(-749 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 
-(-747 R S M) 
+(-750 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 
-(-748 R M) 
+(-751 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}."))) 
-((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . 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)))) 
-(-749 S) 
+((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-865)))) 
+(-752 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4456 . T) (-4467 . T)) 
+((-4460 . T) (-4471 . T)) 
 NIL 
-(-750 S) 
+(-753 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}."))) 
-((-4466 . T) (-4456 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-751) 
+((-4470 . T) (-4460 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-754) 
 ((|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 
-(-752 S) 
+(-755 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 
-(-753 |Coef| |Var|) 
+(-756 |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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-754 OV E R P) 
+(-757 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 
-(-755 E OV R P) 
+(-758 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 
-(-756 S R) 
+(-759 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 
-(-757 R) 
+(-760 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}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-758) 
+(-761) 
 ((|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 
-(-759) 
+(-762) 
 ((|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 
-(-760) 
+(-763) 
 ((|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 
-(-761) 
+(-764) 
 ((|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 
-(-762) 
+(-765) 
 ((|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 
-(-763) 
+(-766) 
 ((|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 
-(-764) 
+(-767) 
 ((|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 
-(-765) 
+(-768) 
 ((|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 
-(-766) 
+(-769) 
 ((|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 
-(-767) 
+(-770) 
 ((|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 
-(-768) 
+(-771) 
 ((|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 
-(-769) 
+(-772) 
 ((|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 
-(-770) 
+(-773) 
 ((|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 
-(-771) 
+(-774) 
 ((|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 
-(-772) 
+(-775) 
 ((|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 
-(-773 S) 
+(-776 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-774) 
+(-777) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-775 S) 
+(-778 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 
-(-776) 
+(-779) 
 ((|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 
-(-777 |Par|) 
+(-780 |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 
-(-778 -2022) 
+(-781 -2051) 
 ((|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 
-(-779 P -2022) 
+(-782 P -2051) 
 ((|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 
-(-780 T$) 
+(-783 T$) 
 NIL 
 NIL 
 NIL 
-(-781 UP -2022) 
+(-784 UP -2051) 
 ((|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 
-(-782) 
+(-785) 
 ((|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 
-(-783 R) 
+(-786 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 
-(-784) 
+(-787) 
 ((|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."))) 
-(((-4468 "*") . T)) 
+(((-4472 "*") . T)) 
 NIL 
-(-785 R -2022) 
+(-788 R -2051) 
 ((|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 
-(-786 S) 
+(-789 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 
-(-787) 
+(-790) 
 ((|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 
-(-788 R |PolR| E |PolE|) 
+(-791 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 
-(-789 R E V P TS) 
+(-792 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 
-(-790 -2022 |ExtF| |SUEx| |ExtP| |n|) 
+(-793 -2051 |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 
-(-791 BP E OV R P) 
+(-794 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 
-(-792 |Par|) 
+(-795 |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 
-(-793 R |VarSet|) 
+(-796 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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
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-(-794 R S) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
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+(-797 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 
-(-795 R) 
+(-798 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)}"))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
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-(-796 R) 
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+(-799 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 -419) (QUOTE (-576)))))) 
-(-797 R E V P) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) 
+(-800 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.}"))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-798 S) 
+(-801 S) 
 ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) 
 NIL 
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-(-799) 
+((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-174)))) 
+(-802) 
 ((|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 
-(-800) 
+(-803) 
 ((|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."))) 
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-(-801) 
+(-804) 
 ((|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 
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-(-802) 
+(-805) 
 ((|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 
-(-803 |Curve|) 
+(-806 |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}."))) 
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-(-804) 
+(-807) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) 
 NIL 
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-(-805) 
+(-808) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-806) 
+(-809) 
 ((|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| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-807) 
+(-810) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-808) 
+(-811) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-809 S R) 
+(-812 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) 
-(-810 R) 
+((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-380)))) 
+(-813 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-811 -2802 R OS S) 
+(-814 -2839 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-812 R) 
+(-815 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4460 . T) (-4461 . T) (-4463 . 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 (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2802 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1021 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-813) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-2839 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2839 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-816) 
 ((|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 
-(-814 R -2022 L) 
+(-817 R -2051 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 
-(-815 R -2022) 
+(-818 R -2051) 
 ((|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 
-(-816) 
+(-819) 
 ((|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 
-(-817 R -2022) 
+(-820 R -2051) 
 ((|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 
-(-818) 
+(-821) 
 ((|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."))) 
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-(-819 -2022 UP UPUP R) 
+(-822 -2051 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
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-(-820 -2022 UP L LQ) 
+(-823 -2051 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."))) 
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-(-821) 
+(-824) 
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
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-(-822 -2022 UP L LQ) 
+(-825 -2051 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}."))) 
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-(-823 -2022 UP) 
+(-826 -2051 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."))) 
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-(-824 -2022 L UP A LO) 
+(-827 -2051 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
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-(-825 -2022 UP) 
+(-828 -2051 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)))) 
-(-826 -2022 LO) 
+(-829 -2051 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 
-(-827 -2022 LODO) 
+(-830 -2051 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 
-(-828 -2755 S |f|) 
+(-831 -2791 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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-(-829 R) 
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(-577))))) (-12 (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (QUOTE (-809))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| (-577) (QUOTE (-865))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1074)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201))))) (-2839 (|HasCategory| |#2| (QUOTE (-1074))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasAttribute| |#2| (QUOTE -4467)) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1074)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))))) 
+(-832 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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-(-830 |Kernels| R |var|) 
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+(-833 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
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-((|HasCategory| |#2| (QUOTE (-374)))) 
-(-831 S) 
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+(-834 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 
-(-832 S) 
+(-835 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 (-862)))) 
-(-833) 
+((|HasCategory| |#1| (QUOTE (-865)))) 
+(-836) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-834) 
+(-837) 
 ((|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 
-(-835) 
+(-838) 
 ((|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 
-(-836) 
+(-839) 
 ((|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 
-(-837) 
+(-840) 
 ((|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 
-(-838) 
+(-841) 
 ((|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|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
 NIL 
 NIL 
-(-839 R) 
+(-842 R) 
 ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
 NIL 
 NIL 
-(-840 P R) 
+(-843 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) 
-(-841) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-239)))) 
+(-844) 
 ((|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 
-(-842) 
+(-845) 
 ((|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 
-(-843 S) 
+(-846 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4466 . T) (-4456 . T) (-4467 . T)) 
+((-4470 . T) (-4460 . T) (-4471 . T)) 
 NIL 
-(-844) 
+(-847) 
 ((|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 
-(-845 R S) 
+(-848 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 
-(-846 R) 
+(-849 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."))) 
-((-4463 |has| |#1| (-861))) 
-((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2802 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-847 A S) 
+((-4467 |has| |#1| (-864))) 
+((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-2839 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2839 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) 
+(-850 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 
-(-848 S) 
+(-851 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-849 R) 
+(-852 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . T)) 
+((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-850) 
+(-853) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) 
 NIL 
 NIL 
-(-851) 
+(-854) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 
-(-852) 
+(-855) 
 ((|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 
-(-853) 
+(-856) 
 ((|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 
-(-854) 
+(-857) 
 ((|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 
-(-855 R S) 
+(-858 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 
-(-856 R) 
+(-859 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4463 |has| |#1| (-861))) 
-((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-21))) (-2802 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-857) 
+((-4467 |has| |#1| (-864))) 
+((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-2839 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2839 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) 
+(-860) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-858 -2755 S) 
+(-861 -2791 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-859) 
+(-862) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-860 S) 
+(-863 S) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
 NIL 
 NIL 
-(-861) 
+(-864) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-862) 
+(-865) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-863 T$ |f|) 
+(-866 T$ |f|) 
 ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) 
-(-864 S) 
+((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) 
+(-867 S) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-865) 
+(-868) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-866 S R) 
+(-869 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-867 R) 
+((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-870 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-868 R C) 
+(-871 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 (-374))) (|HasCategory| |#1| (QUOTE (-568)))) 
-(-869 R |sigma| -4262) 
+((|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) 
+(-872 R |sigma| -4267) 
 ((|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."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-870 |x| R |sigma| -4262) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-873 |x| R |sigma| -4267) 
 ((|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}."))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) 
-(-871 R) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-375)))) 
+(-874 R) 
 ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
-(-872) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) 
+(-875) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-873) 
+(-876) 
 ((|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 
-(-874 S) 
+(-877 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 
-(-875) 
+(-878) 
 ((|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 
-(-876) 
+(-879) 
 ((|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 
-(-877) 
+(-880) 
 ((|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 
-(-878) 
+(-881) 
 ((|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 
-(-879 |VariableList|) 
+(-882 |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 
-(-880) 
+(-883) 
 ((|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 
-(-881 R |vl| |wl| |wtlevel|) 
+(-884 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)"))) 
-((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-882 R PS UP) 
+((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-885 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 
-(-883 R |x| |pt|) 
+(-886 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 
-(-884 |p|) 
+(-887 |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}."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-885 |p|) 
+(-888 |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)."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-886 |p|) 
+(-889 |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)."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-885 |#1|) (QUOTE (-929))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-148))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-885 |#1|) (QUOTE (-1044))) (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862))) (-2802 (|HasCategory| (-885 |#1|) (QUOTE (-833))) (|HasCategory| (-885 |#1|) (QUOTE (-862)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-1174))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| (-885 |#1|) (QUOTE (-237))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (QUOTE (-238))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -526) (QUOTE (-1198)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -885) (|devaluate| |#1|)) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| (-885 |#1|) (QUOTE (-317))) (|HasCategory| (-885 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-885 |#1|) (QUOTE (-929)))) (|HasCategory| (-885 |#1|) (QUOTE (-146))))) 
-(-887 |p| PADIC) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-888 |#1|) (QUOTE (-932))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-148))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-888 |#1|) (QUOTE (-1047))) (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865))) (-2839 (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-1177))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-238))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-239))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -888) (|devaluate| |#1|)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (QUOTE (-318))) (|HasCategory| (-888 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))))) 
+(-890 |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)}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862))) (-2802 (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1198)) (|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))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-888 S T$) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (-2839 (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-891 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 (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))))) 
-(-889) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) 
+(-892) 
 ((|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 
-(-890) 
+(-893) 
 ((|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 
-(-891) 
+(-894) 
 ((|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 
-(-892 CF1 CF2) 
+(-895 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-893 |ComponentFunction|) 
+(-896 |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 
-(-894 CF1 CF2) 
+(-897 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-895 |ComponentFunction|) 
+(-898 |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 
-(-896) 
+(-899) 
 ((|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 
-(-897 CF1 CF2) 
+(-900 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-898 |ComponentFunction|) 
+(-901 |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 
-(-899) 
+(-902) 
 ((|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 
-(-900 R) 
+(-903 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 
-(-901 R S L) 
+(-904 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 
-(-902 S) 
+(-905 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 
-(-903 |Base| |Subject| |Pat|) 
+(-906 |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 (-2712 (|HasCategory| |#2| (QUOTE (-1071)))) (-2712 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (-12 (|HasCategory| |#2| (QUOTE (-1071))) (-2712 (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198))))) 
-(-904 R A B) 
+((-12 (-2749 (|HasCategory| |#2| (QUOTE (-1074)))) (-2749 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (-2749 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) 
+(-907 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 
-(-905 R S) 
+(-908 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 
-(-906 R -2097) 
+(-909 R -2132) 
 ((|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 
-(-907 R S) 
+(-910 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 
-(-908 R) 
+(-911 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 
-(-909 |VarSet|) 
+(-912 |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 
-(-910 UP R) 
+(-913 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-911 A T$ S) 
+(-914 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 
-(-912 T$ S) 
+(-915 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 
-(-913) 
+(-916) 
 ((|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 
-(-914 UP -2022) 
+(-917 UP -2051) 
 ((|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 
-(-915) 
+(-918) 
 ((|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 
-(-916) 
+(-919) 
 ((|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 
-(-917 R S) 
+(-920 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-918 S) 
+(-921 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-919 A S) 
+(-922 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 
-(-920 S) 
+(-923 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 
-(-921 S) 
+(-924 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 (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-922 |n| R) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-925 |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 
-(-923 S) 
+(-926 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."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-924 S) 
+(-927 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-925 S) 
+(-928 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) 
-((-4463 . T)) 
-((-2802 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) 
-(-926 R E |VarSet| S) 
+((-4467 . T)) 
+((-2839 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) 
+(-929 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 
-(-927 R S) 
+(-930 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 
-(-928 S) 
+(-931 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)))) 
-(-929) 
+(-932) 
 ((|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}."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-930 |p|) 
+(-933 |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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) 
-(-931 R0 -2022 UP UPUP R) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-380)))) 
+(-934 R0 -2051 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 
-(-932 UP UPUP R) 
+(-935 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 
-(-933 UP UPUP) 
+(-936 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 
-(-934 R) 
+(-937 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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-935 R) 
+(-938 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 
-(-936 E OV R P) 
+(-939 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 
-(-937) 
+(-940) 
 ((|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 
-(-938 -2022) 
+(-941 -2051) 
 ((|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 
-(-939 R) 
+(-942 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 
-(-940) 
+(-943) 
 ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-941) 
+(-944) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4468 "*") . T)) 
+(((-4472 "*") . T)) 
 NIL 
-(-942 -2022 P) 
+(-945 -2051 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-943 |xx| -2022) 
+(-946 |xx| -2051) 
 ((|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 
-(-944 R |Var| |Expon| GR) 
+(-947 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 
-(-945 S) 
+(-948 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 
-(-946) 
+(-949) 
 ((|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 
-(-947) 
+(-950) 
 ((|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 
-(-948) 
+(-951) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-949 R -2022) 
+(-952 R -2051) 
 ((|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 
-(-950) 
+(-953) 
 ((|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 
-(-951 S A B) 
+(-954 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 
-(-952 S R -2022) 
+(-955 S R -2051) 
 ((|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 
-(-953 I) 
+(-956 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 
-(-954 S E) 
+(-957 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 
-(-955 S R L) 
+(-958 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 
-(-956 S E V R P) 
+(-959 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 -902) (|devaluate| |#1|)))) 
-(-957 R -2022 -2097) 
+((|HasCategory| |#3| (LIST (QUOTE -905) (|devaluate| |#1|)))) 
+(-960 R -2051 -2132) 
 ((|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 
-(-958 -2097) 
+(-961 -2132) 
 ((|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 
-(-959 S R Q) 
+(-962 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 
-(-960 S) 
+(-963 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 
-(-961 S R P) 
+(-964 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 
-(-962) 
+(-965) 
 ((|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 
-(-963 R) 
+(-966 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-964 |lv| R) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-967 |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 
-(-965 |TheField| |ThePols|) 
+(-968 |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 (-861)))) 
-(-966 R S) 
+((|HasCategory| |#1| (QUOTE (-864)))) 
+(-969 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 
-(-967 |x| R) 
+(-970 |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 
-(-968 S R E |VarSet|) 
+(-971 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 (-929))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) 
-(-969 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-932))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#4| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#4| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#4| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) 
+(-972 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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-970 E V R P -2022) 
+(-973 E V R P -2051) 
 ((|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 
-(-971 E |Vars| R P S) 
+(-974 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 
-(-972 R) 
+(-975 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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1198) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-973 E V R P -2022) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-932))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1201) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-976 E V R P -2051) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-464)))) 
-(-974) 
+((|HasCategory| |#3| (QUOTE (-465)))) 
+(-977) 
 ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) 
 NIL 
 NIL 
-(-975) 
+(-978) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-976 R L) 
+(-979 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-977 A B) 
+(-980 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-978 S) 
+(-981 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"))) 
-((-4467 . T) (-4466 . T)) 
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-(-979) 
+((-4471 . T) (-4470 . T)) 
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+(-982) 
 ((|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 
-(-980 -2022) 
+(-983 -2051) 
 ((|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 
-(-981 I) 
+(-984 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 
-(-982) 
+(-985) 
 ((|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 
-(-983 R E) 
+(-986 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}"))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4464))) 
-(-984 A B) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4468))) 
+(-987 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"))) 
-((-4463 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) 
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-(-985) 
+((-4467 -12 (|has| |#2| (-486)) (|has| |#1| (-486)))) 
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+(-988) 
 ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-986 T$) 
+(-989 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-987 T$) 
+(-990 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-988 S T$) 
+(-991 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-989) 
+(-992) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-990 S) 
+(-993 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
-(-991 R |polR|) 
+(-994 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 (-464)))) 
-(-992) 
+((|HasCategory| |#1| (QUOTE (-465)))) 
+(-995) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-993) 
+(-996) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-994 S |Coef| |Expon| |Var|) 
+(-997 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 
-(-995 |Coef| |Expon| |Var|) 
+(-998 |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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-996) 
+(-999) 
 ((|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 
-(-997 S R E |VarSet| P) 
+(-1000 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 (-568)))) 
-(-998 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-569)))) 
+(-1001 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."))) 
-((-4466 . T)) 
+((-4470 . T)) 
 NIL 
-(-999 R E V P) 
+(-1002 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 (-317)))) (|HasCategory| |#1| (QUOTE (-464)))) 
-(-1000 K) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-465)))) 
+(-1003 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
 NIL 
 NIL 
-(-1001 |VarSet| E RC P) 
+(-1004 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
 NIL 
 NIL 
-(-1002 R) 
+(-1005 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}."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1003 R1 R2) 
+(-1006 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-1004 R) 
+(-1007 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
 NIL 
 NIL 
-(-1005 K) 
+(-1008 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-1006 R E OV PPR) 
+(-1009 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-1007 K R UP -2022) 
+(-1010 K R UP -2051) 
 ((|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 
-(-1008 |vl| |nv|) 
+(-1011 |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 
-(-1009 R |Var| |Expon| |Dpoly|) 
+(-1012 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 (-317))))) 
-(-1010 R E V P TS) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-318))))) 
+(-1013 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 
-(-1011) 
+(-1014) 
 ((|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 
-(-1012 A B R S) 
+(-1015 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 
-(-1013 A S) 
+(-1016 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 (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1174)))) 
-(-1014 S) 
+((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177)))) 
+(-1017 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}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1015 |n| K) 
+(-1018 |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 
-(-1016) 
+(-1019) 
 ((|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 
-(-1017 S) 
+(-1020 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."))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
-(-1018 S R) 
+(-1021 S R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1082))) (|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)))) 
-(-1019 R) 
+((|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-301)))) 
+(-1022 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}."))) 
-((-4459 |has| |#1| (-300)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 |has| |#1| (-301)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1020 QR R QS S) 
+(-1023 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 
-(-1021 R) 
+(-1024 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.}"))) 
-((-4459 |has| |#1| (-300)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1198)) (|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 -920) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-1022 S) 
+((-4463 |has| |#1| (-301)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558)))) 
+(-1025 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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1023 S) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1026 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1024) 
+(-1027) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-1025 -2022 UP UPUP |radicnd| |n|) 
+(-1028 -2051 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4459 |has| (-419 |#2|) (-374)) (-4464 |has| (-419 |#2|) (-374)) (-4458 |has| (-419 |#2|) (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2802 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2802 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2802 (-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)))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2802 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1060) (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 -920) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) 
-(-1026 |bb|) 
+((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2839 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2839 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2839 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2839 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2839 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-2839 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) 
+(-1029 |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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-576) (QUOTE (-929))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1044))) (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862))) (-2802 (|HasCategory| (-576) (QUOTE (-833))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1174))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1198)) (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) (LIST (QUOTE -652) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-929)))) (|HasCategory| (-576) (QUOTE (-146))))) 
-(-1027) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2839 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) 
+(-1030) 
 ((|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 
-(-1028) 
+(-1031) 
 ((|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 
-(-1029 RP) 
+(-1032 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 
-(-1030 S) 
+(-1033 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 
-(-1031 A S) 
+(-1034 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 -4467)) (|HasCategory| |#2| (QUOTE (-1122)))) 
-(-1032 S) 
+((|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (QUOTE (-1125)))) 
+(-1035 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 
-(-1033 S) 
+(-1036 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 
-(-1034) 
+(-1037) 
 ((|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}}"))) 
-((-4459 . T) (-4464 . T) (-4458 . T) (-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4463 . T)) 
+((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) 
 NIL 
-(-1035 R -2022) 
+(-1038 R -2051) 
 ((|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 
-(-1036 R -2022) 
+(-1039 R -2051) 
 ((|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 
-(-1037 -2022 UP) 
+(-1040 -2051 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 
-(-1038 -2022 UP) 
+(-1041 -2051 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 
-(-1039 S) 
+(-1042 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 
-(-1040 F1 UP UPUP R F2) 
+(-1043 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 
-(-1041) 
+(-1044) 
 ((|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 
-(-1042 |Pol|) 
+(-1045 |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 
-(-1043 |Pol|) 
+(-1046 |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 
-(-1044) 
+(-1047) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1045) 
+(-1048) 
 ((|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 
-(-1046 |TheField|) 
+(-1049 |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"))) 
-((-4459 . T) (-4464 . T) (-4458 . T) (-4461 . T) (-4460 . T) ((-4468 "*") . T) (-4463 . T)) 
-((-2802 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1060) (QUOTE (-576))))) 
-(-1047 -2022 L) 
+((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) 
+((-2839 (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577))))) 
+(-1050 -2051 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 
-(-1048 S) 
+(-1051 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 (-1122)))) 
-(-1049 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1125)))) 
+(-1052 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."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1050 R) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1053 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 (-4468 "*")))) 
-(-1051 R) 
+((|HasAttribute| |#1| (QUOTE (-4472 "*")))) 
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 ((|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 (-374))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317)))) 
-(-1052 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-318)))) 
+(-1055 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 
-(-1053) 
+(-1056) 
 ((|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 
-(-1054 S) 
+(-1057 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 
-(-1055 S) 
+(-1058 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 
-(-1056 -2022 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1059 -2051 |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"))) 
-(((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1057) 
+(-1060) 
 ((|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.}"))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) 
-(-1058) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -4444) (QUOTE (-52))))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102)))) 
+(-1061) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1059 A S) 
+(-1062 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 
-(-1060 S) 
+(-1063 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 
-(-1061 Q R) 
+(-1064 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 
-(-1062) 
+(-1065) 
 ((|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 
-(-1063 UP) 
+(-1066 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 
-(-1064 R) 
+(-1067 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 
-(-1065 R) 
+(-1068 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 
-(-1066 T$) 
+(-1069 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| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) 
 NIL 
 NIL 
-(-1067 T$) 
+(-1070 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 
-(-1068 R |ls|) 
+(-1071 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}."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| (-793 |#1| (-879 |#2|)) (QUOTE (-1122))) (|HasCategory| (-793 |#1| (-879 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -793) (|devaluate| |#1|) (LIST (QUOTE -879) (|devaluate| |#2|)))))) (|HasCategory| (-793 |#1| (-879 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-793 |#1| (-879 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-879 |#2|) (QUOTE (-379))) (|HasCategory| (-793 |#1| (-879 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-793 |#1| (-879 |#2|)) (QUOTE (-102)))) 
-(-1069) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-1125))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -796) (|devaluate| |#1|) (LIST (QUOTE -882) (|devaluate| |#2|)))))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-882 |#2|) (QUOTE (-380))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-102)))) 
+(-1072) 
 ((|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 
-(-1070 S) 
+(-1073 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 
-(-1071) 
+(-1074) 
 ((|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."))) 
-((-4463 . T)) 
+((-4467 . T)) 
 NIL 
-(-1072 |xx| -2022) 
+(-1075 |xx| -2051) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1073 S) 
+(-1076 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-1074 S |m| |n| R |Row| |Col|) 
+(-1077 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 (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) 
-(-1075 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-375))) (|HasCategory| |#4| (QUOTE (-569))) (|HasCategory| |#4| (QUOTE (-174)))) 
+(-1078 |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"))) 
-((-4466 . T) (-4461 . T) (-4460 . T)) 
+((-4470 . T) (-4465 . T) (-4464 . T)) 
 NIL 
-(-1076 |m| |n| R) 
+(-1079 |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}."))) 
-((-4466 . T) (-4461 . T) (-4460 . T)) 
-((|HasCategory| |#3| (QUOTE (-174))) (-2802 (-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 (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-877))))) 
-(-1077 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4470 . T) (-4465 . T) (-4464 . T)) 
+((|HasCategory| |#3| (QUOTE (-174))) (-2839 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375)))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880))))) 
+(-1080 |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 
-(-1078 R) 
+(-1081 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 
-(-1079 S T$) 
+(-1082 S T$) 
 ((|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 (-1122)))) 
-(-1080) 
+((|HasCategory| |#1| (QUOTE (-1125)))) 
+(-1083) 
 ((|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 
-(-1081 S) 
+(-1084 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1082) 
+(-1085) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1083 |TheField| |ThePolDom|) 
+(-1086 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1084) 
+(-1087) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-4454 . T) (-4458 . T) (-4453 . T) (-4464 . T) (-4465 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1085) 
+(-1088) 
 ((|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}"))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (QUOTE (-1198))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1122))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 (-1198)) (|:| -4440 (-52))) (QUOTE (-102)))) 
-(-1086 S R E V) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -4444) (QUOTE (-52))))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1201)) (|:| -4444 (-52))) (QUOTE (-102)))) 
+(-1089 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1198))))) 
-(-1087 R E V) 
+((|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-1201))))) 
+(-1090 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-1088) 
+(-1091) 
 ((|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 
-(-1089 S |TheField| |ThePols|) 
+(-1092 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 
-(-1090 |TheField| |ThePols|) 
+(-1093 |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 
-(-1091 R E V P TS) 
+(-1094 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 
-(-1092 S R E V P) 
+(-1095 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 
-(-1093 R E V P) 
+(-1096 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}."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1094 R E V P TS) 
+(-1097 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 
-(-1095) 
+(-1098) 
 ((|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 
-(-1096) 
+(-1099) 
 ((|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 
-(-1097 |f|) 
+(-1100 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1098 |Base| R -2022) 
+(-1101 |Base| R -2051) 
 ((|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 
-(-1099 |Base| R -2022) 
+(-1102 |Base| R -2051) 
 ((|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 
-(-1100 R |ls|) 
+(-1103 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 
-(-1101 UP SAE UPA) 
+(-1104 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 
-(-1102 R UP M) 
+(-1105 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."))) 
-((-4459 |has| |#1| (-374)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2802 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198))))) (-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 -918) (QUOTE (-1198)))))) 
-(-1103 UP SAE UPA) 
+((-4463 |has| |#1| (-375)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) 
+(-1106 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 
-(-1104) 
+(-1107) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1105) 
+(-1108) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1106 S) 
+(-1109 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 
-(-1107) 
+(-1110) 
 ((|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 
-(-1108 R) 
+(-1111 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 
-(-1109 R) 
+(-1112 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"))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1110 (-1198)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1110 S) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-932))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1113 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 
-(-1111 R S) 
+(-1114 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 (-861)))) 
-(-1112) 
+((|HasCategory| |#1| (QUOTE (-864)))) 
+(-1115) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1113 R S) 
+(-1116 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1114 S) 
+(-1117 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1116 |#1|) (QUOTE (-1122)))) 
-(-1115 S) 
+((|HasCategory| (-1119 |#1|) (QUOTE (-1125)))) 
+(-1118 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1116 S) 
+(-1119 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) 
-(-1117 S L) 
+((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1125)))) 
+(-1120 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 
-(-1118) 
+(-1121) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1119 A S) 
+(-1122 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1120 S) 
+(-1123 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-4456 . T)) 
+((-4460 . T)) 
 NIL 
-(-1121 S) 
+(-1124 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1122) 
+(-1125) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1123 |m| |n|) 
+(-1126 |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 
-(-1124 S) 
+(-1127 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)}}"))) 
-((-4466 . T) (-4456 . T) (-4467 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-1125 |Str| |Sym| |Int| |Flt| |Expr|) 
+((-4470 . T) (-4460 . T) (-4471 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-1128 |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|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1126) 
+(-1129) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1127 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1130 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1128 R FS) 
+(-1131 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 
-(-1129 R E V P TS) 
+(-1132 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 
-(-1130 R E V P TS) 
+(-1133 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 
-(-1131 R E V P) 
+(-1134 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.}"))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1132) 
+(-1135) 
 ((|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 
-(-1133 S) 
+(-1136 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1134) 
+(-1137) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1135 |dimtot| |dim1| S) 
+(-1138 |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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(QUOTE (-375)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-380)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-742)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-809)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-865)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1074)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1125))))) (-2839 (-12 (|HasCategory| |#3| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-865))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1074))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))))) (-2839 (-12 (|HasCategory| |#3| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-865))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| (-577) (QUOTE (-865))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1074)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -923) (QUOTE (-1201))))) (-2839 (|HasCategory| |#3| (QUOTE (-1074))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1125)))) (|HasAttribute| |#3| (QUOTE -4467)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1074)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -921) (QUOTE (-1201))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) 
+(-1139 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 (-464)))) 
-(-1137) 
+((|HasCategory| |#1| (QUOTE (-465)))) 
+(-1140) 
 ((|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 
-(-1138 R -2022) 
+(-1141 R -2051) 
 ((|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 
-(-1139 R) 
+(-1142 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 
-(-1140) 
+(-1143) 
 ((|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 
-(-1141) 
+(-1144) 
 ((|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 
-(-1142) 
+(-1145) 
 ((|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."))) 
-((-4454 . T) (-4458 . T) (-4453 . T) (-4464 . T) (-4465 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1143 S) 
+(-1146 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4466 . T) (-4467 . T)) 
+((-4470 . T) (-4471 . T)) 
 NIL 
-(-1144 S |ndim| R |Row| |Col|) 
+(-1147 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-374))) (|HasAttribute| |#3| (QUOTE (-4468 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
-(-1145 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-375))) (|HasAttribute| |#3| (QUOTE (-4472 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
+(-1148 |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."))) 
-((-4466 . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4470 . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1146 R |Row| |Col| M) 
+(-1149 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 
-(-1147 R |VarSet|) 
+(-1150 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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-929))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1148 |Coef| |Var| SMP) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-932))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1151 |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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-1149 R E V P) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-1152 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}"))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1150 UP -2022) 
+(-1153 UP -2051) 
 ((|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 
-(-1151 R) 
+(-1154 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 
-(-1152 R) 
+(-1155 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 
-(-1153 R) 
+(-1156 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 
-(-1154 S A) 
+(-1157 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 (-862)))) 
-(-1155 R) 
+((|HasCategory| |#1| (QUOTE (-865)))) 
+(-1158 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 
-(-1156 R) 
+(-1159 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 
-(-1157) 
+(-1160) 
 ((|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 
-(-1158) 
+(-1161) 
 ((|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 
-(-1159) 
+(-1162) 
 ((|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 
-(-1160) 
+(-1163) 
 ((|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 
-(-1161) 
+(-1164) 
 ((|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 
-(-1162 V C) 
+(-1165 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 
-(-1163 V C) 
+(-1166 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."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))) (-2802 (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122)))) (-2802 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (-12 (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1162) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-1122))))) (|HasCategory| (-1162 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-1162 |#1| |#2|) (QUOTE (-102)))) 
-(-1164 |ndim| R) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))) (-2839 (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (-2839 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))))) (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102)))) 
+(-1167 |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}."))) 
-((-4463 . T) (-4455 |has| |#2| (-6 (-4468 "*"))) (-4466 . T) (-4460 . T) (-4461 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-374))) (-2802 (|HasAttribute| |#2| (QUOTE (-4468 "*"))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-1165 S) 
+((-4467 . T) (-4459 |has| |#2| (-6 (-4472 "*"))) (-4470 . T) (-4464 . T) (-4465 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (-2839 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-1168 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1166) 
+(-1169) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1167 R E V P TS) 
+(-1170 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 
-(-1168 R E V P) 
+(-1171 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."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1169 S) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1172 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}."))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1170 A S) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1173 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 
-(-1171 S) 
+(-1174 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 
-(-1172 |Key| |Ent| |dent|) 
+(-1175 |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."))) 
-((-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122)))) 
-(-1173) 
+((-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125)))) 
+(-1176) 
 ((|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 
-(-1174) 
+(-1177) 
 ((|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 
-(-1175 |Coef|) 
+(-1178 |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 
-(-1176 S) 
+(-1179 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 
-(-1177 A B) 
+(-1180 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 
-(-1178 A B C) 
+(-1181 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 
-(-1179 S) 
+(-1182 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."))) 
-((-4467 . T)) 
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-(-1180) 
+((-4471 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1183) 
 ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) 
-((-4467 . T) (-4466 . T)) 
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-(-1181 |Entry|) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2839 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-2839 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) 
+(-1184 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4466 . T) (-4467 . T)) 
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-(-1182 A) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#1|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 (-1183)) (|:| -4444 |#1|)) (QUOTE (-102)))) 
+(-1185 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 (-374))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) 
-(-1183 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) 
+(-1186 |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 
-(-1184 |Coef|) 
+(-1187 |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 
-(-1185 R UP) 
+(-1188 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 (-317)))) 
-(-1186 |n| R) 
+((|HasCategory| |#1| (QUOTE (-318)))) 
+(-1189 |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 
-(-1187 S1 S2) 
+(-1190 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 
-(-1188) 
+(-1191) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1189 |Coef| |var| |cen|) 
+(-1192 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-4468 "*") -2802 (-2724 (|has| |#1| (-374)) (|has| (-1196 |#1| |#2| |#3|) (-833))) (|has| |#1| (-174)) (-2724 (|has| |#1| (-374)) (|has| (-1196 |#1| |#2| |#3|) (-929)))) (-4459 -2802 (-2724 (|has| |#1| (-374)) (|has| (-1196 |#1| |#2| |#3|) (-833))) (|has| |#1| (-568)) (-2724 (|has| |#1| (-374)) (|has| (-1196 |#1| |#2| |#3|) (-929)))) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((-2802 (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-1174))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1196 |#1| |#2| |#3|) (LIST (QUOTE -296) (LIST (QUOTE -1196) (|devaluate| |#1|) (|devaluate| |#2|) 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 ((|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 
-(-1192 R S) 
+(-1195 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1193 E OV R P) 
+(-1196 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 
-(-1194 R) 
+(-1197 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1195 |Coef| |var| |cen|) 
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+(-1198 |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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|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 (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|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 -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|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 -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
-(-1196 |Coef| |var| |cen|) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) 
+(-1199 |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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|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 -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|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 -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
-(-1197) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) 
+(-1200) 
 ((|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 
-(-1198) 
+(-1201) 
 ((|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 
-(-1199 R) 
+(-1202 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 
-(-1200 R) 
+(-1203 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-6 -4464)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2802 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-993) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4464))) 
-(-1201) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2839 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| (-996) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4468))) 
+(-1204) 
 ((|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 
-(-1202) 
+(-1205) 
 ((|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 
-(-1203) 
+(-1206) 
 ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1204 N) 
+(-1207 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1205 N) 
+(-1208 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 
-(-1206) 
+(-1209) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1207 R) 
+(-1210 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 
-(-1208) 
+(-1211) 
 ((|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 
-(-1209 S) 
+(-1212 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 
-(-1210 S) 
+(-1213 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 
-(-1211 |Key| |Entry|) 
+(-1214 |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}"))) 
-((-4466 . T) (-4467 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4291) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122)))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1122))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877))))) (-2802 (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) 
-(-1212 S) 
+((-4470 . T) (-4471 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4295) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4444) (|devaluate| |#2|)))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2839 (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (QUOTE (-102)))) 
+(-1215 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 
-(-1213 R) 
+(-1216 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 
-(-1214 S |Key| |Entry|) 
+(-1217 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 
-(-1215 |Key| |Entry|) 
+(-1218 |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})}."))) 
-((-4467 . T)) 
+((-4471 . T)) 
 NIL 
-(-1216 |Key| |Entry|) 
+(-1219 |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 
-(-1217) 
+(-1220) 
 ((|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 
-(-1218 S) 
+(-1221 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 
-(-1219) 
+(-1222) 
 ((|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 
-(-1220) 
+(-1223) 
 ((|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 
-(-1221 R) 
+(-1224 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 
-(-1222) 
+(-1225) 
 ((|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 
-(-1223 S) 
+(-1226 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1224) 
+(-1227) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1225 S) 
+(-1228 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1226 S) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1229 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1227) 
+(-1230) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1228 R -2022) 
+(-1231 R -2051) 
 ((|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 
-(-1229 R |Row| |Col| M) 
+(-1232 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 
-(-1230 R -2022) 
+(-1233 R -2051) 
 ((|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 -626) (LIST (QUOTE -908) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -902) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -902) (|devaluate| |#1|))))) 
-(-1231 S R E V P) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -905) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -905) (|devaluate| |#1|))))) 
+(-1234 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 (-379)))) 
-(-1232 R E V P) 
+((|HasCategory| |#4| (QUOTE (-380)))) 
+(-1235 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1233 |Coef|) 
+(-1236 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-1234 |Curve|) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-1237 |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 
-(-1235) 
+(-1238) 
 ((|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 
-(-1236 S) 
+(-1239 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 (-1122))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) 
-(-1237 -2022) 
+((|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) 
+(-1240 -2051) 
 ((|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 
-(-1238) 
+(-1241) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1239) 
+(-1242) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1240 S) 
+(-1243 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 (-862)))) 
-(-1241) 
+((|HasCategory| |#1| (QUOTE (-865)))) 
+(-1244) 
 ((|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 
-(-1242 S) 
+(-1245 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 
-(-1243) 
+(-1246) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1244) 
+(-1247) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1245) 
+(-1248) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1246) 
+(-1249) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1247) 
+(-1250) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1248 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1251 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1249 |Coef|) 
+(-1252 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1250 S |Coef| UTS) 
+(-1253 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 (-374)))) 
-(-1251 |Coef| UTS) 
+((|HasCategory| |#2| (QUOTE (-375)))) 
+(-1254 |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)}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1252 |Coef| UTS) 
+(-1255 |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)}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
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(|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3|) (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3|) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1284 |#1| |#2| |#3|) (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-375)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1284 |#1| |#2| |#3|) (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1257 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 
-(-1255 R S) 
+(-1258 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 (-861)))) 
-(-1256 S) 
+((|HasCategory| |#1| (QUOTE (-864)))) 
+(-1259 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 (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) 
-(-1257 |x| R |y| S) 
+((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1125)))) 
+(-1260 |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 
-(-1258 R Q UP) 
+(-1261 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 
-(-1259 R UP) 
+(-1262 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 
-(-1260 R UP) 
+(-1263 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 
-(-1261 R U) 
+(-1264 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 
-(-1262 |x| R) 
+(-1265 |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}"))) 
-(((-4468 "*") |has| |#2| (-174)) (-4459 |has| |#2| (-568)) (-4462 |has| |#2| (-374)) (-4464 |has| |#2| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-390))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -902) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-576))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-390)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -908) (QUOTE (-576)))))) (-12 (|HasCategory| (-1104) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -652) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (QUOTE (-576)))) (-2802 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (-2802 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasCategory| |#2| (LIST (QUOTE -920) (QUOTE (-1198)))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (-2802 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-1263 R PR S PS) 
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+((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2839 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2839 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2839 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2839 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-1266 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 
-(-1264 S R) 
+(-1267 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 -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1174)))) 
-(-1265 R) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1177)))) 
+(-1268 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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4464 |has| |#1| (-6 -4464)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-1266 S |Coef| |Expon|) 
+(-1269 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 -918) (QUOTE (-1198)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1134))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3501) (LIST (|devaluate| |#2|) (QUOTE (-1198)))))) 
-(-1267 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1137))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3544) (LIST (|devaluate| |#2|) (QUOTE (-1201)))))) 
+(-1270 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1268 RC P) 
+(-1271 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1269 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1272 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1270 |Coef|) 
+(-1273 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4464 |has| |#1| (-374)) (-4458 |has| |#1| (-374)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1271 S |Coef| ULS) 
+(-1274 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 
-(-1272 |Coef| ULS) 
+(-1275 |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)}."))) 
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+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1273 |Coef| ULS) 
+(-1276 |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)}."))) 
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-(-1274 |Coef| |var| |cen|) 
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+((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) 
+(-1277 |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."))) 
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-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1198)))) (|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 (-1134))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2802 (|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 -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|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 -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
-(-1275 R FE |var| |cen|) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2839 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) 
+(-1278 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))}."))) 
-(((-4468 "*") |has| (-1274 |#2| |#3| |#4|) (-174)) (-4459 |has| (-1274 |#2| |#3| |#4|) (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-174))) (-2802 (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1274 |#2| |#3| |#4|) (LIST (QUOTE -1060) (QUOTE (-576)))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1274 |#2| |#3| |#4|) (QUOTE (-568)))) 
-(-1276 A S) 
+(((-4472 "*") |has| (-1277 |#2| |#3| |#4|) (-174)) (-4463 |has| (-1277 |#2| |#3| |#4|) (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-174))) (-2839 (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-375))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-465))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) 
+(-1279 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4467))) 
-(-1277 S) 
+((|HasAttribute| |#1| (QUOTE -4471))) 
+(-1280 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1278 |Coef1| |Coef2| UTS1 UTS2) 
+(-1281 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1279 S |Coef|) 
+(-1282 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasSignature| |#2| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4190) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1198))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) 
-(-1280 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasSignature| |#2| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4147) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1201))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375)))) 
+(-1283 |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."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1281 |Coef| |var| |cen|) 
+(-1284 |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}."))) 
-(((-4468 "*") |has| |#1| (-174)) (-4459 |has| |#1| (-568)) (-4460 . T) (-4461 . T) (-4463 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2802 (|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 -918) (QUOTE (-1198)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-784)) (|devaluate| |#1|)))) (|HasCategory| (-784) (QUOTE (-1134))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasSignature| |#1| (LIST (QUOTE -3501) (LIST (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-784))))) (|HasCategory| |#1| (QUOTE (-374))) (-2802 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|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 -4190) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (LIST (QUOTE -2029) (LIST (LIST (QUOTE -657) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
-(-1282 |Coef| UTS) 
+(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2839 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -3544) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-2839 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4147) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -2058) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) 
+(-1285 |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 
-(-1283 -2022 UP L UTS) 
+(-1286 -2051 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 (-568)))) 
-(-1284) 
+((|HasCategory| |#1| (QUOTE (-569)))) 
+(-1287) 
 ((|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 
-(-1285 |sym|) 
+(-1288 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1286 S R) 
+(-1289 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 (-1024))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1287 R) 
+((|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1290 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4467 . T) (-4466 . T)) 
+((-4471 . T) (-4470 . T)) 
 NIL 
-(-1288 A B) 
+(-1291 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1289 R) 
+(-1292 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4467 . T) (-4466 . T)) 
-((-2802 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2802 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2802 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-862))) (-2802 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-739))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1071)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) 
-(-1290) 
+((-4471 . T) (-4470 . T)) 
+((-2839 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2839 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2839 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2839 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) 
+(-1293) 
 ((|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 
-(-1291) 
+(-1294) 
 ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) 
 NIL 
 NIL 
-(-1292) 
+(-1295) 
 ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) 
 NIL 
 NIL 
-(-1293) 
+(-1296) 
 ((|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 
 NIL 
-(-1294) 
+(-1297) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1295 A S) 
+(-1298 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1296 S) 
+(-1299 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}."))) 
-((-4461 . T) (-4460 . T)) 
+((-4465 . T) (-4464 . T)) 
 NIL 
-(-1297 R) 
+(-1300 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1298 K R UP -2022) 
+(-1301 K R UP -2051) 
 ((|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 
-(-1299) 
+(-1302) 
 ((|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 
-(-1300) 
+(-1303) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1301 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1304 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)"))) 
-((-4461 |has| |#1| (-174)) (-4460 |has| |#1| (-174)) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) 
-(-1302 R E V P) 
+((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375)))) 
+(-1305 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}}."))) 
-((-4467 . T) (-4466 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1303 R) 
+((-4471 . T) (-4470 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1306 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})"))) 
-((-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1304 |vl| R) 
+(-1307 |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."))) 
-((-4463 . T) (-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4459))) 
-(-1305 R |VarSet| XPOLY) 
+((-4467 . T) (-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4463))) 
+(-1308 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 
-(-1306 |vl| R) 
+(-1309 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-1307 S -2022) 
+(-1310 S -2051) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-1308 -2022) 
+((|HasCategory| |#2| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
+(-1311 -2051) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4458 . T) (-4464 . T) (-4459 . T) ((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
-(-1309 |VarSet| R) 
+(-1312 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) 
-((-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -730) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4459))) 
-(-1310 |vl| R) 
+((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -733) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasAttribute| |#2| (QUOTE -4463))) 
+(-1313 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) 
+((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) 
 NIL 
-(-1311 R) 
+(-1314 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4459 |has| |#1| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4459))) 
-(-1312 R E) 
+((-4463 |has| |#1| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4463))) 
+(-1315 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-4463 . T) (-4464 |has| |#1| (-6 -4464)) (-4459 |has| |#1| (-6 -4459)) (-4461 . T) (-4460 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4459))) 
-(-1313 |VarSet| R) 
+((-4467 . T) (-4468 |has| |#1| (-6 -4468)) (-4463 |has| |#1| (-6 -4463)) (-4465 . T) (-4464 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4467)) (|HasAttribute| |#1| (QUOTE -4468)) (|HasAttribute| |#1| (QUOTE -4463))) 
+(-1316 |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."))) 
-((-4459 |has| |#2| (-6 -4459)) (-4461 . T) (-4460 . T) (-4463 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4459))) 
-(-1314) 
+((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4463))) 
+(-1317) 
 ((|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 
-(-1315 A) 
+(-1318 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 
-(-1316 R |ls| |ls2|) 
+(-1319 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 
-(-1317 R) 
+(-1320 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 
-(-1318 |p|) 
+(-1321 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4468 "*") . T) (-4460 . T) (-4461 . T) (-4463 . T)) 
+(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5220,4 +5232,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2294940 2294945 2294950 2294955) (-2 NIL 2294920 2294925 2294930 2294935) (-1 NIL 2294900 2294905 2294910 2294915) (0 NIL 2294880 2294885 2294890 2294895) (-1318 "ZMOD.spad" 2294689 2294702 2294818 2294875) (-1317 "ZLINDEP.spad" 2293755 2293766 2294679 2294684) (-1316 "ZDSOLVE.spad" 2283700 2283722 2293745 2293750) (-1315 "YSTREAM.spad" 2283195 2283206 2283690 2283695) (-1314 "YDIAGRAM.spad" 2282829 2282838 2283185 2283190) (-1313 "XRPOLY.spad" 2282049 2282069 2282685 2282754) (-1312 "XPR.spad" 2279844 2279857 2281767 2281866) (-1311 "XPOLY.spad" 2279399 2279410 2279700 2279769) (-1310 "XPOLYC.spad" 2278718 2278734 2279325 2279394) (-1309 "XPBWPOLY.spad" 2277155 2277175 2278498 2278567) (-1308 "XF.spad" 2275618 2275633 2277057 2277150) (-1307 "XF.spad" 2274061 2274078 2275502 2275507) (-1306 "XFALG.spad" 2271109 2271125 2273987 2274056) (-1305 "XEXPPKG.spad" 2270360 2270386 2271099 2271104) (-1304 "XDPOLY.spad" 2269974 2269990 2270216 2270285) (-1303 "XALG.spad" 2269634 2269645 2269930 2269969) (-1302 "WUTSET.spad" 2265437 2265454 2269244 2269271) (-1301 "WP.spad" 2264636 2264680 2265295 2265362) (-1300 "WHILEAST.spad" 2264434 2264443 2264626 2264631) (-1299 "WHEREAST.spad" 2264105 2264114 2264424 2264429) (-1298 "WFFINTBS.spad" 2261768 2261790 2264095 2264100) (-1297 "WEIER.spad" 2259990 2260001 2261758 2261763) (-1296 "VSPACE.spad" 2259663 2259674 2259958 2259985) (-1295 "VSPACE.spad" 2259356 2259369 2259653 2259658) (-1294 "VOID.spad" 2259033 2259042 2259346 2259351) (-1293 "VIEW.spad" 2256713 2256722 2259023 2259028) (-1292 "VIEWDEF.spad" 2251914 2251923 2256703 2256708) (-1291 "VIEW3D.spad" 2235875 2235884 2251904 2251909) (-1290 "VIEW2D.spad" 2223766 2223775 2235865 2235870) (-1289 "VECTOR.spad" 2222287 2222298 2222538 2222565) (-1288 "VECTOR2.spad" 2220926 2220939 2222277 2222282) (-1287 "VECTCAT.spad" 2218830 2218841 2220894 2220921) (-1286 "VECTCAT.spad" 2216541 2216554 2218607 2218612) (-1285 "VARIABLE.spad" 2216321 2216336 2216531 2216536) (-1284 "UTYPE.spad" 2215965 2215974 2216311 2216316) (-1283 "UTSODETL.spad" 2215260 2215284 2215921 2215926) (-1282 "UTSODE.spad" 2213476 2213496 2215250 2215255) (-1281 "UTS.spad" 2208423 2208451 2211943 2212040) (-1280 "UTSCAT.spad" 2205902 2205918 2208321 2208418) (-1279 "UTSCAT.spad" 2203025 2203043 2205446 2205451) (-1278 "UTS2.spad" 2202620 2202655 2203015 2203020) (-1277 "URAGG.spad" 2197293 2197304 2202610 2202615) (-1276 "URAGG.spad" 2191930 2191943 2197249 2197254) (-1275 "UPXSSING.spad" 2189575 2189601 2191011 2191144) (-1274 "UPXS.spad" 2186871 2186899 2187707 2187856) (-1273 "UPXSCONS.spad" 2184630 2184650 2185003 2185152) (-1272 "UPXSCCA.spad" 2183201 2183221 2184476 2184625) (-1271 "UPXSCCA.spad" 2181914 2181936 2183191 2183196) (-1270 "UPXSCAT.spad" 2180503 2180519 2181760 2181909) (-1269 "UPXS2.spad" 2180046 2180099 2180493 2180498) (-1268 "UPSQFREE.spad" 2178460 2178474 2180036 2180041) (-1267 "UPSCAT.spad" 2176247 2176271 2178358 2178455) (-1266 "UPSCAT.spad" 2173740 2173766 2175853 2175858) (-1265 "UPOLYC.spad" 2168780 2168791 2173582 2173735) (-1264 "UPOLYC.spad" 2163712 2163725 2168516 2168521) (-1263 "UPOLYC2.spad" 2163183 2163202 2163702 2163707) (-1262 "UP.spad" 2160289 2160304 2160676 2160829) (-1261 "UPMP.spad" 2159189 2159202 2160279 2160284) (-1260 "UPDIVP.spad" 2158754 2158768 2159179 2159184) (-1259 "UPDECOMP.spad" 2156999 2157013 2158744 2158749) (-1258 "UPCDEN.spad" 2156208 2156224 2156989 2156994) (-1257 "UP2.spad" 2155572 2155593 2156198 2156203) (-1256 "UNISEG.spad" 2154925 2154936 2155491 2155496) (-1255 "UNISEG2.spad" 2154422 2154435 2154881 2154886) (-1254 "UNIFACT.spad" 2153525 2153537 2154412 2154417) (-1253 "ULS.spad" 2143309 2143337 2144254 2144683) (-1252 "ULSCONS.spad" 2134443 2134463 2134813 2134962) (-1251 "ULSCCAT.spad" 2132180 2132200 2134289 2134438) (-1250 "ULSCCAT.spad" 2130025 2130047 2132136 2132141) (-1249 "ULSCAT.spad" 2128257 2128273 2129871 2130020) (-1248 "ULS2.spad" 2127771 2127824 2128247 2128252) (-1247 "UINT8.spad" 2127648 2127657 2127761 2127766) (-1246 "UINT64.spad" 2127524 2127533 2127638 2127643) (-1245 "UINT32.spad" 2127400 2127409 2127514 2127519) (-1244 "UINT16.spad" 2127276 2127285 2127390 2127395) (-1243 "UFD.spad" 2126341 2126350 2127202 2127271) (-1242 "UFD.spad" 2125468 2125479 2126331 2126336) (-1241 "UDVO.spad" 2124349 2124358 2125458 2125463) (-1240 "UDPO.spad" 2121842 2121853 2124305 2124310) (-1239 "TYPE.spad" 2121774 2121783 2121832 2121837) (-1238 "TYPEAST.spad" 2121693 2121702 2121764 2121769) (-1237 "TWOFACT.spad" 2120345 2120360 2121683 2121688) (-1236 "TUPLE.spad" 2119831 2119842 2120244 2120249) (-1235 "TUBETOOL.spad" 2116698 2116707 2119821 2119826) (-1234 "TUBE.spad" 2115345 2115362 2116688 2116693) (-1233 "TS.spad" 2113944 2113960 2114910 2115007) (-1232 "TSETCAT.spad" 2101071 2101088 2113912 2113939) (-1231 "TSETCAT.spad" 2088184 2088203 2101027 2101032) (-1230 "TRMANIP.spad" 2082550 2082567 2087890 2087895) (-1229 "TRIMAT.spad" 2081513 2081538 2082540 2082545) (-1228 "TRIGMNIP.spad" 2080040 2080057 2081503 2081508) (-1227 "TRIGCAT.spad" 2079552 2079561 2080030 2080035) (-1226 "TRIGCAT.spad" 2079062 2079073 2079542 2079547) (-1225 "TREE.spad" 2077520 2077531 2078552 2078579) (-1224 "TRANFUN.spad" 2077359 2077368 2077510 2077515) (-1223 "TRANFUN.spad" 2077196 2077207 2077349 2077354) (-1222 "TOPSP.spad" 2076870 2076879 2077186 2077191) (-1221 "TOOLSIGN.spad" 2076533 2076544 2076860 2076865) (-1220 "TEXTFILE.spad" 2075094 2075103 2076523 2076528) (-1219 "TEX.spad" 2072240 2072249 2075084 2075089) (-1218 "TEX1.spad" 2071796 2071807 2072230 2072235) (-1217 "TEMUTL.spad" 2071351 2071360 2071786 2071791) (-1216 "TBCMPPK.spad" 2069444 2069467 2071341 2071346) (-1215 "TBAGG.spad" 2068494 2068517 2069424 2069439) (-1214 "TBAGG.spad" 2067552 2067577 2068484 2068489) (-1213 "TANEXP.spad" 2066960 2066971 2067542 2067547) (-1212 "TALGOP.spad" 2066684 2066695 2066950 2066955) (-1211 "TABLE.spad" 2064653 2064676 2064923 2064950) (-1210 "TABLEAU.spad" 2064134 2064145 2064643 2064648) (-1209 "TABLBUMP.spad" 2060937 2060948 2064124 2064129) (-1208 "SYSTEM.spad" 2060165 2060174 2060927 2060932) (-1207 "SYSSOLP.spad" 2057648 2057659 2060155 2060160) (-1206 "SYSPTR.spad" 2057547 2057556 2057638 2057643) (-1205 "SYSNNI.spad" 2056729 2056740 2057537 2057542) (-1204 "SYSINT.spad" 2056133 2056144 2056719 2056724) (-1203 "SYNTAX.spad" 2052339 2052348 2056123 2056128) (-1202 "SYMTAB.spad" 2050407 2050416 2052329 2052334) (-1201 "SYMS.spad" 2046430 2046439 2050397 2050402) (-1200 "SYMPOLY.spad" 2045437 2045448 2045519 2045646) (-1199 "SYMFUNC.spad" 2044938 2044949 2045427 2045432) (-1198 "SYMBOL.spad" 2042441 2042450 2044928 2044933) (-1197 "SWITCH.spad" 2039212 2039221 2042431 2042436) (-1196 "SUTS.spad" 2036260 2036288 2037679 2037776) (-1195 "SUPXS.spad" 2033543 2033571 2034392 2034541) (-1194 "SUP.spad" 2030263 2030274 2031036 2031189) (-1193 "SUPFRACF.spad" 2029368 2029386 2030253 2030258) (-1192 "SUP2.spad" 2028760 2028773 2029358 2029363) (-1191 "SUMRF.spad" 2027734 2027745 2028750 2028755) (-1190 "SUMFS.spad" 2027371 2027388 2027724 2027729) (-1189 "SULS.spad" 2017142 2017170 2018100 2018529) (-1188 "SUCHTAST.spad" 2016911 2016920 2017132 2017137) (-1187 "SUCH.spad" 2016593 2016608 2016901 2016906) (-1186 "SUBSPACE.spad" 2008708 2008723 2016583 2016588) (-1185 "SUBRESP.spad" 2007878 2007892 2008664 2008669) (-1184 "STTF.spad" 2003977 2003993 2007868 2007873) (-1183 "STTFNC.spad" 2000445 2000461 2003967 2003972) (-1182 "STTAYLOR.spad" 1993080 1993091 2000326 2000331) (-1181 "STRTBL.spad" 1991131 1991148 1991280 1991307) (-1180 "STRING.spad" 1989918 1989927 1990139 1990166) (-1179 "STREAM.spad" 1986719 1986730 1989326 1989341) (-1178 "STREAM3.spad" 1986292 1986307 1986709 1986714) (-1177 "STREAM2.spad" 1985420 1985433 1986282 1986287) (-1176 "STREAM1.spad" 1985126 1985137 1985410 1985415) (-1175 "STINPROD.spad" 1984062 1984078 1985116 1985121) (-1174 "STEP.spad" 1983263 1983272 1984052 1984057) (-1173 "STEPAST.spad" 1982497 1982506 1983253 1983258) (-1172 "STBL.spad" 1980581 1980609 1980748 1980763) (-1171 "STAGG.spad" 1979656 1979667 1980571 1980576) (-1170 "STAGG.spad" 1978729 1978742 1979646 1979651) (-1169 "STACK.spad" 1977969 1977980 1978219 1978246) (-1168 "SREGSET.spad" 1975637 1975654 1977579 1977606) (-1167 "SRDCMPK.spad" 1974198 1974218 1975627 1975632) (-1166 "SRAGG.spad" 1969341 1969350 1974166 1974193) (-1165 "SRAGG.spad" 1964504 1964515 1969331 1969336) (-1164 "SQMATRIX.spad" 1962047 1962065 1962963 1963050) (-1163 "SPLTREE.spad" 1956443 1956456 1961327 1961354) (-1162 "SPLNODE.spad" 1953031 1953044 1956433 1956438) (-1161 "SPFCAT.spad" 1951840 1951849 1953021 1953026) (-1160 "SPECOUT.spad" 1950392 1950401 1951830 1951835) (-1159 "SPADXPT.spad" 1941987 1941996 1950382 1950387) (-1158 "spad-parser.spad" 1941452 1941461 1941977 1941982) (-1157 "SPADAST.spad" 1941153 1941162 1941442 1941447) (-1156 "SPACEC.spad" 1925352 1925363 1941143 1941148) (-1155 "SPACE3.spad" 1925128 1925139 1925342 1925347) (-1154 "SORTPAK.spad" 1924677 1924690 1925084 1925089) (-1153 "SOLVETRA.spad" 1922440 1922451 1924667 1924672) (-1152 "SOLVESER.spad" 1920968 1920979 1922430 1922435) (-1151 "SOLVERAD.spad" 1916994 1917005 1920958 1920963) (-1150 "SOLVEFOR.spad" 1915456 1915474 1916984 1916989) (-1149 "SNTSCAT.spad" 1915056 1915073 1915424 1915451) (-1148 "SMTS.spad" 1913328 1913354 1914621 1914718) (-1147 "SMP.spad" 1910803 1910823 1911193 1911320) (-1146 "SMITH.spad" 1909648 1909673 1910793 1910798) (-1145 "SMATCAT.spad" 1907758 1907788 1909592 1909643) (-1144 "SMATCAT.spad" 1905800 1905832 1907636 1907641) (-1143 "SKAGG.spad" 1904763 1904774 1905768 1905795) (-1142 "SINT.spad" 1903703 1903712 1904629 1904758) (-1141 "SIMPAN.spad" 1903431 1903440 1903693 1903698) (-1140 "SIG.spad" 1902761 1902770 1903421 1903426) (-1139 "SIGNRF.spad" 1901879 1901890 1902751 1902756) (-1138 "SIGNEF.spad" 1901158 1901175 1901869 1901874) (-1137 "SIGAST.spad" 1900543 1900552 1901148 1901153) (-1136 "SHP.spad" 1898471 1898486 1900499 1900504) (-1135 "SHDP.spad" 1886149 1886176 1886658 1886757) (-1134 "SGROUP.spad" 1885757 1885766 1886139 1886144) (-1133 "SGROUP.spad" 1885363 1885374 1885747 1885752) (-1132 "SGCF.spad" 1878502 1878511 1885353 1885358) (-1131 "SFRTCAT.spad" 1877432 1877449 1878470 1878497) (-1130 "SFRGCD.spad" 1876495 1876515 1877422 1877427) (-1129 "SFQCMPK.spad" 1871132 1871152 1876485 1876490) (-1128 "SFORT.spad" 1870571 1870585 1871122 1871127) (-1127 "SEXOF.spad" 1870414 1870454 1870561 1870566) (-1126 "SEX.spad" 1870306 1870315 1870404 1870409) (-1125 "SEXCAT.spad" 1868078 1868118 1870296 1870301) (-1124 "SET.spad" 1866366 1866377 1867463 1867502) (-1123 "SETMN.spad" 1864816 1864833 1866356 1866361) (-1122 "SETCAT.spad" 1864301 1864310 1864806 1864811) (-1121 "SETCAT.spad" 1863784 1863795 1864291 1864296) (-1120 "SETAGG.spad" 1860333 1860344 1863764 1863779) (-1119 "SETAGG.spad" 1856890 1856903 1860323 1860328) (-1118 "SEQAST.spad" 1856593 1856602 1856880 1856885) (-1117 "SEGXCAT.spad" 1855749 1855762 1856583 1856588) (-1116 "SEG.spad" 1855562 1855573 1855668 1855673) (-1115 "SEGCAT.spad" 1854487 1854498 1855552 1855557) (-1114 "SEGBIND.spad" 1854245 1854256 1854434 1854439) (-1113 "SEGBIND2.spad" 1853943 1853956 1854235 1854240) (-1112 "SEGAST.spad" 1853657 1853666 1853933 1853938) (-1111 "SEG2.spad" 1853092 1853105 1853613 1853618) (-1110 "SDVAR.spad" 1852368 1852379 1853082 1853087) (-1109 "SDPOL.spad" 1849701 1849712 1849992 1850119) (-1108 "SCPKG.spad" 1847790 1847801 1849691 1849696) (-1107 "SCOPE.spad" 1846943 1846952 1847780 1847785) (-1106 "SCACHE.spad" 1845639 1845650 1846933 1846938) (-1105 "SASTCAT.spad" 1845548 1845557 1845629 1845634) (-1104 "SAOS.spad" 1845420 1845429 1845538 1845543) (-1103 "SAERFFC.spad" 1845133 1845153 1845410 1845415) (-1102 "SAE.spad" 1842603 1842619 1843214 1843349) (-1101 "SAEFACT.spad" 1842304 1842324 1842593 1842598) (-1100 "RURPK.spad" 1839963 1839979 1842294 1842299) (-1099 "RULESET.spad" 1839416 1839440 1839953 1839958) (-1098 "RULE.spad" 1837656 1837680 1839406 1839411) (-1097 "RULECOLD.spad" 1837508 1837521 1837646 1837651) (-1096 "RTVALUE.spad" 1837243 1837252 1837498 1837503) (-1095 "RSTRCAST.spad" 1836960 1836969 1837233 1837238) (-1094 "RSETGCD.spad" 1833338 1833358 1836950 1836955) (-1093 "RSETCAT.spad" 1823274 1823291 1833306 1833333) (-1092 "RSETCAT.spad" 1813230 1813249 1823264 1823269) (-1091 "RSDCMPK.spad" 1811682 1811702 1813220 1813225) (-1090 "RRCC.spad" 1810066 1810096 1811672 1811677) (-1089 "RRCC.spad" 1808448 1808480 1810056 1810061) (-1088 "RPTAST.spad" 1808150 1808159 1808438 1808443) (-1087 "RPOLCAT.spad" 1787510 1787525 1808018 1808145) (-1086 "RPOLCAT.spad" 1766583 1766600 1787093 1787098) (-1085 "ROUTINE.spad" 1762004 1762013 1764768 1764795) (-1084 "ROMAN.spad" 1761332 1761341 1761870 1761999) (-1083 "ROIRC.spad" 1760412 1760444 1761322 1761327) (-1082 "RNS.spad" 1759315 1759324 1760314 1760407) (-1081 "RNS.spad" 1758304 1758315 1759305 1759310) (-1080 "RNG.spad" 1758039 1758048 1758294 1758299) (-1079 "RNGBIND.spad" 1757199 1757213 1757994 1757999) (-1078 "RMODULE.spad" 1756964 1756975 1757189 1757194) (-1077 "RMCAT2.spad" 1756384 1756441 1756954 1756959) (-1076 "RMATRIX.spad" 1755172 1755191 1755515 1755554) (-1075 "RMATCAT.spad" 1750751 1750782 1755128 1755167) (-1074 "RMATCAT.spad" 1746220 1746253 1750599 1750604) (-1073 "RLINSET.spad" 1745924 1745935 1746210 1746215) (-1072 "RINTERP.spad" 1745812 1745832 1745914 1745919) (-1071 "RING.spad" 1745282 1745291 1745792 1745807) (-1070 "RING.spad" 1744760 1744771 1745272 1745277) (-1069 "RIDIST.spad" 1744152 1744161 1744750 1744755) (-1068 "RGCHAIN.spad" 1742680 1742696 1743582 1743609) (-1067 "RGBCSPC.spad" 1742461 1742473 1742670 1742675) (-1066 "RGBCMDL.spad" 1741991 1742003 1742451 1742456) (-1065 "RF.spad" 1739633 1739644 1741981 1741986) (-1064 "RFFACTOR.spad" 1739095 1739106 1739623 1739628) (-1063 "RFFACT.spad" 1738830 1738842 1739085 1739090) (-1062 "RFDIST.spad" 1737826 1737835 1738820 1738825) (-1061 "RETSOL.spad" 1737245 1737258 1737816 1737821) (-1060 "RETRACT.spad" 1736673 1736684 1737235 1737240) (-1059 "RETRACT.spad" 1736099 1736112 1736663 1736668) (-1058 "RETAST.spad" 1735911 1735920 1736089 1736094) (-1057 "RESULT.spad" 1733509 1733518 1734096 1734123) (-1056 "RESRING.spad" 1732856 1732903 1733447 1733504) (-1055 "RESLATC.spad" 1732180 1732191 1732846 1732851) (-1054 "REPSQ.spad" 1731911 1731922 1732170 1732175) (-1053 "REP.spad" 1729465 1729474 1731901 1731906) (-1052 "REPDB.spad" 1729172 1729183 1729455 1729460) (-1051 "REP2.spad" 1718830 1718841 1729014 1729019) (-1050 "REP1.spad" 1713026 1713037 1718780 1718785) (-1049 "REGSET.spad" 1710787 1710804 1712636 1712663) (-1048 "REF.spad" 1710122 1710133 1710742 1710747) (-1047 "REDORDER.spad" 1709328 1709345 1710112 1710117) (-1046 "RECLOS.spad" 1708111 1708131 1708815 1708908) (-1045 "REALSOLV.spad" 1707251 1707260 1708101 1708106) (-1044 "REAL.spad" 1707123 1707132 1707241 1707246) (-1043 "REAL0Q.spad" 1704421 1704436 1707113 1707118) (-1042 "REAL0.spad" 1701265 1701280 1704411 1704416) (-1041 "RDUCEAST.spad" 1700986 1700995 1701255 1701260) (-1040 "RDIV.spad" 1700641 1700666 1700976 1700981) (-1039 "RDIST.spad" 1700208 1700219 1700631 1700636) (-1038 "RDETRS.spad" 1699072 1699090 1700198 1700203) (-1037 "RDETR.spad" 1697211 1697229 1699062 1699067) (-1036 "RDEEFS.spad" 1696310 1696327 1697201 1697206) (-1035 "RDEEF.spad" 1695320 1695337 1696300 1696305) (-1034 "RCFIELD.spad" 1692506 1692515 1695222 1695315) (-1033 "RCFIELD.spad" 1689778 1689789 1692496 1692501) (-1032 "RCAGG.spad" 1687706 1687717 1689768 1689773) (-1031 "RCAGG.spad" 1685561 1685574 1687625 1687630) (-1030 "RATRET.spad" 1684921 1684932 1685551 1685556) (-1029 "RATFACT.spad" 1684613 1684625 1684911 1684916) (-1028 "RANDSRC.spad" 1683932 1683941 1684603 1684608) (-1027 "RADUTIL.spad" 1683688 1683697 1683922 1683927) (-1026 "RADIX.spad" 1680512 1680526 1682058 1682151) (-1025 "RADFF.spad" 1678251 1678288 1678370 1678526) (-1024 "RADCAT.spad" 1677846 1677855 1678241 1678246) (-1023 "RADCAT.spad" 1677439 1677450 1677836 1677841) (-1022 "QUEUE.spad" 1676670 1676681 1676929 1676956) (-1021 "QUAT.spad" 1675158 1675169 1675501 1675566) (-1020 "QUATCT2.spad" 1674778 1674797 1675148 1675153) (-1019 "QUATCAT.spad" 1672948 1672959 1674708 1674773) (-1018 "QUATCAT.spad" 1670869 1670882 1672631 1672636) (-1017 "QUAGG.spad" 1669696 1669707 1670837 1670864) (-1016 "QQUTAST.spad" 1669464 1669473 1669686 1669691) (-1015 "QFORM.spad" 1669082 1669097 1669454 1669459) (-1014 "QFCAT.spad" 1667784 1667795 1668984 1669077) (-1013 "QFCAT.spad" 1666077 1666090 1667279 1667284) (-1012 "QFCAT2.spad" 1665769 1665786 1666067 1666072) (-1011 "QEQUAT.spad" 1665327 1665336 1665759 1665764) (-1010 "QCMPACK.spad" 1660073 1660093 1665317 1665322) (-1009 "QALGSET.spad" 1656151 1656184 1659987 1659992) (-1008 "QALGSET2.spad" 1654146 1654165 1656141 1656146) (-1007 "PWFFINTB.spad" 1651561 1651583 1654136 1654141) (-1006 "PUSHVAR.spad" 1650899 1650919 1651551 1651556) (-1005 "PTRANFN.spad" 1647026 1647037 1650889 1650894) (-1004 "PTPACK.spad" 1644113 1644124 1647016 1647021) (-1003 "PTFUNC2.spad" 1643935 1643950 1644103 1644108) (-1002 "PTCAT.spad" 1643189 1643200 1643903 1643930) (-1001 "PSQFR.spad" 1642495 1642520 1643179 1643184) (-1000 "PSEUDLIN.spad" 1641380 1641391 1642485 1642490) (-999 "PSETPK.spad" 1626813 1626829 1641258 1641263) (-998 "PSETCAT.spad" 1620733 1620756 1626793 1626808) (-997 "PSETCAT.spad" 1614627 1614652 1620689 1620694) (-996 "PSCURVE.spad" 1613610 1613618 1614617 1614622) (-995 "PSCAT.spad" 1612393 1612422 1613508 1613605) (-994 "PSCAT.spad" 1611266 1611297 1612383 1612388) (-993 "PRTITION.spad" 1609964 1609972 1611256 1611261) (-992 "PRTDAST.spad" 1609683 1609691 1609954 1609959) (-991 "PRS.spad" 1599245 1599262 1609639 1609644) (-990 "PRQAGG.spad" 1598680 1598690 1599213 1599240) (-989 "PROPLOG.spad" 1598252 1598260 1598670 1598675) (-988 "PROPFUN2.spad" 1597875 1597888 1598242 1598247) (-987 "PROPFUN1.spad" 1597273 1597284 1597865 1597870) (-986 "PROPFRML.spad" 1595841 1595852 1597263 1597268) (-985 "PROPERTY.spad" 1595329 1595337 1595831 1595836) (-984 "PRODUCT.spad" 1593011 1593023 1593295 1593350) (-983 "PR.spad" 1591403 1591415 1592102 1592229) (-982 "PRINT.spad" 1591155 1591163 1591393 1591398) (-981 "PRIMES.spad" 1589408 1589418 1591145 1591150) (-980 "PRIMELT.spad" 1587489 1587503 1589398 1589403) (-979 "PRIMCAT.spad" 1587116 1587124 1587479 1587484) (-978 "PRIMARR.spad" 1585968 1585978 1586146 1586173) (-977 "PRIMARR2.spad" 1584735 1584747 1585958 1585963) (-976 "PREASSOC.spad" 1584117 1584129 1584725 1584730) (-975 "PPCURVE.spad" 1583254 1583262 1584107 1584112) (-974 "PORTNUM.spad" 1583029 1583037 1583244 1583249) (-973 "POLYROOT.spad" 1581878 1581900 1582985 1582990) (-972 "POLY.spad" 1579213 1579223 1579728 1579855) (-971 "POLYLIFT.spad" 1578478 1578501 1579203 1579208) (-970 "POLYCATQ.spad" 1576596 1576618 1578468 1578473) (-969 "POLYCAT.spad" 1570066 1570087 1576464 1576591) (-968 "POLYCAT.spad" 1562874 1562897 1569274 1569279) (-967 "POLY2UP.spad" 1562326 1562340 1562864 1562869) (-966 "POLY2.spad" 1561923 1561935 1562316 1562321) (-965 "POLUTIL.spad" 1560864 1560893 1561879 1561884) (-964 "POLTOPOL.spad" 1559612 1559627 1560854 1560859) (-963 "POINT.spad" 1558297 1558307 1558384 1558411) (-962 "PNTHEORY.spad" 1554999 1555007 1558287 1558292) (-961 "PMTOOLS.spad" 1553774 1553788 1554989 1554994) (-960 "PMSYM.spad" 1553323 1553333 1553764 1553769) (-959 "PMQFCAT.spad" 1552914 1552928 1553313 1553318) (-958 "PMPRED.spad" 1552393 1552407 1552904 1552909) (-957 "PMPREDFS.spad" 1551847 1551869 1552383 1552388) (-956 "PMPLCAT.spad" 1550927 1550945 1551779 1551784) (-955 "PMLSAGG.spad" 1550512 1550526 1550917 1550922) (-954 "PMKERNEL.spad" 1550091 1550103 1550502 1550507) (-953 "PMINS.spad" 1549671 1549681 1550081 1550086) (-952 "PMFS.spad" 1549248 1549266 1549661 1549666) (-951 "PMDOWN.spad" 1548538 1548552 1549238 1549243) (-950 "PMASS.spad" 1547548 1547556 1548528 1548533) (-949 "PMASSFS.spad" 1546515 1546531 1547538 1547543) (-948 "PLOTTOOL.spad" 1546295 1546303 1546505 1546510) (-947 "PLOT.spad" 1541218 1541226 1546285 1546290) (-946 "PLOT3D.spad" 1537682 1537690 1541208 1541213) (-945 "PLOT1.spad" 1536839 1536849 1537672 1537677) (-944 "PLEQN.spad" 1524129 1524156 1536829 1536834) (-943 "PINTERP.spad" 1523751 1523770 1524119 1524124) (-942 "PINTERPA.spad" 1523535 1523551 1523741 1523746) (-941 "PI.spad" 1523144 1523152 1523509 1523530) (-940 "PID.spad" 1522114 1522122 1523070 1523139) (-939 "PICOERCE.spad" 1521771 1521781 1522104 1522109) (-938 "PGROEB.spad" 1520372 1520386 1521761 1521766) (-937 "PGE.spad" 1511989 1511997 1520362 1520367) (-936 "PGCD.spad" 1510879 1510896 1511979 1511984) (-935 "PFRPAC.spad" 1510028 1510038 1510869 1510874) (-934 "PFR.spad" 1506691 1506701 1509930 1510023) (-933 "PFOTOOLS.spad" 1505949 1505965 1506681 1506686) (-932 "PFOQ.spad" 1505319 1505337 1505939 1505944) (-931 "PFO.spad" 1504738 1504765 1505309 1505314) (-930 "PF.spad" 1504312 1504324 1504543 1504636) (-929 "PFECAT.spad" 1501994 1502002 1504238 1504307) (-928 "PFECAT.spad" 1499704 1499714 1501950 1501955) (-927 "PFBRU.spad" 1497592 1497604 1499694 1499699) (-926 "PFBR.spad" 1495152 1495175 1497582 1497587) (-925 "PERM.spad" 1490959 1490969 1494982 1494997) (-924 "PERMGRP.spad" 1485729 1485739 1490949 1490954) (-923 "PERMCAT.spad" 1484390 1484400 1485709 1485724) (-922 "PERMAN.spad" 1482922 1482936 1484380 1484385) (-921 "PENDTREE.spad" 1482146 1482156 1482434 1482439) (-920 "PDSPC.spad" 1480959 1480969 1482136 1482141) (-919 "PDSPC.spad" 1479770 1479782 1480949 1480954) (-918 "PDRING.spad" 1479612 1479622 1479750 1479765) (-917 "PDMOD.spad" 1479428 1479440 1479580 1479607) (-916 "PDEPROB.spad" 1478443 1478451 1479418 1479423) (-915 "PDEPACK.spad" 1472483 1472491 1478433 1478438) (-914 "PDECOMP.spad" 1471953 1471970 1472473 1472478) (-913 "PDECAT.spad" 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384565 384573 385019 385024) (-282 "E04NAFA.spad" 384142 384150 384555 384560) (-281 "E04MBFA.spad" 383722 383730 384132 384137) (-280 "E04JAFA.spad" 383258 383266 383712 383717) (-279 "E04GCFA.spad" 382794 382802 383248 383253) (-278 "E04FDFA.spad" 382330 382338 382784 382789) (-277 "E04DGFA.spad" 381866 381874 382320 382325) (-276 "E04AGNT.spad" 377716 377724 381856 381861) (-275 "DVARCAT.spad" 374606 374616 377706 377711) (-274 "DVARCAT.spad" 371494 371506 374596 374601) (-273 "DSMP.spad" 368868 368882 369173 369300) (-272 "DSEXT.spad" 368170 368180 368858 368863) (-271 "DSEXT.spad" 367379 367391 368069 368074) (-270 "DROPT.spad" 361338 361346 367369 367374) (-269 "DROPT1.spad" 361003 361013 361328 361333) (-268 "DROPT0.spad" 355860 355868 360993 360998) (-267 "DRAWPT.spad" 354033 354041 355850 355855) (-266 "DRAW.spad" 346909 346922 354023 354028) (-265 "DRAWHACK.spad" 346217 346227 346899 346904) (-264 "DRAWCX.spad" 343687 343695 346207 346212) (-263 "DRAWCURV.spad" 343234 343249 343677 343682) (-262 "DRAWCFUN.spad" 332766 332774 343224 343229) (-261 "DQAGG.spad" 330944 330954 332734 332761) (-260 "DPOLCAT.spad" 326293 326309 330812 330939) (-259 "DPOLCAT.spad" 321728 321746 326249 326254) (-258 "DPMO.spad" 313488 313504 313626 313839) (-257 "DPMM.spad" 305261 305279 305386 305599) (-256 "DOMTMPLT.spad" 305032 305040 305251 305256) (-255 "DOMCTOR.spad" 304787 304795 305022 305027) (-254 "DOMAIN.spad" 303874 303882 304777 304782) (-253 "DMP.spad" 301134 301149 301704 301831) (-252 "DMEXT.spad" 301001 301011 301102 301129) (-251 "DLP.spad" 300353 300363 300991 300996) (-250 "DLIST.spad" 298779 298789 299383 299410) (-249 "DLAGG.spad" 297196 297206 298769 298774) (-248 "DIVRING.spad" 296738 296746 297140 297191) (-247 "DIVRING.spad" 296324 296334 296728 296733) (-246 "DISPLAY.spad" 294514 294522 296314 296319) (-245 "DIRPROD.spad" 282061 282077 282701 282800) (-244 "DIRPROD2.spad" 280879 280897 282051 282056) (-243 "DIRPCAT.spad" 280072 280088 280775 280874) (-242 "DIRPCAT.spad" 278892 278910 279597 279602) (-241 "DIOSP.spad" 277717 277725 278882 278887) (-240 "DIOPS.spad" 276713 276723 277697 277712) (-239 "DIOPS.spad" 275683 275695 276669 276674) (-238 "DIFRING.spad" 275521 275529 275663 275678) (-237 "DIFFSPC.spad" 275100 275108 275511 275516) (-236 "DIFFSPC.spad" 274677 274687 275090 275095) (-235 "DIFFMOD.spad" 274166 274176 274645 274672) (-234 "DIFFDOM.spad" 273331 273342 274156 274161) (-233 "DIFFDOM.spad" 272494 272507 273321 273326) (-232 "DIFEXT.spad" 272313 272323 272474 272489) (-231 "DIAGG.spad" 271943 271953 272293 272308) (-230 "DIAGG.spad" 271581 271593 271933 271938) (-229 "DHMATRIX.spad" 269776 269786 270921 270948) (-228 "DFSFUN.spad" 263416 263424 269766 269771) (-227 "DFLOAT.spad" 260147 260155 263306 263411) (-226 "DFINTTLS.spad" 258378 258394 260137 260142) (-225 "DERHAM.spad" 256292 256324 258358 258373) (-224 "DEQUEUE.spad" 255499 255509 255782 255809) (-223 "DEGRED.spad" 255116 255130 255489 255494) (-222 "DEFINTRF.spad" 252653 252663 255106 255111) (-221 "DEFINTEF.spad" 251163 251179 252643 252648) (-220 "DEFAST.spad" 250531 250539 251153 251158) (-219 "DECIMAL.spad" 248540 248548 248901 248994) (-218 "DDFACT.spad" 246353 246370 248530 248535) (-217 "DBLRESP.spad" 245953 245977 246343 246348) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-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 2296249 2296254 2296259 2296264) (-2 NIL 2296229 2296234 2296239 2296244) (-1 NIL 2296209 2296214 2296219 2296224) (0 NIL 2296189 2296194 2296199 2296204) (-1321 "ZMOD.spad" 2295998 2296011 2296127 2296184) (-1320 "ZLINDEP.spad" 2295064 2295075 2295988 2295993) (-1319 "ZDSOLVE.spad" 2285009 2285031 2295054 2295059) (-1318 "YSTREAM.spad" 2284504 2284515 2284999 2285004) (-1317 "YDIAGRAM.spad" 2284138 2284147 2284494 2284499) (-1316 "XRPOLY.spad" 2283358 2283378 2283994 2284063) (-1315 "XPR.spad" 2281153 2281166 2283076 2283175) (-1314 "XPOLY.spad" 2280708 2280719 2281009 2281078) (-1313 "XPOLYC.spad" 2280027 2280043 2280634 2280703) (-1312 "XPBWPOLY.spad" 2278464 2278484 2279807 2279876) (-1311 "XF.spad" 2276927 2276942 2278366 2278459) (-1310 "XF.spad" 2275370 2275387 2276811 2276816) (-1309 "XFALG.spad" 2272418 2272434 2275296 2275365) (-1308 "XEXPPKG.spad" 2271669 2271695 2272408 2272413) (-1307 "XDPOLY.spad" 2271283 2271299 2271525 2271594) (-1306 "XALG.spad" 2270943 2270954 2271239 2271278) (-1305 "WUTSET.spad" 2266746 2266763 2270553 2270580) (-1304 "WP.spad" 2265945 2265989 2266604 2266671) (-1303 "WHILEAST.spad" 2265743 2265752 2265935 2265940) (-1302 "WHEREAST.spad" 2265414 2265423 2265733 2265738) (-1301 "WFFINTBS.spad" 2263077 2263099 2265404 2265409) (-1300 "WEIER.spad" 2261299 2261310 2263067 2263072) (-1299 "VSPACE.spad" 2260972 2260983 2261267 2261294) (-1298 "VSPACE.spad" 2260665 2260678 2260962 2260967) (-1297 "VOID.spad" 2260342 2260351 2260655 2260660) (-1296 "VIEW.spad" 2258022 2258031 2260332 2260337) (-1295 "VIEWDEF.spad" 2253223 2253232 2258012 2258017) (-1294 "VIEW3D.spad" 2237184 2237193 2253213 2253218) (-1293 "VIEW2D.spad" 2225075 2225084 2237174 2237179) (-1292 "VECTOR.spad" 2223596 2223607 2223847 2223874) (-1291 "VECTOR2.spad" 2222235 2222248 2223586 2223591) (-1290 "VECTCAT.spad" 2220139 2220150 2222203 2222230) (-1289 "VECTCAT.spad" 2217850 2217863 2219916 2219921) (-1288 "VARIABLE.spad" 2217630 2217645 2217840 2217845) (-1287 "UTYPE.spad" 2217274 2217283 2217620 2217625) (-1286 "UTSODETL.spad" 2216569 2216593 2217230 2217235) (-1285 "UTSODE.spad" 2214785 2214805 2216559 2216564) (-1284 "UTS.spad" 2209732 2209760 2213252 2213349) (-1283 "UTSCAT.spad" 2207211 2207227 2209630 2209727) (-1282 "UTSCAT.spad" 2204334 2204352 2206755 2206760) (-1281 "UTS2.spad" 2203929 2203964 2204324 2204329) (-1280 "URAGG.spad" 2198602 2198613 2203919 2203924) (-1279 "URAGG.spad" 2193239 2193252 2198558 2198563) (-1278 "UPXSSING.spad" 2190884 2190910 2192320 2192453) (-1277 "UPXS.spad" 2188180 2188208 2189016 2189165) (-1276 "UPXSCONS.spad" 2185939 2185959 2186312 2186461) (-1275 "UPXSCCA.spad" 2184510 2184530 2185785 2185934) (-1274 "UPXSCCA.spad" 2183223 2183245 2184500 2184505) (-1273 "UPXSCAT.spad" 2181812 2181828 2183069 2183218) (-1272 "UPXS2.spad" 2181355 2181408 2181802 2181807) (-1271 "UPSQFREE.spad" 2179769 2179783 2181345 2181350) (-1270 "UPSCAT.spad" 2177556 2177580 2179667 2179764) (-1269 "UPSCAT.spad" 2175049 2175075 2177162 2177167) (-1268 "UPOLYC.spad" 2170089 2170100 2174891 2175044) (-1267 "UPOLYC.spad" 2165021 2165034 2169825 2169830) (-1266 "UPOLYC2.spad" 2164492 2164511 2165011 2165016) (-1265 "UP.spad" 2161598 2161613 2161985 2162138) (-1264 "UPMP.spad" 2160498 2160511 2161588 2161593) (-1263 "UPDIVP.spad" 2160063 2160077 2160488 2160493) (-1262 "UPDECOMP.spad" 2158308 2158322 2160053 2160058) (-1261 "UPCDEN.spad" 2157517 2157533 2158298 2158303) (-1260 "UP2.spad" 2156881 2156902 2157507 2157512) (-1259 "UNISEG.spad" 2156234 2156245 2156800 2156805) (-1258 "UNISEG2.spad" 2155731 2155744 2156190 2156195) (-1257 "UNIFACT.spad" 2154834 2154846 2155721 2155726) (-1256 "ULS.spad" 2144618 2144646 2145563 2145992) (-1255 "ULSCONS.spad" 2135752 2135772 2136122 2136271) (-1254 "ULSCCAT.spad" 2133489 2133509 2135598 2135747) (-1253 "ULSCCAT.spad" 2131334 2131356 2133445 2133450) (-1252 "ULSCAT.spad" 2129566 2129582 2131180 2131329) (-1251 "ULS2.spad" 2129080 2129133 2129556 2129561) (-1250 "UINT8.spad" 2128957 2128966 2129070 2129075) (-1249 "UINT64.spad" 2128833 2128842 2128947 2128952) (-1248 "UINT32.spad" 2128709 2128718 2128823 2128828) (-1247 "UINT16.spad" 2128585 2128594 2128699 2128704) (-1246 "UFD.spad" 2127650 2127659 2128511 2128580) (-1245 "UFD.spad" 2126777 2126788 2127640 2127645) (-1244 "UDVO.spad" 2125658 2125667 2126767 2126772) (-1243 "UDPO.spad" 2123151 2123162 2125614 2125619) (-1242 "TYPE.spad" 2123083 2123092 2123141 2123146) (-1241 "TYPEAST.spad" 2123002 2123011 2123073 2123078) (-1240 "TWOFACT.spad" 2121654 2121669 2122992 2122997) (-1239 "TUPLE.spad" 2121140 2121151 2121553 2121558) (-1238 "TUBETOOL.spad" 2118007 2118016 2121130 2121135) (-1237 "TUBE.spad" 2116654 2116671 2117997 2118002) (-1236 "TS.spad" 2115253 2115269 2116219 2116316) (-1235 "TSETCAT.spad" 2102380 2102397 2115221 2115248) (-1234 "TSETCAT.spad" 2089493 2089512 2102336 2102341) (-1233 "TRMANIP.spad" 2083859 2083876 2089199 2089204) (-1232 "TRIMAT.spad" 2082822 2082847 2083849 2083854) (-1231 "TRIGMNIP.spad" 2081349 2081366 2082812 2082817) (-1230 "TRIGCAT.spad" 2080861 2080870 2081339 2081344) (-1229 "TRIGCAT.spad" 2080371 2080382 2080851 2080856) (-1228 "TREE.spad" 2078829 2078840 2079861 2079888) (-1227 "TRANFUN.spad" 2078668 2078677 2078819 2078824) (-1226 "TRANFUN.spad" 2078505 2078516 2078658 2078663) (-1225 "TOPSP.spad" 2078179 2078188 2078495 2078500) (-1224 "TOOLSIGN.spad" 2077842 2077853 2078169 2078174) (-1223 "TEXTFILE.spad" 2076403 2076412 2077832 2077837) (-1222 "TEX.spad" 2073549 2073558 2076393 2076398) (-1221 "TEX1.spad" 2073105 2073116 2073539 2073544) (-1220 "TEMUTL.spad" 2072660 2072669 2073095 2073100) (-1219 "TBCMPPK.spad" 2070753 2070776 2072650 2072655) (-1218 "TBAGG.spad" 2069803 2069826 2070733 2070748) (-1217 "TBAGG.spad" 2068861 2068886 2069793 2069798) (-1216 "TANEXP.spad" 2068269 2068280 2068851 2068856) (-1215 "TALGOP.spad" 2067993 2068004 2068259 2068264) (-1214 "TABLE.spad" 2065962 2065985 2066232 2066259) (-1213 "TABLEAU.spad" 2065443 2065454 2065952 2065957) (-1212 "TABLBUMP.spad" 2062246 2062257 2065433 2065438) (-1211 "SYSTEM.spad" 2061474 2061483 2062236 2062241) (-1210 "SYSSOLP.spad" 2058957 2058968 2061464 2061469) (-1209 "SYSPTR.spad" 2058856 2058865 2058947 2058952) (-1208 "SYSNNI.spad" 2058038 2058049 2058846 2058851) (-1207 "SYSINT.spad" 2057442 2057453 2058028 2058033) (-1206 "SYNTAX.spad" 2053648 2053657 2057432 2057437) (-1205 "SYMTAB.spad" 2051716 2051725 2053638 2053643) (-1204 "SYMS.spad" 2047739 2047748 2051706 2051711) (-1203 "SYMPOLY.spad" 2046746 2046757 2046828 2046955) (-1202 "SYMFUNC.spad" 2046247 2046258 2046736 2046741) (-1201 "SYMBOL.spad" 2043750 2043759 2046237 2046242) (-1200 "SWITCH.spad" 2040521 2040530 2043740 2043745) (-1199 "SUTS.spad" 2037569 2037597 2038988 2039085) (-1198 "SUPXS.spad" 2034852 2034880 2035701 2035850) (-1197 "SUP.spad" 2031572 2031583 2032345 2032498) (-1196 "SUPFRACF.spad" 2030677 2030695 2031562 2031567) (-1195 "SUP2.spad" 2030069 2030082 2030667 2030672) (-1194 "SUMRF.spad" 2029043 2029054 2030059 2030064) (-1193 "SUMFS.spad" 2028680 2028697 2029033 2029038) (-1192 "SULS.spad" 2018451 2018479 2019409 2019838) (-1191 "SUCHTAST.spad" 2018220 2018229 2018441 2018446) (-1190 "SUCH.spad" 2017902 2017917 2018210 2018215) (-1189 "SUBSPACE.spad" 2010017 2010032 2017892 2017897) (-1188 "SUBRESP.spad" 2009187 2009201 2009973 2009978) (-1187 "STTF.spad" 2005286 2005302 2009177 2009182) (-1186 "STTFNC.spad" 2001754 2001770 2005276 2005281) (-1185 "STTAYLOR.spad" 1994389 1994400 2001635 2001640) (-1184 "STRTBL.spad" 1992440 1992457 1992589 1992616) (-1183 "STRING.spad" 1991227 1991236 1991448 1991475) (-1182 "STREAM.spad" 1988028 1988039 1990635 1990650) (-1181 "STREAM3.spad" 1987601 1987616 1988018 1988023) (-1180 "STREAM2.spad" 1986729 1986742 1987591 1987596) (-1179 "STREAM1.spad" 1986435 1986446 1986719 1986724) (-1178 "STINPROD.spad" 1985371 1985387 1986425 1986430) (-1177 "STEP.spad" 1984572 1984581 1985361 1985366) (-1176 "STEPAST.spad" 1983806 1983815 1984562 1984567) (-1175 "STBL.spad" 1981890 1981918 1982057 1982072) (-1174 "STAGG.spad" 1980965 1980976 1981880 1981885) (-1173 "STAGG.spad" 1980038 1980051 1980955 1980960) (-1172 "STACK.spad" 1979278 1979289 1979528 1979555) (-1171 "SREGSET.spad" 1976946 1976963 1978888 1978915) (-1170 "SRDCMPK.spad" 1975507 1975527 1976936 1976941) (-1169 "SRAGG.spad" 1970650 1970659 1975475 1975502) (-1168 "SRAGG.spad" 1965813 1965824 1970640 1970645) (-1167 "SQMATRIX.spad" 1963356 1963374 1964272 1964359) (-1166 "SPLTREE.spad" 1957752 1957765 1962636 1962663) (-1165 "SPLNODE.spad" 1954340 1954353 1957742 1957747) (-1164 "SPFCAT.spad" 1953149 1953158 1954330 1954335) (-1163 "SPECOUT.spad" 1951701 1951710 1953139 1953144) (-1162 "SPADXPT.spad" 1943296 1943305 1951691 1951696) (-1161 "spad-parser.spad" 1942761 1942770 1943286 1943291) (-1160 "SPADAST.spad" 1942462 1942471 1942751 1942756) (-1159 "SPACEC.spad" 1926661 1926672 1942452 1942457) (-1158 "SPACE3.spad" 1926437 1926448 1926651 1926656) (-1157 "SORTPAK.spad" 1925986 1925999 1926393 1926398) (-1156 "SOLVETRA.spad" 1923749 1923760 1925976 1925981) (-1155 "SOLVESER.spad" 1922277 1922288 1923739 1923744) (-1154 "SOLVERAD.spad" 1918303 1918314 1922267 1922272) (-1153 "SOLVEFOR.spad" 1916765 1916783 1918293 1918298) (-1152 "SNTSCAT.spad" 1916365 1916382 1916733 1916760) (-1151 "SMTS.spad" 1914637 1914663 1915930 1916027) (-1150 "SMP.spad" 1912112 1912132 1912502 1912629) (-1149 "SMITH.spad" 1910957 1910982 1912102 1912107) (-1148 "SMATCAT.spad" 1909067 1909097 1910901 1910952) (-1147 "SMATCAT.spad" 1907109 1907141 1908945 1908950) (-1146 "SKAGG.spad" 1906072 1906083 1907077 1907104) (-1145 "SINT.spad" 1905012 1905021 1905938 1906067) (-1144 "SIMPAN.spad" 1904740 1904749 1905002 1905007) (-1143 "SIG.spad" 1904070 1904079 1904730 1904735) (-1142 "SIGNRF.spad" 1903188 1903199 1904060 1904065) (-1141 "SIGNEF.spad" 1902467 1902484 1903178 1903183) (-1140 "SIGAST.spad" 1901852 1901861 1902457 1902462) (-1139 "SHP.spad" 1899780 1899795 1901808 1901813) (-1138 "SHDP.spad" 1887458 1887485 1887967 1888066) (-1137 "SGROUP.spad" 1887066 1887075 1887448 1887453) (-1136 "SGROUP.spad" 1886672 1886683 1887056 1887061) (-1135 "SGCF.spad" 1879811 1879820 1886662 1886667) (-1134 "SFRTCAT.spad" 1878741 1878758 1879779 1879806) (-1133 "SFRGCD.spad" 1877804 1877824 1878731 1878736) (-1132 "SFQCMPK.spad" 1872441 1872461 1877794 1877799) (-1131 "SFORT.spad" 1871880 1871894 1872431 1872436) (-1130 "SEXOF.spad" 1871723 1871763 1871870 1871875) (-1129 "SEX.spad" 1871615 1871624 1871713 1871718) (-1128 "SEXCAT.spad" 1869387 1869427 1871605 1871610) (-1127 "SET.spad" 1867675 1867686 1868772 1868811) (-1126 "SETMN.spad" 1866125 1866142 1867665 1867670) (-1125 "SETCAT.spad" 1865610 1865619 1866115 1866120) (-1124 "SETCAT.spad" 1865093 1865104 1865600 1865605) (-1123 "SETAGG.spad" 1861642 1861653 1865073 1865088) (-1122 "SETAGG.spad" 1858199 1858212 1861632 1861637) (-1121 "SEQAST.spad" 1857902 1857911 1858189 1858194) (-1120 "SEGXCAT.spad" 1857058 1857071 1857892 1857897) (-1119 "SEG.spad" 1856871 1856882 1856977 1856982) (-1118 "SEGCAT.spad" 1855796 1855807 1856861 1856866) (-1117 "SEGBIND.spad" 1855554 1855565 1855743 1855748) (-1116 "SEGBIND2.spad" 1855252 1855265 1855544 1855549) (-1115 "SEGAST.spad" 1854966 1854975 1855242 1855247) (-1114 "SEG2.spad" 1854401 1854414 1854922 1854927) (-1113 "SDVAR.spad" 1853677 1853688 1854391 1854396) (-1112 "SDPOL.spad" 1851010 1851021 1851301 1851428) (-1111 "SCPKG.spad" 1849099 1849110 1851000 1851005) (-1110 "SCOPE.spad" 1848252 1848261 1849089 1849094) (-1109 "SCACHE.spad" 1846948 1846959 1848242 1848247) (-1108 "SASTCAT.spad" 1846857 1846866 1846938 1846943) (-1107 "SAOS.spad" 1846729 1846738 1846847 1846852) (-1106 "SAERFFC.spad" 1846442 1846462 1846719 1846724) (-1105 "SAE.spad" 1843912 1843928 1844523 1844658) (-1104 "SAEFACT.spad" 1843613 1843633 1843902 1843907) (-1103 "RURPK.spad" 1841272 1841288 1843603 1843608) (-1102 "RULESET.spad" 1840725 1840749 1841262 1841267) (-1101 "RULE.spad" 1838965 1838989 1840715 1840720) (-1100 "RULECOLD.spad" 1838817 1838830 1838955 1838960) (-1099 "RTVALUE.spad" 1838552 1838561 1838807 1838812) (-1098 "RSTRCAST.spad" 1838269 1838278 1838542 1838547) (-1097 "RSETGCD.spad" 1834647 1834667 1838259 1838264) (-1096 "RSETCAT.spad" 1824583 1824600 1834615 1834642) (-1095 "RSETCAT.spad" 1814539 1814558 1824573 1824578) (-1094 "RSDCMPK.spad" 1812991 1813011 1814529 1814534) (-1093 "RRCC.spad" 1811375 1811405 1812981 1812986) (-1092 "RRCC.spad" 1809757 1809789 1811365 1811370) (-1091 "RPTAST.spad" 1809459 1809468 1809747 1809752) (-1090 "RPOLCAT.spad" 1788819 1788834 1809327 1809454) (-1089 "RPOLCAT.spad" 1767892 1767909 1788402 1788407) (-1088 "ROUTINE.spad" 1763313 1763322 1766077 1766104) (-1087 "ROMAN.spad" 1762641 1762650 1763179 1763308) (-1086 "ROIRC.spad" 1761721 1761753 1762631 1762636) (-1085 "RNS.spad" 1760624 1760633 1761623 1761716) (-1084 "RNS.spad" 1759613 1759624 1760614 1760619) (-1083 "RNG.spad" 1759348 1759357 1759603 1759608) (-1082 "RNGBIND.spad" 1758508 1758522 1759303 1759308) (-1081 "RMODULE.spad" 1758273 1758284 1758498 1758503) (-1080 "RMCAT2.spad" 1757693 1757750 1758263 1758268) (-1079 "RMATRIX.spad" 1756481 1756500 1756824 1756863) (-1078 "RMATCAT.spad" 1752060 1752091 1756437 1756476) (-1077 "RMATCAT.spad" 1747529 1747562 1751908 1751913) (-1076 "RLINSET.spad" 1747233 1747244 1747519 1747524) (-1075 "RINTERP.spad" 1747121 1747141 1747223 1747228) (-1074 "RING.spad" 1746591 1746600 1747101 1747116) (-1073 "RING.spad" 1746069 1746080 1746581 1746586) (-1072 "RIDIST.spad" 1745461 1745470 1746059 1746064) (-1071 "RGCHAIN.spad" 1743989 1744005 1744891 1744918) (-1070 "RGBCSPC.spad" 1743770 1743782 1743979 1743984) (-1069 "RGBCMDL.spad" 1743300 1743312 1743760 1743765) (-1068 "RF.spad" 1740942 1740953 1743290 1743295) (-1067 "RFFACTOR.spad" 1740404 1740415 1740932 1740937) (-1066 "RFFACT.spad" 1740139 1740151 1740394 1740399) (-1065 "RFDIST.spad" 1739135 1739144 1740129 1740134) (-1064 "RETSOL.spad" 1738554 1738567 1739125 1739130) (-1063 "RETRACT.spad" 1737982 1737993 1738544 1738549) (-1062 "RETRACT.spad" 1737408 1737421 1737972 1737977) (-1061 "RETAST.spad" 1737220 1737229 1737398 1737403) (-1060 "RESULT.spad" 1734818 1734827 1735405 1735432) (-1059 "RESRING.spad" 1734165 1734212 1734756 1734813) (-1058 "RESLATC.spad" 1733489 1733500 1734155 1734160) (-1057 "REPSQ.spad" 1733220 1733231 1733479 1733484) (-1056 "REP.spad" 1730774 1730783 1733210 1733215) (-1055 "REPDB.spad" 1730481 1730492 1730764 1730769) (-1054 "REP2.spad" 1720139 1720150 1730323 1730328) (-1053 "REP1.spad" 1714335 1714346 1720089 1720094) (-1052 "REGSET.spad" 1712096 1712113 1713945 1713972) (-1051 "REF.spad" 1711431 1711442 1712051 1712056) (-1050 "REDORDER.spad" 1710637 1710654 1711421 1711426) (-1049 "RECLOS.spad" 1709420 1709440 1710124 1710217) (-1048 "REALSOLV.spad" 1708560 1708569 1709410 1709415) (-1047 "REAL.spad" 1708432 1708441 1708550 1708555) (-1046 "REAL0Q.spad" 1705730 1705745 1708422 1708427) (-1045 "REAL0.spad" 1702574 1702589 1705720 1705725) (-1044 "RDUCEAST.spad" 1702295 1702304 1702564 1702569) (-1043 "RDIV.spad" 1701950 1701975 1702285 1702290) (-1042 "RDIST.spad" 1701517 1701528 1701940 1701945) (-1041 "RDETRS.spad" 1700381 1700399 1701507 1701512) (-1040 "RDETR.spad" 1698520 1698538 1700371 1700376) (-1039 "RDEEFS.spad" 1697619 1697636 1698510 1698515) (-1038 "RDEEF.spad" 1696629 1696646 1697609 1697614) (-1037 "RCFIELD.spad" 1693815 1693824 1696531 1696624) (-1036 "RCFIELD.spad" 1691087 1691098 1693805 1693810) (-1035 "RCAGG.spad" 1689015 1689026 1691077 1691082) (-1034 "RCAGG.spad" 1686870 1686883 1688934 1688939) (-1033 "RATRET.spad" 1686230 1686241 1686860 1686865) (-1032 "RATFACT.spad" 1685922 1685934 1686220 1686225) (-1031 "RANDSRC.spad" 1685241 1685250 1685912 1685917) (-1030 "RADUTIL.spad" 1684997 1685006 1685231 1685236) (-1029 "RADIX.spad" 1681821 1681835 1683367 1683460) (-1028 "RADFF.spad" 1679560 1679597 1679679 1679835) (-1027 "RADCAT.spad" 1679155 1679164 1679550 1679555) (-1026 "RADCAT.spad" 1678748 1678759 1679145 1679150) (-1025 "QUEUE.spad" 1677979 1677990 1678238 1678265) (-1024 "QUAT.spad" 1676467 1676478 1676810 1676875) (-1023 "QUATCT2.spad" 1676087 1676106 1676457 1676462) (-1022 "QUATCAT.spad" 1674257 1674268 1676017 1676082) (-1021 "QUATCAT.spad" 1672178 1672191 1673940 1673945) (-1020 "QUAGG.spad" 1671005 1671016 1672146 1672173) (-1019 "QQUTAST.spad" 1670773 1670782 1670995 1671000) (-1018 "QFORM.spad" 1670391 1670406 1670763 1670768) (-1017 "QFCAT.spad" 1669093 1669104 1670293 1670386) (-1016 "QFCAT.spad" 1667386 1667399 1668588 1668593) (-1015 "QFCAT2.spad" 1667078 1667095 1667376 1667381) (-1014 "QEQUAT.spad" 1666636 1666645 1667068 1667073) (-1013 "QCMPACK.spad" 1661382 1661402 1666626 1666631) (-1012 "QALGSET.spad" 1657460 1657493 1661296 1661301) (-1011 "QALGSET2.spad" 1655455 1655474 1657450 1657455) (-1010 "PWFFINTB.spad" 1652870 1652892 1655445 1655450) (-1009 "PUSHVAR.spad" 1652208 1652228 1652860 1652865) (-1008 "PTRANFN.spad" 1648335 1648346 1652198 1652203) (-1007 "PTPACK.spad" 1645422 1645433 1648325 1648330) (-1006 "PTFUNC2.spad" 1645244 1645259 1645412 1645417) (-1005 "PTCAT.spad" 1644498 1644509 1645212 1645239) (-1004 "PSQFR.spad" 1643804 1643829 1644488 1644493) (-1003 "PSEUDLIN.spad" 1642689 1642700 1643794 1643799) (-1002 "PSETPK.spad" 1628121 1628138 1642567 1642572) (-1001 "PSETCAT.spad" 1622040 1622064 1628101 1628116) (-1000 "PSETCAT.spad" 1615933 1615959 1621996 1622001) (-999 "PSCURVE.spad" 1614916 1614924 1615923 1615928) (-998 "PSCAT.spad" 1613699 1613728 1614814 1614911) (-997 "PSCAT.spad" 1612572 1612603 1613689 1613694) (-996 "PRTITION.spad" 1611270 1611278 1612562 1612567) (-995 "PRTDAST.spad" 1610989 1610997 1611260 1611265) (-994 "PRS.spad" 1600551 1600568 1610945 1610950) (-993 "PRQAGG.spad" 1599986 1599996 1600519 1600546) (-992 "PROPLOG.spad" 1599558 1599566 1599976 1599981) (-991 "PROPFUN2.spad" 1599181 1599194 1599548 1599553) (-990 "PROPFUN1.spad" 1598579 1598590 1599171 1599176) (-989 "PROPFRML.spad" 1597147 1597158 1598569 1598574) (-988 "PROPERTY.spad" 1596635 1596643 1597137 1597142) (-987 "PRODUCT.spad" 1594317 1594329 1594601 1594656) (-986 "PR.spad" 1592709 1592721 1593408 1593535) (-985 "PRINT.spad" 1592461 1592469 1592699 1592704) (-984 "PRIMES.spad" 1590714 1590724 1592451 1592456) (-983 "PRIMELT.spad" 1588795 1588809 1590704 1590709) (-982 "PRIMCAT.spad" 1588422 1588430 1588785 1588790) (-981 "PRIMARR.spad" 1587274 1587284 1587452 1587479) (-980 "PRIMARR2.spad" 1586041 1586053 1587264 1587269) (-979 "PREASSOC.spad" 1585423 1585435 1586031 1586036) (-978 "PPCURVE.spad" 1584560 1584568 1585413 1585418) (-977 "PORTNUM.spad" 1584335 1584343 1584550 1584555) (-976 "POLYROOT.spad" 1583184 1583206 1584291 1584296) (-975 "POLY.spad" 1580519 1580529 1581034 1581161) (-974 "POLYLIFT.spad" 1579784 1579807 1580509 1580514) (-973 "POLYCATQ.spad" 1577902 1577924 1579774 1579779) (-972 "POLYCAT.spad" 1571372 1571393 1577770 1577897) (-971 "POLYCAT.spad" 1564180 1564203 1570580 1570585) (-970 "POLY2UP.spad" 1563632 1563646 1564170 1564175) (-969 "POLY2.spad" 1563229 1563241 1563622 1563627) (-968 "POLUTIL.spad" 1562170 1562199 1563185 1563190) (-967 "POLTOPOL.spad" 1560918 1560933 1562160 1562165) (-966 "POINT.spad" 1559603 1559613 1559690 1559717) (-965 "PNTHEORY.spad" 1556305 1556313 1559593 1559598) (-964 "PMTOOLS.spad" 1555080 1555094 1556295 1556300) (-963 "PMSYM.spad" 1554629 1554639 1555070 1555075) (-962 "PMQFCAT.spad" 1554220 1554234 1554619 1554624) (-961 "PMPRED.spad" 1553699 1553713 1554210 1554215) (-960 "PMPREDFS.spad" 1553153 1553175 1553689 1553694) (-959 "PMPLCAT.spad" 1552233 1552251 1553085 1553090) (-958 "PMLSAGG.spad" 1551818 1551832 1552223 1552228) (-957 "PMKERNEL.spad" 1551397 1551409 1551808 1551813) (-956 "PMINS.spad" 1550977 1550987 1551387 1551392) (-955 "PMFS.spad" 1550554 1550572 1550967 1550972) (-954 "PMDOWN.spad" 1549844 1549858 1550544 1550549) (-953 "PMASS.spad" 1548854 1548862 1549834 1549839) (-952 "PMASSFS.spad" 1547821 1547837 1548844 1548849) (-951 "PLOTTOOL.spad" 1547601 1547609 1547811 1547816) (-950 "PLOT.spad" 1542524 1542532 1547591 1547596) (-949 "PLOT3D.spad" 1538988 1538996 1542514 1542519) (-948 "PLOT1.spad" 1538145 1538155 1538978 1538983) (-947 "PLEQN.spad" 1525435 1525462 1538135 1538140) (-946 "PINTERP.spad" 1525057 1525076 1525425 1525430) (-945 "PINTERPA.spad" 1524841 1524857 1525047 1525052) (-944 "PI.spad" 1524450 1524458 1524815 1524836) (-943 "PID.spad" 1523420 1523428 1524376 1524445) (-942 "PICOERCE.spad" 1523077 1523087 1523410 1523415) (-941 "PGROEB.spad" 1521678 1521692 1523067 1523072) (-940 "PGE.spad" 1513295 1513303 1521668 1521673) (-939 "PGCD.spad" 1512185 1512202 1513285 1513290) (-938 "PFRPAC.spad" 1511334 1511344 1512175 1512180) (-937 "PFR.spad" 1507997 1508007 1511236 1511329) (-936 "PFOTOOLS.spad" 1507255 1507271 1507987 1507992) (-935 "PFOQ.spad" 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1471615 1471623 1473249 1473254) (-915 "PDDOM.spad" 1471053 1471066 1471605 1471610) (-914 "PDDOM.spad" 1470489 1470504 1471043 1471048) (-913 "PCOMP.spad" 1470342 1470355 1470479 1470484) (-912 "PBWLB.spad" 1468930 1468947 1470332 1470337) (-911 "PATTERN.spad" 1463469 1463479 1468920 1468925) (-910 "PATTERN2.spad" 1463207 1463219 1463459 1463464) (-909 "PATTERN1.spad" 1461543 1461559 1463197 1463202) (-908 "PATRES.spad" 1459118 1459130 1461533 1461538) (-907 "PATRES2.spad" 1458790 1458804 1459108 1459113) (-906 "PATMATCH.spad" 1456987 1457018 1458498 1458503) (-905 "PATMAB.spad" 1456416 1456426 1456977 1456982) (-904 "PATLRES.spad" 1455502 1455516 1456406 1456411) (-903 "PATAB.spad" 1455266 1455276 1455492 1455497) (-902 "PARTPERM.spad" 1453274 1453282 1455256 1455261) (-901 "PARSURF.spad" 1452708 1452736 1453264 1453269) (-900 "PARSU2.spad" 1452505 1452521 1452698 1452703) (-899 "script-parser.spad" 1452025 1452033 1452495 1452500) (-898 "PARSCURV.spad" 1451459 1451487 1452015 1452020) (-897 "PARSC2.spad" 1451250 1451266 1451449 1451454) (-896 "PARPCURV.spad" 1450712 1450740 1451240 1451245) (-895 "PARPC2.spad" 1450503 1450519 1450702 1450707) (-894 "PARAMAST.spad" 1449631 1449639 1450493 1450498) (-893 "PAN2EXPR.spad" 1449043 1449051 1449621 1449626) (-892 "PALETTE.spad" 1448013 1448021 1449033 1449038) (-891 "PAIR.spad" 1447000 1447013 1447601 1447606) (-890 "PADICRC.spad" 1444241 1444259 1445412 1445505) (-889 "PADICRAT.spad" 1442149 1442161 1442370 1442463) (-888 "PADIC.spad" 1441844 1441856 1442075 1442144) (-887 "PADICCT.spad" 1440393 1440405 1441770 1441839) (-886 "PADEPAC.spad" 1439082 1439101 1440383 1440388) (-885 "PADE.spad" 1437834 1437850 1439072 1439077) (-884 "OWP.spad" 1437074 1437104 1437692 1437759) (-883 "OVERSET.spad" 1436647 1436655 1437064 1437069) (-882 "OVAR.spad" 1436428 1436451 1436637 1436642) (-881 "OUT.spad" 1435514 1435522 1436418 1436423) (-880 "OUTFORM.spad" 1424906 1424914 1435504 1435509) (-879 "OUTBFILE.spad" 1424324 1424332 1424896 1424901) (-878 "OUTBCON.spad" 1423330 1423338 1424314 1424319) (-877 "OUTBCON.spad" 1422334 1422344 1423320 1423325) (-876 "OSI.spad" 1421809 1421817 1422324 1422329) (-875 "OSGROUP.spad" 1421727 1421735 1421799 1421804) (-874 "ORTHPOL.spad" 1420212 1420222 1421644 1421649) (-873 "OREUP.spad" 1419665 1419693 1419892 1419931) (-872 "ORESUP.spad" 1418966 1418990 1419345 1419384) (-871 "OREPCTO.spad" 1416823 1416835 1418886 1418891) (-870 "OREPCAT.spad" 1410970 1410980 1416779 1416818) (-869 "OREPCAT.spad" 1405007 1405019 1410818 1410823) (-868 "ORDTYPE.spad" 1404244 1404252 1404997 1405002) (-867 "ORDTYPE.spad" 1403479 1403489 1404234 1404239) (-866 "ORDSTRCT.spad" 1403252 1403267 1403415 1403420) (-865 "ORDSET.spad" 1402952 1402960 1403242 1403247) (-864 "ORDRING.spad" 1402342 1402350 1402932 1402947) (-863 "ORDRING.spad" 1401740 1401750 1402332 1402337) (-862 "ORDMON.spad" 1401595 1401603 1401730 1401735) (-861 "ORDFUNS.spad" 1400727 1400743 1401585 1401590) (-860 "ORDFIN.spad" 1400547 1400555 1400717 1400722) (-859 "ORDCOMP.spad" 1399012 1399022 1400094 1400123) (-858 "ORDCOMP2.spad" 1398305 1398317 1399002 1399007) (-857 "OPTPROB.spad" 1396943 1396951 1398295 1398300) (-856 "OPTPACK.spad" 1389352 1389360 1396933 1396938) (-855 "OPTCAT.spad" 1387031 1387039 1389342 1389347) (-854 "OPSIG.spad" 1386685 1386693 1387021 1387026) (-853 "OPQUERY.spad" 1386234 1386242 1386675 1386680) (-852 "OP.spad" 1385976 1385986 1386056 1386123) (-851 "OPERCAT.spad" 1385442 1385452 1385966 1385971) (-850 "OPERCAT.spad" 1384906 1384918 1385432 1385437) (-849 "ONECOMP.spad" 1383651 1383661 1384453 1384482) (-848 "ONECOMP2.spad" 1383075 1383087 1383641 1383646) (-847 "OMSERVER.spad" 1382081 1382089 1383065 1383070) (-846 "OMSAGG.spad" 1381869 1381879 1382037 1382076) (-845 "OMPKG.spad" 1380485 1380493 1381859 1381864) (-844 "OM.spad" 1379458 1379466 1380475 1380480) (-843 "OMLO.spad" 1378883 1378895 1379344 1379383) (-842 "OMEXPR.spad" 1378717 1378727 1378873 1378878) (-841 "OMERR.spad" 1378262 1378270 1378707 1378712) (-840 "OMERRK.spad" 1377296 1377304 1378252 1378257) (-839 "OMENC.spad" 1376640 1376648 1377286 1377291) (-838 "OMDEV.spad" 1370949 1370957 1376630 1376635) (-837 "OMCONN.spad" 1370358 1370366 1370939 1370944) (-836 "OINTDOM.spad" 1370121 1370129 1370284 1370353) (-835 "OFMONOID.spad" 1368244 1368254 1370077 1370082) (-834 "ODVAR.spad" 1367505 1367515 1368234 1368239) (-833 "ODR.spad" 1367149 1367175 1367317 1367466) (-832 "ODPOL.spad" 1364438 1364448 1364778 1364905) (-831 "ODP.spad" 1352252 1352272 1352625 1352724) (-830 "ODETOOLS.spad" 1350901 1350920 1352242 1352247) (-829 "ODESYS.spad" 1348595 1348612 1350891 1350896) (-828 "ODERTRIC.spad" 1344604 1344621 1348552 1348557) (-827 "ODERED.spad" 1344003 1344027 1344594 1344599) (-826 "ODERAT.spad" 1341618 1341635 1343993 1343998) (-825 "ODEPRRIC.spad" 1338655 1338677 1341608 1341613) (-824 "ODEPROB.spad" 1337912 1337920 1338645 1338650) (-823 "ODEPRIM.spad" 1335246 1335268 1337902 1337907) (-822 "ODEPAL.spad" 1334632 1334656 1335236 1335241) (-821 "ODEPACK.spad" 1321298 1321306 1334622 1334627) (-820 "ODEINT.spad" 1320733 1320749 1321288 1321293) (-819 "ODEIFTBL.spad" 1318128 1318136 1320723 1320728) (-818 "ODEEF.spad" 1313619 1313635 1318118 1318123) (-817 "ODECONST.spad" 1313156 1313174 1313609 1313614) (-816 "ODECAT.spad" 1311754 1311762 1313146 1313151) (-815 "OCT.spad" 1309890 1309900 1310604 1310643) (-814 "OCTCT2.spad" 1309536 1309557 1309880 1309885) (-813 "OC.spad" 1307332 1307342 1309492 1309531) (-812 "OC.spad" 1304853 1304865 1307015 1307020) (-811 "OCAMON.spad" 1304701 1304709 1304843 1304848) (-810 "OASGP.spad" 1304516 1304524 1304691 1304696) (-809 "OAMONS.spad" 1304038 1304046 1304506 1304511) (-808 "OAMON.spad" 1303899 1303907 1304028 1304033) (-807 "OAGROUP.spad" 1303761 1303769 1303889 1303894) (-806 "NUMTUBE.spad" 1303352 1303368 1303751 1303756) (-805 "NUMQUAD.spad" 1291328 1291336 1303342 1303347) (-804 "NUMODE.spad" 1282682 1282690 1291318 1291323) (-803 "NUMINT.spad" 1280248 1280256 1282672 1282677) (-802 "NUMFMT.spad" 1279088 1279096 1280238 1280243) (-801 "NUMERIC.spad" 1271202 1271212 1278893 1278898) (-800 "NTSCAT.spad" 1269710 1269726 1271170 1271197) (-799 "NTPOLFN.spad" 1269261 1269271 1269627 1269632) (-798 "NSUP.spad" 1262214 1262224 1266754 1266907) (-797 "NSUP2.spad" 1261606 1261618 1262204 1262209) (-796 "NSMP.spad" 1257836 1257855 1258144 1258271) (-795 "NREP.spad" 1256214 1256228 1257826 1257831) (-794 "NPCOEF.spad" 1255460 1255480 1256204 1256209) (-793 "NORMRETR.spad" 1255058 1255097 1255450 1255455) (-792 "NORMPK.spad" 1252960 1252979 1255048 1255053) (-791 "NORMMA.spad" 1252648 1252674 1252950 1252955) (-790 "NONE.spad" 1252389 1252397 1252638 1252643) (-789 "NONE1.spad" 1252065 1252075 1252379 1252384) (-788 "NODE1.spad" 1251552 1251568 1252055 1252060) (-787 "NNI.spad" 1250447 1250455 1251526 1251547) (-786 "NLINSOL.spad" 1249073 1249083 1250437 1250442) (-785 "NIPROB.spad" 1247614 1247622 1249063 1249068) (-784 "NFINTBAS.spad" 1245174 1245191 1247604 1247609) (-783 "NETCLT.spad" 1245148 1245159 1245164 1245169) (-782 "NCODIV.spad" 1243364 1243380 1245138 1245143) (-781 "NCNTFRAC.spad" 1243006 1243020 1243354 1243359) (-780 "NCEP.spad" 1241172 1241186 1242996 1243001) (-779 "NASRING.spad" 1240768 1240776 1241162 1241167) (-778 "NASRING.spad" 1240362 1240372 1240758 1240763) (-777 "NARNG.spad" 1239714 1239722 1240352 1240357) (-776 "NARNG.spad" 1239064 1239074 1239704 1239709) (-775 "NAGSP.spad" 1238141 1238149 1239054 1239059) (-774 "NAGS.spad" 1227802 1227810 1238131 1238136) (-773 "NAGF07.spad" 1226233 1226241 1227792 1227797) (-772 "NAGF04.spad" 1220635 1220643 1226223 1226228) (-771 "NAGF02.spad" 1214704 1214712 1220625 1220630) (-770 "NAGF01.spad" 1210465 1210473 1214694 1214699) (-769 "NAGE04.spad" 1204165 1204173 1210455 1210460) (-768 "NAGE02.spad" 1194825 1194833 1204155 1204160) (-767 "NAGE01.spad" 1190827 1190835 1194815 1194820) (-766 "NAGD03.spad" 1188831 1188839 1190817 1190822) (-765 "NAGD02.spad" 1181578 1181586 1188821 1188826) (-764 "NAGD01.spad" 1175871 1175879 1181568 1181573) (-763 "NAGC06.spad" 1171746 1171754 1175861 1175866) (-762 "NAGC05.spad" 1170247 1170255 1171736 1171741) (-761 "NAGC02.spad" 1169514 1169522 1170237 1170242) (-760 "NAALG.spad" 1169055 1169065 1169482 1169509) (-759 "NAALG.spad" 1168616 1168628 1169045 1169050) (-758 "MULTSQFR.spad" 1165574 1165591 1168606 1168611) (-757 "MULTFACT.spad" 1164957 1164974 1165564 1165569) (-756 "MTSCAT.spad" 1163051 1163072 1164855 1164952) (-755 "MTHING.spad" 1162710 1162720 1163041 1163046) (-754 "MSYSCMD.spad" 1162144 1162152 1162700 1162705) (-753 "MSET.spad" 1160066 1160076 1161814 1161853) (-752 "MSETAGG.spad" 1159911 1159921 1160034 1160061) (-751 "MRING.spad" 1156888 1156900 1159619 1159686) (-750 "MRF2.spad" 1156458 1156472 1156878 1156883) (-749 "MRATFAC.spad" 1156004 1156021 1156448 1156453) (-748 "MPRFF.spad" 1154044 1154063 1155994 1155999) (-747 "MPOLY.spad" 1151515 1151530 1151874 1152001) (-746 "MPCPF.spad" 1150779 1150798 1151505 1151510) (-745 "MPC3.spad" 1150596 1150636 1150769 1150774) (-744 "MPC2.spad" 1150242 1150275 1150586 1150591) (-743 "MONOTOOL.spad" 1148593 1148610 1150232 1150237) (-742 "MONOID.spad" 1147912 1147920 1148583 1148588) (-741 "MONOID.spad" 1147229 1147239 1147902 1147907) (-740 "MONOGEN.spad" 1145977 1145990 1147089 1147224) (-739 "MONOGEN.spad" 1144747 1144762 1145861 1145866) (-738 "MONADWU.spad" 1142777 1142785 1144737 1144742) (-737 "MONADWU.spad" 1140805 1140815 1142767 1142772) (-736 "MONAD.spad" 1139965 1139973 1140795 1140800) (-735 "MONAD.spad" 1139123 1139133 1139955 1139960) (-734 "MOEBIUS.spad" 1137859 1137873 1139103 1139118) (-733 "MODULE.spad" 1137729 1137739 1137827 1137854) (-732 "MODULE.spad" 1137619 1137631 1137719 1137724) (-731 "MODRING.spad" 1136954 1136993 1137599 1137614) (-730 "MODOP.spad" 1135619 1135631 1136776 1136843) (-729 "MODMONOM.spad" 1135350 1135368 1135609 1135614) (-728 "MODMON.spad" 1132052 1132068 1132771 1132924) (-727 "MODFIELD.spad" 1131414 1131453 1131954 1132047) (-726 "MMLFORM.spad" 1130274 1130282 1131404 1131409) (-725 "MMAP.spad" 1130016 1130050 1130264 1130269) (-724 "MLO.spad" 1128475 1128485 1129972 1130011) (-723 "MLIFT.spad" 1127087 1127104 1128465 1128470) (-722 "MKUCFUNC.spad" 1126622 1126640 1127077 1127082) (-721 "MKRECORD.spad" 1126226 1126239 1126612 1126617) (-720 "MKFUNC.spad" 1125633 1125643 1126216 1126221) (-719 "MKFLCFN.spad" 1124601 1124611 1125623 1125628) (-718 "MKBCFUNC.spad" 1124096 1124114 1124591 1124596) (-717 "MINT.spad" 1123535 1123543 1123998 1124091) (-716 "MHROWRED.spad" 1122046 1122056 1123525 1123530) (-715 "MFLOAT.spad" 1120566 1120574 1121936 1122041) (-714 "MFINFACT.spad" 1119966 1119988 1120556 1120561) (-713 "MESH.spad" 1117748 1117756 1119956 1119961) (-712 "MDDFACT.spad" 1115959 1115969 1117738 1117743) (-711 "MDAGG.spad" 1115250 1115260 1115939 1115954) (-710 "MCMPLX.spad" 1110681 1110689 1111295 1111496) (-709 "MCDEN.spad" 1109891 1109903 1110671 1110676) (-708 "MCALCFN.spad" 1107013 1107039 1109881 1109886) (-707 "MAYBE.spad" 1106297 1106308 1107003 1107008) (-706 "MATSTOR.spad" 1103605 1103615 1106287 1106292) (-705 "MATRIX.spad" 1102192 1102202 1102676 1102703) (-704 "MATLIN.spad" 1099536 1099560 1102076 1102081) (-703 "MATCAT.spad" 1091058 1091080 1099504 1099531) (-702 "MATCAT.spad" 1082452 1082476 1090900 1090905) (-701 "MATCAT2.spad" 1081734 1081782 1082442 1082447) (-700 "MAPPKG3.spad" 1080649 1080663 1081724 1081729) (-699 "MAPPKG2.spad" 1079987 1079999 1080639 1080644) (-698 "MAPPKG1.spad" 1078815 1078825 1079977 1079982) (-697 "MAPPAST.spad" 1078130 1078138 1078805 1078810) (-696 "MAPHACK3.spad" 1077942 1077956 1078120 1078125) (-695 "MAPHACK2.spad" 1077711 1077723 1077932 1077937) (-694 "MAPHACK1.spad" 1077355 1077365 1077701 1077706) (-693 "MAGMA.spad" 1075145 1075162 1077345 1077350) (-692 "MACROAST.spad" 1074724 1074732 1075135 1075140) (-691 "M3D.spad" 1072327 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"EXPR.spad" 469883 469893 470597 470892) (-326 "EXPR2UPS.spad" 466005 466018 469873 469878) (-325 "EXPR2.spad" 465710 465722 465995 466000) (-324 "EXPEXPAN.spad" 462511 462536 463143 463236) (-323 "EXIT.spad" 462182 462190 462501 462506) (-322 "EXITAST.spad" 461918 461926 462172 462177) (-321 "EVALCYC.spad" 461378 461392 461908 461913) (-320 "EVALAB.spad" 460950 460960 461368 461373) (-319 "EVALAB.spad" 460520 460532 460940 460945) (-318 "EUCDOM.spad" 458094 458102 460446 460515) (-317 "EUCDOM.spad" 455730 455740 458084 458089) (-316 "ESTOOLS.spad" 447576 447584 455720 455725) (-315 "ESTOOLS2.spad" 447179 447193 447566 447571) (-314 "ESTOOLS1.spad" 446864 446875 447169 447174) (-313 "ES.spad" 439679 439687 446854 446859) (-312 "ES.spad" 432400 432410 439577 439582) (-311 "ESCONT.spad" 429193 429201 432390 432395) (-310 "ESCONT1.spad" 428942 428954 429183 429188) (-309 "ES2.spad" 428447 428463 428932 428937) (-308 "ES1.spad" 428017 428033 428437 428442) (-307 "ERROR.spad" 425344 425352 428007 428012) (-306 "EQTBL.spad" 423374 423396 423583 423610) (-305 "EQ.spad" 418179 418189 420966 421078) (-304 "EQ2.spad" 417897 417909 418169 418174) (-303 "EP.spad" 414223 414233 417887 417892) (-302 "ENV.spad" 412901 412909 414213 414218) (-301 "ENTIRER.spad" 412569 412577 412845 412896) (-300 "EMR.spad" 411857 411898 412495 412564) (-299 "ELTAGG.spad" 410111 410130 411847 411852) (-298 "ELTAGG.spad" 408329 408350 410067 410072) (-297 "ELTAB.spad" 407804 407817 408319 408324) (-296 "ELFUTS.spad" 407191 407210 407794 407799) (-295 "ELEMFUN.spad" 406880 406888 407181 407186) (-294 "ELEMFUN.spad" 406567 406577 406870 406875) (-293 "ELAGG.spad" 404538 404548 406547 406562) (-292 "ELAGG.spad" 402446 402458 404457 404462) (-291 "ELABOR.spad" 401792 401800 402436 402441) (-290 "ELABEXPR.spad" 400724 400732 401782 401787) (-289 "EFUPXS.spad" 397500 397530 400680 400685) (-288 "EFULS.spad" 394336 394359 397456 397461) (-287 "EFSTRUC.spad" 392351 392367 394326 394331) (-286 "EF.spad" 387127 387143 392341 392346) (-285 "EAB.spad" 385403 385411 387117 387122) (-284 "E04UCFA.spad" 384939 384947 385393 385398) (-283 "E04NAFA.spad" 384516 384524 384929 384934) (-282 "E04MBFA.spad" 384096 384104 384506 384511) (-281 "E04JAFA.spad" 383632 383640 384086 384091) (-280 "E04GCFA.spad" 383168 383176 383622 383627) (-279 "E04FDFA.spad" 382704 382712 383158 383163) (-278 "E04DGFA.spad" 382240 382248 382694 382699) (-277 "E04AGNT.spad" 378090 378098 382230 382235) (-276 "DVARCAT.spad" 374980 374990 378080 378085) (-275 "DVARCAT.spad" 371868 371880 374970 374975) (-274 "DSMP.spad" 369242 369256 369547 369674) (-273 "DSEXT.spad" 368544 368554 369232 369237) (-272 "DSEXT.spad" 367753 367765 368443 368448) (-271 "DROPT.spad" 361712 361720 367743 367748) (-270 "DROPT1.spad" 361377 361387 361702 361707) (-269 "DROPT0.spad" 356234 356242 361367 361372) (-268 "DRAWPT.spad" 354407 354415 356224 356229) (-267 "DRAW.spad" 347283 347296 354397 354402) (-266 "DRAWHACK.spad" 346591 346601 347273 347278) (-265 "DRAWCX.spad" 344061 344069 346581 346586) (-264 "DRAWCURV.spad" 343608 343623 344051 344056) (-263 "DRAWCFUN.spad" 333140 333148 343598 343603) (-262 "DQAGG.spad" 331318 331328 333108 333135) (-261 "DPOLCAT.spad" 326667 326683 331186 331313) (-260 "DPOLCAT.spad" 322102 322120 326623 326628) (-259 "DPMO.spad" 313862 313878 314000 314213) (-258 "DPMM.spad" 305635 305653 305760 305973) (-257 "DOMTMPLT.spad" 305406 305414 305625 305630) (-256 "DOMCTOR.spad" 305161 305169 305396 305401) (-255 "DOMAIN.spad" 304248 304256 305151 305156) (-254 "DMP.spad" 301508 301523 302078 302205) (-253 "DMEXT.spad" 301375 301385 301476 301503) (-252 "DLP.spad" 300727 300737 301365 301370) (-251 "DLIST.spad" 299153 299163 299757 299784) (-250 "DLAGG.spad" 297570 297580 299143 299148) (-249 "DIVRING.spad" 297112 297120 297514 297565) (-248 "DIVRING.spad" 296698 296708 297102 297107) (-247 "DISPLAY.spad" 294888 294896 296688 296693) (-246 "DIRPROD.spad" 282435 282451 283075 283174) (-245 "DIRPROD2.spad" 281253 281271 282425 282430) (-244 "DIRPCAT.spad" 280446 280462 281149 281248) (-243 "DIRPCAT.spad" 279266 279284 279971 279976) (-242 "DIOSP.spad" 278091 278099 279256 279261) (-241 "DIOPS.spad" 277087 277097 278071 278086) (-240 "DIOPS.spad" 276057 276069 277043 277048) (-239 "DIFRING.spad" 275895 275903 276037 276052) (-238 "DIFFSPC.spad" 275474 275482 275885 275890) (-237 "DIFFSPC.spad" 275051 275061 275464 275469) (-236 "DIFFMOD.spad" 274540 274550 275019 275046) (-235 "DIFFDOM.spad" 273705 273716 274530 274535) (-234 "DIFFDOM.spad" 272868 272881 273695 273700) (-233 "DIFEXT.spad" 272687 272697 272848 272863) (-232 "DIAGG.spad" 272317 272327 272667 272682) (-231 "DIAGG.spad" 271955 271967 272307 272312) (-230 "DHMATRIX.spad" 270150 270160 271295 271322) (-229 "DFSFUN.spad" 263790 263798 270140 270145) (-228 "DFLOAT.spad" 260521 260529 263680 263785) (-227 "DFINTTLS.spad" 258752 258768 260511 260516) (-226 "DERHAM.spad" 256666 256698 258732 258747) (-225 "DEQUEUE.spad" 255873 255883 256156 256183) (-224 "DEGRED.spad" 255490 255504 255863 255868) (-223 "DEFINTRF.spad" 253027 253037 255480 255485) (-222 "DEFINTEF.spad" 251537 251553 253017 253022) (-221 "DEFAST.spad" 250905 250913 251527 251532) (-220 "DECIMAL.spad" 248914 248922 249275 249368) (-219 "DDFACT.spad" 246727 246744 248904 248909) (-218 "DBLRESP.spad" 246327 246351 246717 246722) (-217 "DBASIS.spad" 245953 245968 246317 246322) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-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
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 7f7190d7..c161147c 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,1158 +1,1162 @@
 
-(205224 . 3486967795)        
-(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))) ((#0=(-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) #0#) |has| (-2 (|:| -4291 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4291 |#1|) (|:| -4440 |#2|))))) 
-((((-576)) . T) (($) -2802 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1060 (-419 (-576))))) ((|#1|) . T)) 
+(205510 . 3487133936)        
+(((|#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((#0=(-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) #0#) |has| (-2 (|:| -4295 |#1|) (|:| -4444 |#2|)) (-320 (-2 (|:| -4295 |#1|) (|:| -4444 |#2|))))) 
+((((-577)) . T) (($) -2839 (|has| |#1| (-318)) (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-569))) (((-420 (-577))) -2839 (|has| |#1| (-375)) (|has| |#1| (-361)) (|has| |#1| (-1063 (-420 (-577))))) ((|#1|) . T)) 
 (((|#2| |#2|) . T)) 
-((((-576)) . T)) 
-((($ $) -2802 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-929))) ((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576))))) 
+((((-577)) . T)) 
+((($ $) -2839 (|has| |#2| (-174)) (|has| |#2| (-375)) (|has| |#2| (-465)) (|has| |#2| (-569)) (|has| |#2| (-932))) ((|#2| |#2|) . T) ((#0=(-420 (-577)) #0#) |has| |#2| (-38 (-420 (-577))))) 
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-300) 187283) ((-1208 . -1239) T) ((-1205 . -379) T) ((-1204 . -379) T) ((-1168 . -152) 187267) ((-1142 . -102) T) ((-1140 . -1122) T) ((-1102 . -23) T) ((-1102 . -1134) T) ((-1097 . -102) T) ((-1079 . -625) 187234) ((-1025 . -421) 187206) ((-947 . -975) T) ((-750 . -319) 187144) ((-75 . -1239) T) ((-677 . -393) 187116) ((-171 . -929) 187069) ((-30 . -975) T) ((-112 . -857) T) ((-1 . -625) 187051) ((-1021 . -912) 186972) ((-129 . -664) 186954) ((-50 . -632) 186938) ((-707 . -659) 186873) ((-607 . -918) 186786) ((-450 . -102) T) ((-129 . -384) 186768) ((-142 . -319) NIL) ((-887 . -1071) T) ((-846 . -862) 186747) ((-81 . -1239) T) ((-724 . -300) T) ((-40 . -1080) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 186729) ((-171 . -661) 186603) ((-519 . -625) 186585) ((-362 . -148) 186567) ((-362 . -146) T) ((-370 . -1134) T) ((-364 . -1134) T) ((-356 . -1134) T) ((-1026 . -317) T) ((-934 . -317) T) ((-887 . -248) T) ((-108 . -1134) T) ((-887 . -238) 186546) ((-1273 . -111) 186367) 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-113) T) ((-354 . -1122) T) ((-323 . -1174) NIL) ((-299 . -132) T) ((-406 . -1122) T) ((-885 . -1080) T) ((-707 . -381) 184492) ((-365 . -659) 184422) ((-225 . -632) 184399) ((-337 . -296) 184351) ((-486 . -111) 184172) ((-1273 . -1071) T) ((-1252 . -1071) T) ((-829 . -388) 184156) ((-837 . -1239) T) ((-171 . -739) T) ((-1304 . -1239) T) ((-667 . -102) T) ((-1273 . -248) 184135) ((-1273 . -238) 184087) ((-1252 . -238) 183992) ((-1252 . -248) 183971) ((-1025 . -414) NIL) ((-683 . -652) 183919) ((-326 . -38) 183829) ((-323 . -38) 183758) ((-69 . -625) 183740) ((-329 . -505) 183706) ((-48 . -659) 183656) ((-1211 . -298) 183635) ((-1247 . -862) T) ((-1135 . -1134) 183613) ((-83 . -1239) T) ((-61 . -625) 183595) ((-879 . -865) T) ((-491 . -298) 183574) ((-1304 . -1060) 183551) ((-1186 . -1122) T) ((-1135 . -23) 183403) ((-829 . -918) 183339) ((-1262 . -739) T) ((-1124 . -1239) T) ((-486 . -628) 183165) ((-362 . -237) T) ((-1109 . -300) 183096) ((-986 . -1122) T) ((-909 . -102) T) ((-795 . -300) 183007) ((-337 . -19) 182991) ((-59 . -298) 182968) ((-793 . -300) 182899) ((-870 . -739) T) ((-118 . -861) NIL) ((-528 . -298) 182876) ((-337 . -616) 182853) ((-508 . -298) 182830) ((-466 . -300) 182761) ((-1057 . -319) 182612) ((-891 . -502) 182593) ((-891 . -625) 182559) ((-694 . -502) 182540) ((-583 . -739) T) ((-689 . -502) 182521) ((-694 . -625) 182471) ((-689 . -625) 182437) ((-675 . -625) 182419) ((-490 . -502) 182400) ((-490 . -625) 182366) ((-250 . -626) 182327) ((-250 . -502) 182304) ((-139 . -502) 182285) ((-138 . -502) 182266) ((-134 . -502) 182247) ((-250 . -625) 182139) ((-215 . -102) T) ((-139 . -625) 182105) ((-138 . -625) 182071) ((-134 . -625) 182037) ((-1169 . -34) T) ((-963 . -1239) T) ((-354 . -730) 181982) ((-683 . -25) T) ((-683 . -21) T) ((-1198 . -628) 181963) ((-341 . -1239) T) ((-486 . -1071) T) ((-647 . -429) 181928) ((-619 . -429) 181893) ((-1142 . -1174) T) ((-1274 . -317) 181872) ((-725 . -1073) 181695) ((-593 . -300) T) ((-530 . -300) T) ((-1253 . -317) 181674) ((-486 . -238) 181626) ((-486 . -248) 181605) ((-451 . -1239) T) ((-725 . -653) 181434) ((-1253 . -1044) NIL) ((-1102 . -132) T) ((-887 . -808) 181413) ((-145 . -102) T) ((-40 . -1122) T) ((-887 . -805) 181392) ((-657 . -1032) 181376) ((-592 . -1080) T) ((-576 . -1080) T) ((-507 . -1080) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 181360) ((-323 . -412) 181321) ((-364 . -132) T) ((-356 . -132) T) ((-1203 . -1122) T) ((-1142 . -38) 181308) ((-1116 . -625) 181275) ((-108 . -132) T) ((-974 . -1122) T) ((-941 . -1122) T) ((-784 . -1122) T) ((-685 . -1122) T) ((-714 . -148) T) ((-117 . -148) T) ((-1311 . -21) T) ((-1311 . -25) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-677 . -1078) 181259) ((-543 . -862) T) ((-512 . -862) T) ((-376 . -1239) T) ((-366 . -1078) 181211) ((-363 . -1078) 181163) ((-355 . -1078) 181115) ((-258 . -1239) T) ((-257 . -1239) T) ((-273 . -1078) 180958) ((-253 . -1078) 180801) ((-677 . -111) 180780) ((-830 . -1243) 180759) ((-559 . -857) T) 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-234) 176926) ((-1233 . -1024) 176892) ((-1195 . -940) 176871) ((-1189 . -940) 176850) ((-1189 . -833) NIL) ((-1021 . -1073) 176746) ((-987 . -1239) T) ((-930 . -248) T) ((-830 . -374) 176725) ((-396 . -23) T) ((-128 . -1122) 176703) ((-122 . -1122) 176681) ((-930 . -238) T) ((-129 . -34) T) ((-390 . -661) 176646) ((-1021 . -653) 176594) ((-885 . -730) 176581) ((-1318 . -659) 176553) ((-1068 . -152) 176518) ((-1015 . -1239) T) ((-877 . -1239) T) ((-40 . -174) T) ((-707 . -423) 176500) ((-725 . -319) 176487) ((-849 . -661) 176447) ((-840 . -661) 176421) ((-329 . -25) T) ((-329 . -21) T) ((-671 . -296) 176400) ((-592 . -1122) T) ((-576 . -1122) T) ((-507 . -1122) T) ((-1194 . -1239) T) ((-250 . -298) 176377) ((-1147 . -1239) T) ((-869 . -1239) T) ((-323 . -272) 176338) ((-323 . -232) 176299) ((-1244 . -865) T) ((-1194 . -902) NIL) ((-55 . -1122) T) ((-1147 . -902) 176158) ((-130 . -862) T) ((-1194 . -1060) 176038) ((-1147 . -1060) 175921) ((-185 . -625) 175903) ((-869 . -1060) 175799) 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174059) ((-651 . -661) 174043) ((-219 . -1243) T) ((-419 . -912) 173964) ((-227 . -1060) 173924) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 173905) ((-370 . -25) T) ((-326 . -659) 173560) ((-323 . -659) 173474) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 173420) ((-250 . -628) 173397) ((-139 . -628) 173378) ((-138 . -628) 173359) ((-134 . -628) 173340) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1080) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1084 . -1239) T) ((-972 . -1239) T) ((-726 . -1239) T) ((-671 . -625) 173322) ((-493 . -1239) T) ((-750 . -749) 173306) ((-347 . -625) 173288) ((-68 . -394) T) ((-68 . -407) T) ((-1124 . -107) 173272) ((-1084 . -902) 173254) ((-972 . -902) 173179) ((-666 . -1134) T) ((-635 . -730) 173166) ((-493 . -902) NIL) ((-1168 . -102) T) ((-1116 . -630) 173150) ((-1084 . -1060) 173132) ((-97 . -625) 173114) ((-489 . -148) T) ((-972 . -1060) 172994) ((-118 . 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-1308) 171237) ((-886 . -1239) T) ((-714 . -464) T) ((-507 . -526) 171203) ((-1300 . -1239) T) ((-1299 . -1239) T) ((-499 . -374) T) ((-366 . -379) 171182) ((-363 . -379) 171161) ((-355 . -379) 171140) ((-727 . -739) T) ((-219 . -374) T) ((-117 . -464) T) ((-1312 . -1303) 171124) ((-886 . -900) 171101) ((-886 . -902) NIL) ((-984 . -862) 171000) ((-828 . -862) 170951) ((-1246 . -102) T) ((-667 . -669) 170935) ((-1225 . -34) T) ((-173 . -625) 170917) ((-1135 . -25) 170750) ((-1135 . -21) 170661) ((-886 . -1060) 170638) ((-972 . -918) 170619) ((-1262 . -47) 170596) ((-930 . -379) T) ((-605 . -865) T) ((-59 . -664) 170580) ((-528 . -664) 170564) ((-493 . -918) 170541) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -664) 170525) ((-59 . -384) 170509) ((-635 . -174) T) ((-528 . -384) 170493) ((-508 . -384) 170477) ((-558 . -1239) T) ((-840 . -721) 170461) ((-1194 . -317) 170440) ((-1200 . -132) T) ((-1164 . -1073) 170424) ((-118 . -174) T) ((-1164 . -653) 170356) ((-1168 . -319) 170294) ((-171 . -1239) T) ((-1301 . -132) T) ((-1274 . -940) 170273) ((-1253 . -940) 170252) ((-1253 . -833) NIL) ((-881 . -1073) 170222) ((-647 . -757) 170206) ((-619 . -757) 170190) ((-1252 . -929) 170143) ((-1046 . -1122) T) ((-925 . -1134) T) ((-881 . -653) 170113) ((-707 . -730) 170063) ((-916 . -1239) T) ((-886 . -388) 170040) ((-886 . -349) 170017) ((-854 . -1239) T) ((-821 . -1239) T) ((-171 . -900) 170001) ((-171 . -902) 169926) ((-782 . -1239) T) ((-690 . -1239) T) ((-1289 . -526) 169859) ((-1273 . -661) 169756) ((-1102 . -234) 169629) ((-499 . -1134) T) ((-365 . -1122) T) ((-219 . -1134) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1060) 169525) ((-304 . -912) 169482) ((-329 . -862) T) ((-1252 . -661) 169290) ((-887 . -807) 169269) ((-887 . -804) 169248) ((-887 . -739) T) ((-499 . -23) T) ((-370 . -234) 169221) ((-364 . -234) 169194) ((-356 . -234) 169167) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 169105) ((-86 . -407) T) ((-225 . -625) 169087) ((-108 . -234) 169074) ((-219 . -23) T) ((-1313 . -1306) 169053) ((-690 . -1060) 169037) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1262 . -1239) T) ((-137 . -482) 168992) ((-870 . -1239) T) ((-667 . -659) 168951) ((-48 . -1122) T) ((-725 . -272) 168935) ((-725 . -232) 168919) ((-886 . -918) NIL) ((-583 . -1239) T) ((-1262 . -902) NIL) ((-905 . -102) T) ((-901 . -102) T) ((-400 . -1122) T) ((-171 . -388) 168903) ((-171 . -349) 168887) ((-1262 . -1060) 168767) ((-870 . -1060) 168663) ((-1164 . -102) T) ((-1021 . -920) 168586) ((-675 . -805) 168565) ((-666 . -132) T) ((-675 . -808) 168544) ((-118 . -526) 168452) ((-583 . -1060) 168434) ((-304 . -1296) 168404) ((-1189 . -865) NIL) ((-881 . -102) T) ((-983 . -568) 168383) ((-1233 . -1078) 168266) ((-1025 . -1073) 168211) ((-494 . -652) 168117) ((-924 . -1122) T) ((-1046 . -730) 168054) ((-724 . -1078) 168019) ((-1025 . -653) 167964) ((-629 . -102) T) ((-614 . -34) T) ((-1169 . -1239) T) ((-1233 . -111) 167833) ((-486 . -661) 167730) ((-365 . -730) 167675) ((-171 . -918) 167634) ((-712 . -300) T) ((-707 . -174) T) ((-724 . -111) 167590) ((-1318 . -1080) T) ((-1262 . -388) 167574) ((-430 . -1243) 167552) ((-1140 . -625) 167534) ((-323 . -861) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1252 . -804) 167487) ((-1252 . -807) 167440) ((-1273 . -739) T) ((-1252 . -739) T) ((-48 . -730) 167405) ((-227 . -1044) T) ((-1275 . -423) 167371) ((-1262 . -918) 167314) ((-362 . -1296) 167291) ((-1233 . -628) 167173) ((-731 . -739) T) ((-343 . -625) 167155) ((-532 . -865) 167134) ((-1135 . -234) 167025) ((-112 . -625) 167007) ((-112 . -626) 166989) ((-731 . -485) T) ((-724 . -628) 166939) ((-1312 . -1073) 166923) ((-494 . -25) 166756) ((-128 . -501) 166740) ((-122 . -501) 166724) ((-494 . -21) 166635) ((-1312 . -653) 166605) ((-635 . -300) T) ((-598 . -1078) 166580) ((-449 . -1122) T) ((-1084 . -317) T) ((-118 . -300) T) ((-1126 . -102) T) ((-1025 . -102) T) ((-598 . -111) 166548) ((-1233 . -1071) T) ((-1164 . -319) 166486) ((-1084 . -1044) T) ((-1076 . -25) T) 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-929) 165735) ((-253 . -929) 165714) ((-795 . -1078) 165537) ((-793 . -1078) 165380) ((-620 . -1239) T) ((-1186 . -625) 165362) ((-1109 . -111) 165191) ((-1068 . -102) T) ((-487 . -1239) T) ((-473 . -1078) 165162) ((-466 . -1078) 165005) ((-677 . -661) 164989) ((-886 . -317) T) ((-795 . -111) 164798) ((-793 . -111) 164627) ((-366 . -661) 164579) ((-363 . -661) 164531) ((-355 . -661) 164483) ((-273 . -661) 164372) ((-253 . -661) 164261) ((-1180 . -862) T) ((-1110 . -1060) 164245) ((-1098 . -1060) 164222) ((-1026 . -865) T) ((-1022 . -34) T) ((-473 . -111) 164183) ((-466 . -111) 164012) ((-993 . -865) T) ((-986 . -625) 163994) ((-983 . -1134) T) ((-978 . -1239) T) ((-127 . -1032) 163978) ((-863 . -1239) T) ((-886 . -1044) NIL) ((-748 . -1134) T) ((-728 . -1134) T) ((-671 . -628) 163896) ((-1289 . -501) 163880) ((-1206 . -1239) T) ((-1205 . -1239) T) ((-1164 . -38) 163840) ((-983 . -23) T) ((-930 . -661) 163805) ((-880 . -1122) T) ((-856 . -102) T) ((-830 . -21) T) ((-647 . -1073) 163789) 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-800) T) ((-199 . -800) T) ((-198 . -800) T) ((-197 . -800) T) ((-196 . -800) T) ((-559 . -625) 160356) ((-507 . -1024) T) ((-283 . -852) T) ((-282 . -852) T) ((-281 . -852) T) ((-280 . -852) T) ((-48 . -300) T) ((-279 . -852) T) ((-278 . -852) T) ((-277 . -852) T) ((-195 . -800) T) ((-624 . -862) T) ((-667 . -423) 160340) ((-683 . -237) 160291) ((-225 . -628) 160253) ((-110 . -862) T) ((-666 . -21) T) ((-666 . -25) T) ((-1312 . -38) 160223) ((-118 . -296) 160174) ((-1289 . -19) 160158) ((-1253 . -865) NIL) ((-1289 . -616) 160135) ((-1302 . -1122) T) ((-362 . -1073) 160080) ((-1099 . -1122) T) ((-1009 . -1122) T) ((-983 . -132) T) ((-830 . -234) 160067) ((-750 . -1122) T) ((-362 . -653) 160012) ((-748 . -132) T) ((-728 . -132) T) ((-523 . -806) T) ((-523 . -807) T) ((-465 . -132) T) ((-419 . -1174) 159990) ((-225 . -1071) T) ((-304 . -102) 159772) ((-142 . -1122) T) ((-712 . -1024) T) ((-1127 . -296) 159728) ((-91 . -1239) T) ((-128 . -625) 159660) ((-122 . -625) 159592) ((-1318 . 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-174) T) ((-1212 . -625) 158104) ((-250 . -34) T) ((-354 . -628) 158034) ((-406 . -628) 158016) ((-946 . -996) T) ((-1225 . -1239) T) ((-675 . -804) 157995) ((-675 . -807) 157974) ((-410 . -407) T) ((-535 . -102) 157924) ((-1245 . -1239) T) ((-1057 . -1122) T) ((-419 . -920) 157847) ((-224 . -1017) 157831) ((-851 . -1239) T) ((-516 . -102) T) ((-635 . -625) 157813) ((-45 . -862) NIL) ((-635 . -626) 157790) ((-1057 . -622) 157765) ((-921 . -526) 157698) ((-329 . -237) 157650) ((-354 . -1071) T) ((-118 . -626) NIL) ((-118 . -625) 157632) ((-887 . -1239) T) ((-683 . -429) 157616) ((-683 . -1145) 157561) ((-512 . -152) 157543) ((-354 . -238) T) ((-354 . -248) T) ((-40 . -1078) 157488) ((-887 . -900) 157472) ((-887 . -902) 157397) ((-725 . -1080) T) ((-707 . -1024) NIL) ((-1273 . -47) 157367) ((-1252 . -47) 157344) ((-1163 . -1032) 157315) ((-1142 . -730) 157302) ((-3 . |UnionCategory|) T) ((-1127 . -625) 157284) ((-1102 . -148) 157263) ((-1102 . -146) 157214) ((-1026 . -374) T) ((-986 . -628) 157198) ((-227 . -940) T) ((-40 . -111) 157127) ((-887 . -1060) 156991) ((-1025 . -232) 156968) ((-1025 . -272) 156945) ((-714 . -1073) 156932) ((-934 . -374) T) ((-714 . -653) 156919) ((-329 . -1227) 156885) ((-390 . -317) T) ((-329 . -1224) 156851) ((-326 . -174) 156830) ((-323 . -174) T) ((-620 . -1215) 156806) ((-593 . -1308) 156793) ((-530 . -1308) 156770) ((-117 . -1073) 156757) ((-370 . -148) 156736) ((-370 . -146) 156687) ((-364 . -148) 156666) ((-364 . -146) 156617) ((-356 . -148) 156596) ((-117 . -653) 156583) ((-356 . -146) 156534) ((-329 . -35) 156500) ((-487 . -1215) 156479) ((0 . |EnumerationCategory|) T) ((-329 . -95) 156445) ((-390 . -1044) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -240) 156395) ((-667 . -1122) T) ((-620 . -107) 156342) ((-497 . -132) T) ((-487 . -107) 156292) ((-245 . -1134) 156270) ((-31 . -1239) T) ((-887 . -388) 156254) ((-887 . -349) 156238) ((-245 . -23) 156090) ((-40 . -628) 156020) ((-1302 . -526) 155953) ((-1084 . -940) T) ((-1084 . -833) T) ((-593 . -379) T) ((-530 . -379) T) ((-1281 . -568) 155932) ((-1274 . -1243) 155911) ((-1274 . -568) 155862) ((-1273 . -1239) T) ((-1253 . -1243) 155841) ((-362 . -1174) T) ((-337 . -34) T) ((-44 . -429) 155825) ((-1203 . -628) 155761) ((-888 . -1239) T) ((-402 . -757) 155745) ((-1253 . -568) 155696) ((-1252 . -1239) T) ((-1164 . -659) 155655) ((-744 . -132) T) ((-685 . -628) 155639) ((-1252 . -902) 155512) ((-1252 . -900) 155482) ((-1196 . -132) T) ((-1195 . -132) T) ((-1189 . -132) T) ((-1148 . -132) T) ((-321 . -1105) T) ((-1046 . -1024) T) ((-750 . -526) 155415) ((-1026 . -23) T) ((-1026 . -1134) T) ((-909 . -1122) T) ((-145 . -857) T) ((-1025 . -360) NIL) ((-704 . -625) 155397) ((-963 . -865) 155376) ((-535 . -319) 155314) ((-993 . -23) T) ((-142 . -526) NIL) ((-881 . -659) 155259) ((-934 . -1134) T) ((-934 . -23) T) ((-887 . -918) 155218) ((-362 . -38) 155183) ((-885 . -1078) 155170) ((-341 . -865) T) ((-82 . -625) 155152) ((-40 . -1071) T) ((-885 . -111) 155137) 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. -568) T) ((-972 . -568) 142148) ((-1194 . -23) T) ((-1173 . -1105) T) ((-1147 . -23) T) ((-869 . -23) T) ((-493 . -568) 142079) ((-1164 . -730) 142011) ((-683 . -1073) 141995) ((-1168 . -526) 141928) ((-683 . -653) 141912) ((-1057 . -626) NIL) ((-1057 . -625) 141894) ((-96 . -1105) T) ((-1318 . -1078) 141881) ((-881 . -730) 141851) ((-1318 . -111) 141836) ((-1233 . -47) 141805) ((-1189 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1126 . -1122) T) ((-1025 . -1122) T) ((-62 . -625) 141787) ((-1102 . -912) 141656) ((-1046 . -805) T) ((-1046 . -808) T) ((-1281 . -25) T) ((-1281 . -21) T) ((-1274 . -21) T) ((-1274 . -25) T) ((-885 . -661) 141643) ((-1253 . -21) T) ((-1253 . -25) T) ((-1049 . -152) 141627) ((-1026 . -234) 141614) ((-887 . -833) 141593) ((-887 . -940) T) ((-725 . -296) 141520) ((-608 . -21) T) ((-350 . -659) 141479) ((-108 . -912) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -659) 141396) ((-40 . -739) T) ((-224 . -526) 141329) ((-607 . -25) T) ((-488 . -152) 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123893) ((-1281 . -146) 123872) ((-1262 . -652) 123820) ((-1021 . -1071) T) ((-1126 . -625) 123802) ((-1025 . -625) 123784) ((-592 . -1239) T) ((-576 . -1239) T) ((-507 . -1239) T) ((-527 . -23) T) ((-522 . -23) T) ((-354 . -317) T) ((-520 . -23) T) ((-332 . -132) T) ((-3 . -1122) T) ((-1025 . -626) 123768) ((-1021 . -248) 123747) ((-1021 . -238) 123726) ((-1281 . -148) 123705) ((-1274 . -148) 123684) ((-846 . -1122) T) ((-1274 . -146) 123663) ((-1273 . -1243) 123642) ((-1253 . -146) 123549) ((-1253 . -148) 123456) ((-1252 . -1243) 123435) ((-390 . -132) T) ((-227 . -234) 123422) ((-176 . -174) T) ((-576 . -902) 123404) ((0 . -1122) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1239) T) ((-49 . -1122) T) ((-1275 . -661) 123309) ((-1273 . -568) 123260) ((-1252 . -568) 123211) ((-727 . -1134) T) ((-651 . -23) T) ((-576 . -1060) 123193) ((-607 . -148) 123172) ((-607 . -146) 123151) ((-507 . -1060) 123094) ((-1157 . -1159) T) ((-87 . -395) T) ((-87 . -407) T) ((-887 . -374) T) ((-849 . 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119186) ((-1253 . -35) 119152) ((-1252 . -1134) T) ((-605 . -152) 119134) ((-1102 . -360) 119113) ((-176 . -300) T) ((-118 . -388) 119090) ((-118 . -349) 119067) ((-171 . -234) 118992) ((-885 . -317) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-326 . -739) 118841) ((-323 . -739) T) ((-651 . -132) T) ((-486 . -374) 118820) ((-370 . -360) 118799) ((-364 . -360) 118778) ((-356 . -360) 118757) ((-326 . -485) 118736) ((-1273 . -23) T) ((-1252 . -23) T) ((-731 . -1134) T) ((-727 . -132) T) ((-666 . -102) T) ((-489 . -730) 118701) ((-675 . -865) 118680) ((-45 . -292) 118630) ((-105 . -1122) T) ((-68 . -625) 118612) ((-250 . -865) 118591) ((-992 . -102) T) ((-879 . -102) T) ((-635 . -918) 118550) ((-1313 . -1122) T) ((-392 . -1122) T) ((-1262 . -234) 118537) ((-1238 . -1122) T) ((-82 . -1239) T) ((-1135 . -272) 118506) ((-1084 . -862) T) ((-118 . -918) NIL) ((-795 . -940) 118485) ((-726 . -862) T) ((-543 . -1122) T) ((-512 . -1122) T) ((-366 . -1243) T) ((-363 . -1243) T) ((-355 . -1243) T) 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. -21) T) ((-519 . -25) T) ((-1189 . -38) 98848) ((-350 . -1071) T) ((-145 . -1239) T) ((-1102 . -174) T) ((-176 . -1071) T) ((-1148 . -38) 98745) ((-725 . -47) 98722) ((-370 . -174) T) ((-364 . -174) T) ((-531 . -57) 98696) ((-509 . -57) 98646) ((-362 . -1308) 98623) ((-227 . -464) T) ((-329 . -300) 98574) ((-356 . -174) T) ((-176 . -248) T) ((-1252 . -862) 98473) ((-108 . -174) T) ((-887 . -1014) 98457) ((-671 . -1134) T) ((-593 . -374) T) ((-593 . -339) 98444) ((-530 . -339) 98421) ((-530 . -374) T) ((-326 . -317) 98400) ((-323 . -317) T) ((-614 . -862) 98379) ((-1135 . -730) 98321) ((-532 . -292) 98305) ((-671 . -23) T) ((-430 . -232) 98289) ((-430 . -272) 98273) ((-323 . -1044) NIL) ((-347 . -23) T) ((-103 . -1032) 98257) ((-45 . -36) 98236) ((-624 . -1122) T) ((-362 . -379) T) ((-536 . -102) T) ((-507 . -27) T) ((-245 . -319) 98174) ((-1109 . -1134) T) ((-1312 . -661) 98148) ((-795 . -1134) T) ((-793 . -1134) T) ((-1200 . -423) 98132) ((-466 . -1134) T) ((-1084 . -464) T) ((-1173 . -1122) T) ((-972 . -464) 98083) ((-1137 . -1105) T) ((-110 . -1122) T) ((-1109 . -23) T) ((-1181 . -526) 97866) ((-830 . -1080) T) ((-795 . -23) T) ((-793 . -23) T) ((-493 . -464) 97817) ((-473 . -23) T) ((-392 . -393) 97796) ((-366 . -234) 97769) ((-363 . -234) 97742) ((-355 . -234) 97715) ((-466 . -23) T) ((-273 . -234) 97660) ((-258 . -912) 97527) ((-257 . -912) 97394) ((-96 . -1122) T) ((-725 . -1239) T) ((-683 . -296) 97371) ((-496 . -526) 97304) ((-1281 . -1073) 97187) ((-1281 . -653) 97084) ((-1274 . -653) 96925) ((-1274 . -1073) 96760) ((-1253 . -653) 96556) ((-1253 . -1073) 96346) ((-299 . -300) T) ((-1104 . -625) 96328) ((-559 . -865) T) ((-1104 . -626) 96309) ((-419 . -929) 96288) ((-1233 . -132) T) ((-50 . -1134) T) ((-1189 . -412) 96240) ((-1046 . -940) T) ((-1025 . -739) T) ((-856 . -661) 96213) ((-725 . -902) NIL) ((-608 . -1073) 96173) ((-593 . -1134) T) ((-530 . -1134) T) ((-607 . -1073) 96056) ((-1179 . -34) T) ((-1026 . -319) NIL) ((-828 . -501) 96040) ((-608 . 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\ No newline at end of file
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192544) ((-1256 . -1063) 192510) ((-1236 . -527) 192477) ((-1214 . -627) NIL) ((-528 . -629) 192461) ((-1214 . -626) 192443) ((-1167 . -1148) 192388) ((-1112 . -733) 192237) ((-494 . -932) 192216) ((-1102 . -102) T) ((-1087 . -664) 192188) ((-975 . -664) 192077) ((-834 . -868) T) ((-798 . -733) 191906) ((-610 . -503) 191887) ((-598 . -503) 191868) ((-610 . -626) 191834) ((-598 . -626) 191800) ((-549 . -626) 191782) ((-592 . -1242) T) ((-549 . -627) 191763) ((-796 . -733) 191612) ((-1071 . -1235) 191541) ((-636 . -662) 191513) ((-393 . -25) T) ((-393 . -21) T) ((-494 . -664) 191402) ((-474 . -733) 191373) ((-467 . -733) 191222) ((-1012 . -102) T) ((-924 . -320) 191160) ((-894 . -93) T) ((-753 . -102) T) ((-653 . -629) 191137) ((-118 . -662) 191067) ((-618 . -629) 191049) ((-730 . -629) 191003) ((-697 . -93) T) ((-544 . -25) T) ((-692 . -93) T) ((-680 . -626) 190985) ((-661 . -503) 190966) ((-661 . -626) 190919) ((-142 . -102) T) ((-44 . -132) T) ((-609 . -1242) T) ((-608 . -1242) T) ((-355 . -1083) T) ((-300 . -1137) T) ((-491 . -93) T) ((-420 . -238) 190870) ((-367 . -626) 190852) ((-364 . -626) 190834) ((-356 . -626) 190816) ((-274 . -627) 190564) ((-274 . -626) 190546) ((-254 . -626) 190528) ((-254 . -627) 190389) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1166 . -626) 190371) ((-1145 . -656) 190358) ((-1145 . -1076) 190345) ((-835 . -742) T) ((-835 . -875) T) ((-615 . -299) 190322) ((-594 . -733) 190287) ((-492 . -627) NIL) ((-492 . -626) 190269) ((-531 . -733) 190214) ((-327 . -102) T) ((-324 . -102) T) ((-300 . -23) T) ((-153 . -132) T) ((-933 . -626) 190196) ((-933 . -627) 190178) ((-399 . -742) T) ((-890 . -1081) 190130) ((-890 . -111) 190068) ((-730 . -1074) T) ((-728 . -1268) 190052) ((-710 . -361) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-532 . -626) 189984) ((-391 . -811) T) ((-169 . -1242) T) ((-226 . -1125) T) ((-391 . -808) T) ((-59 . -627) 189945) ((-228 . -810) T) ((-228 . -807) T) ((-59 . -626) 189857) ((-228 . -742) T) ((-529 . -627) 189818) ((-529 . -626) 189730) ((-510 . -626) 189662) ((-509 . -627) 189623) ((-509 . -626) 189535) ((-1105 . -375) 189486) ((-40 . -424) 189463) ((-77 . -1242) T) ((-889 . -932) NIL) ((-371 . -340) 189447) ((-371 . -375) T) ((-365 . -340) 189431) ((-365 . -375) T) ((-357 . -340) 189415) ((-357 . -375) T) ((-327 . -295) 189394) ((-108 . -375) T) ((-70 . -1242) T) ((-655 . -1125) T) ((-1256 . -350) 189346) ((-889 . -664) 189291) ((-1256 . -389) 189243) ((-987 . -132) 189098) ((-831 . -132) 188969) ((-45 . -868) NIL) ((-981 . -667) 188953) ((-1112 . -174) 188864) ((-981 . -385) 188848) ((-1087 . -810) T) ((-1087 . -807) T) ((-890 . -629) 188746) ((-798 . -174) 188637) ((-796 . -174) 188548) ((-832 . -47) 188510) ((-1087 . -742) T) ((-338 . -502) 188494) ((-975 . -742) T) ((-1305 . -320) 188432) ((-1284 . -921) 188345) ((-467 . -174) 188256) ((-251 . -297) 188208) ((-1277 . -921) 188114) ((-1276 . -1081) 187949) ((-1256 . -921) 187782) ((-494 . -742) T) ((-1255 . -1081) 187590) ((-1236 . -301) 187569) ((-1211 . -1242) T) ((-1208 . -380) T) ((-1207 . -380) T) ((-1171 . -152) 187553) ((-1145 . -102) T) ((-1143 . -1125) T) ((-1105 . -23) T) ((-1105 . -1137) T) ((-1100 . -102) T) ((-1082 . -626) 187520) ((-1028 . -422) 187492) ((-950 . -978) T) ((-753 . -320) 187430) ((-75 . -1242) T) ((-680 . -394) 187402) ((-171 . -932) 187355) ((-30 . -978) T) ((-112 . -860) T) ((-1 . -626) 187337) ((-1024 . -915) 187258) ((-129 . -667) 187240) ((-50 . -633) 187224) ((-710 . -662) 187159) ((-608 . -921) 187072) ((-451 . -102) T) ((-129 . -385) 187054) ((-142 . -320) NIL) ((-890 . -1074) T) ((-849 . -865) 187033) ((-81 . -1242) T) ((-727 . -301) T) ((-40 . -1083) T) ((-594 . -174) T) ((-531 . -174) T) ((-524 . -626) 187015) ((-171 . -664) 186889) ((-520 . -626) 186871) ((-363 . -148) 186853) ((-363 . -146) T) ((-371 . -1137) T) ((-365 . -1137) T) ((-357 . -1137) T) ((-1029 . -318) T) ((-937 . -318) T) ((-890 . -249) T) ((-108 . -1137) T) ((-890 . -239) 186832) ((-1276 . -111) 186653) ((-1255 . -111) 186442) ((-251 . -1280) 186426) ((-577 . -864) T) ((-371 . -23) T) ((-366 . -361) T) ((-327 . -320) 186413) ((-324 . -320) 186354) ((-365 . -23) T) ((-330 . -132) T) ((-357 . -23) T) ((-1029 . -1047) T) ((-31 . -629) 186335) ((-108 . -23) T) ((-670 . -1076) 186319) ((-251 . -617) 186296) ((-655 . -733) 186280) ((-344 . -1125) T) ((-670 . -656) 186250) ((-1278 . -38) 186142) ((-1265 . -932) 186121) ((-112 . -1125) T) ((-832 . -1242) T) ((-426 . -1242) T) ((-1060 . -102) T) ((-1265 . -664) 186010) ((-889 . -810) NIL) ((-873 . -664) 185984) ((-889 . -807) NIL) ((-832 . -905) NIL) ((-889 . -742) T) ((-1112 . -527) 185857) ((-798 . -527) 185804) ((-796 . -527) 185756) ((-584 . -664) 185743) ((-832 . -1063) 185571) ((-467 . -527) 185514) ((-401 . -402) T) ((-1276 . -629) 185327) ((-1255 . -629) 185075) ((-60 . -1242) T) ((-634 . -865) 185054) ((-513 . -677) T) ((-1171 . -1001) 185023) ((-1049 . -662) 184960) ((-1028 . -465) T) ((-715 . -864) T) ((-523 . -808) T) ((-487 . -1081) 184795) ((-513 . -113) T) ((-355 . -1125) T) ((-324 . -1177) NIL) ((-300 . -132) T) ((-407 . -1125) T) ((-888 . -1083) T) ((-710 . -382) 184762) ((-366 . -662) 184692) ((-226 . -633) 184669) ((-338 . -297) 184621) ((-487 . -111) 184442) ((-1276 . -1074) T) ((-1255 . -1074) T) ((-832 . -389) 184426) ((-840 . -1242) T) ((-171 . -742) T) ((-1307 . -1242) T) ((-670 . -102) T) ((-1276 . -249) 184405) ((-1276 . -239) 184357) ((-1255 . -239) 184262) ((-1255 . -249) 184241) ((-1028 . -415) NIL) ((-686 . -654) 184189) ((-327 . -38) 184099) ((-324 . -38) 184028) ((-69 . -626) 184010) ((-330 . -506) 183976) ((-48 . -662) 183926) ((-1214 . -299) 183905) ((-1250 . -865) T) ((-1138 . -1137) 183883) ((-83 . -1242) T) ((-61 . -626) 183865) ((-882 . -868) T) ((-492 . -299) 183844) ((-1307 . -1063) 183821) ((-1189 . -1125) T) ((-1138 . -23) 183673) ((-832 . -921) 183609) ((-1265 . -742) T) ((-1127 . -1242) T) ((-487 . -629) 183435) ((-363 . -238) T) ((-1112 . -301) 183366) ((-989 . -1125) T) ((-912 . -102) T) ((-798 . -301) 183277) ((-338 . -19) 183261) ((-59 . -299) 183238) ((-796 . -301) 183169) ((-873 . -742) T) ((-118 . -864) NIL) ((-529 . -299) 183146) ((-338 . -617) 183123) ((-509 . -299) 183100) ((-467 . -301) 183031) ((-1060 . -320) 182882) ((-894 . -503) 182863) ((-894 . -626) 182829) ((-697 . -503) 182810) ((-584 . -742) T) ((-692 . -503) 182791) ((-697 . -626) 182741) ((-692 . -626) 182707) ((-678 . -626) 182689) ((-491 . -503) 182670) ((-491 . -626) 182636) ((-251 . -627) 182597) ((-251 . -503) 182574) ((-139 . -503) 182555) ((-138 . -503) 182536) ((-134 . -503) 182517) ((-251 . -626) 182409) ((-215 . -102) T) ((-139 . -626) 182375) ((-138 . -626) 182341) ((-134 . -626) 182307) ((-1172 . -34) T) ((-966 . -1242) T) ((-355 . -733) 182252) ((-686 . -25) T) ((-686 . -21) T) ((-1201 . -629) 182233) ((-342 . -1242) T) ((-487 . -1074) T) ((-648 . -430) 182198) ((-620 . -430) 182163) ((-1145 . -1177) T) ((-1277 . -318) 182142) ((-728 . -1076) 181965) ((-594 . -301) T) ((-531 . -301) T) ((-1256 . -318) 181944) ((-487 . -239) 181896) ((-487 . -249) 181875) ((-452 . -1242) T) ((-728 . -656) 181704) ((-1256 . -1047) NIL) ((-1105 . -132) T) ((-890 . -811) 181683) ((-145 . -102) T) ((-40 . -1125) T) ((-890 . -808) 181662) ((-660 . -1035) 181646) ((-593 . -1083) T) ((-577 . -1083) T) ((-508 . -1083) T) ((-420 . -465) T) ((-371 . -132) T) ((-327 . -413) 181630) ((-324 . -413) 181591) ((-365 . -132) T) ((-357 . -132) T) ((-1206 . -1125) T) ((-1145 . -38) 181578) ((-1119 . -626) 181545) ((-108 . -132) T) ((-977 . -1125) T) ((-944 . -1125) T) ((-787 . -1125) T) ((-688 . -1125) T) ((-717 . -148) T) ((-117 . -148) T) ((-1314 . -21) T) ((-1314 . -25) T) ((-1312 . -21) T) ((-1312 . -25) T) ((-680 . -1081) 181529) ((-544 . -865) T) ((-513 . -865) T) ((-377 . -1242) T) ((-367 . -1081) 181481) ((-364 . -1081) 181433) ((-356 . -1081) 181385) ((-259 . -1242) T) ((-258 . -1242) T) ((-274 . -1081) 181228) ((-254 . -1081) 181071) ((-680 . -111) 181050) ((-833 . -1246) 181029) ((-560 . -860) T) ((-327 . -923) 180995) ((-367 . -111) 180933) ((-364 . -111) 180871) ((-356 . -111) 180809) ((-274 . -111) 180638) ((-254 . -111) 180467) ((-324 . -923) NIL) ((-636 . -424) 180451) ((-44 . -21) T) ((-44 . -25) T) ((-928 . -868) 180402) ((-831 . -654) 180308) ((-833 . -569) 180287) ((-500 . -868) T) ((-259 . -1063) 180114) ((-258 . -1063) 179941) ((-127 . -120) 179925) ((-220 . -868) T) ((-933 . -1081) 179890) ((-728 . -102) T) ((-715 . -1083) T) ((-610 . -629) 179871) ((-598 . -629) 179852) ((-549 . -631) 179755) ((-355 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -626) 179737) ((-933 . -111) 179693) ((-40 . -733) 179638) ((-888 . -1125) T) ((-680 . -629) 179615) ((-661 . -629) 179596) ((-367 . -629) 179533) ((-364 . -629) 179470) ((-356 . -629) 179407) ((-560 . -1125) T) ((-338 . -627) 179368) ((-338 . -626) 179280) ((-274 . -629) 179033) ((-254 . -629) 178818) ((-188 . -1242) T) ((-1255 . -808) 178771) ((-1255 . -811) 178724) ((-259 . -389) 178693) ((-258 . -389) 178662) ((-562 . -868) T) ((-670 . -38) 178632) ((-621 . -34) T) ((-495 . -1137) 178610) ((-488 . -34) T) ((-1138 . -132) 178481) ((-987 . -25) 178292) ((-933 . -629) 178242) ((-892 . -626) 178224) ((-217 . -860) T) ((-987 . -21) 178179) ((-831 . -25) 178012) ((-831 . -21) 177923) ((-1248 . -380) T) ((-636 . -1083) T) ((-1203 . -569) 177902) ((-1197 . -47) 177879) ((-367 . -1074) T) ((-364 . -1074) T) ((-495 . -23) 177731) ((-356 . -1074) T) ((-274 . -1074) T) ((-254 . -1074) T) ((-1150 . -47) 177703) ((-118 . -1083) T) ((-1059 . -664) 177677) ((-981 . -34) T) ((-367 . -239) 177656) ((-367 . -249) T) ((-364 . -239) 177635) ((-364 . -249) T) ((-356 . -239) 177614) ((-356 . -249) T) ((-274 . -337) 177586) ((-254 . -337) 177543) ((-274 . -239) 177522) ((-1182 . -152) 177506) ((-259 . -921) 177438) ((-258 . -921) 177370) ((-1167 . -915) 177291) ((-1107 . -865) T) ((-1259 . -1242) 177269) ((-427 . -1137) T) ((-1236 . -1027) 177235) ((-1079 . -23) T) ((-1049 . -864) T) ((-933 . -1074) T) ((-333 . -664) 177217) ((-717 . -238) T) ((-686 . -235) 177162) ((-1198 . -943) 177141) ((-1192 . -943) 177120) ((-1192 . -836) NIL) ((-1024 . -1076) 177016) ((-990 . -1242) T) ((-933 . -249) T) ((-833 . -375) 176995) ((-217 . -1125) T) ((-397 . -23) T) ((-128 . -1125) 176973) ((-122 . -1125) 176951) ((-933 . -239) T) ((-129 . -34) T) ((-391 . -664) 176916) ((-1024 . -656) 176864) ((-888 . -733) 176851) ((-1321 . -662) 176823) ((-1071 . -152) 176788) ((-1018 . -1242) T) ((-880 . -1242) T) ((-40 . -174) T) ((-710 . -424) 176770) ((-728 . -320) 176757) ((-852 . -664) 176717) ((-843 . -664) 176691) ((-330 . -25) T) ((-330 . -21) T) ((-674 . -297) 176670) ((-593 . -1125) T) ((-577 . -1125) T) ((-508 . -1125) T) ((-1197 . -1242) T) ((-251 . -299) 176647) ((-1150 . -1242) T) ((-872 . -1242) T) ((-324 . -273) 176608) ((-324 . -233) 176569) ((-1247 . -868) T) ((-1197 . -905) NIL) ((-55 . -1125) T) ((-1150 . -905) 176428) ((-130 . -865) T) ((-1197 . -1063) 176308) ((-1150 . -1063) 176191) ((-185 . -626) 176173) ((-872 . -1063) 176069) ((-798 . -297) 175996) ((-833 . -1137) T) ((-1059 . -742) T) ((-1071 . -1001) 175925) ((-615 . -667) 175909) ((-1028 . -915) 175816) ((-1024 . -102) T) ((-833 . -23) T) ((-728 . -1177) 175794) ((-710 . -1083) T) ((-615 . -385) 175778) ((-363 . -465) T) ((-355 . -301) T) ((-1293 . -1125) T) ((-255 . -1125) T) ((-412 . -102) T) ((-300 . -21) T) ((-300 . -25) T) ((-373 . -742) T) ((-726 . -1125) T) ((-715 . -1125) T) ((-373 . -486) T) ((-1236 . -626) 175760) ((-1197 . -389) 175744) ((-1150 . -389) 175728) ((-1049 . -424) 175690) ((-142 . -232) 175672) ((-391 . -810) T) ((-391 . -807) T) ((-888 . -174) T) ((-391 . -742) T) ((-727 . -626) 175654) ((-728 . -38) 175483) ((-1292 . -1290) 175467) ((-363 . -415) T) ((-1292 . -1125) 175417) ((-1215 . -1125) T) ((-593 . -733) 175404) ((-577 . -733) 175391) ((-508 . -733) 175356) ((-1278 . -662) 175246) ((-327 . -642) 175225) ((-852 . -742) T) ((-843 . -742) T) ((-1140 . -1242) T) ((-660 . -1242) T) ((-1105 . -654) 175173) ((-1197 . -921) 175116) ((-1150 . -921) 175100) ((-831 . -235) 174991) ((-678 . -1081) 174975) ((-108 . -654) 174957) ((-495 . -132) 174828) ((-1203 . -1137) T) ((-835 . -1242) T) ((-975 . -47) 174797) ((-636 . -1125) T) ((-678 . -111) 174776) ((-504 . -626) 174742) ((-338 . -299) 174719) ((-399 . -1242) T) ((-335 . -1242) T) ((-494 . -47) 174676) ((-1203 . -23) T) ((-118 . -1125) T) ((-103 . -102) 174626) ((-1304 . -1137) T) ((-561 . -865) T) ((-228 . -1242) T) ((-1079 . -132) T) ((-1049 . -1083) T) ((-1304 . -23) T) ((-1222 . -626) 174608) ((-835 . -1063) 174592) ((-1145 . -844) T) ((-1028 . -740) 174564) ((-1130 . -1125) T) ((-715 . -733) 174529) ((-599 . -626) 174511) ((-399 . -1063) 174495) ((-366 . -1083) T) ((-397 . -132) T) ((-335 . -1063) 174479) ((-1105 . -21) T) ((-1105 . -25) T) ((-1029 . -836) T) ((-228 . -905) 174461) ((-1029 . -943) T) ((-91 . -34) T) ((-1024 . -320) 174426) ((-937 . -943) T) ((-894 . -629) 174407) ((-730 . -664) 174367) ((-500 . -1246) T) ((-697 . -629) 174348) ((-692 . -629) 174329) ((-653 . -664) 174313) ((-220 . -1246) T) ((-420 . -915) 174234) ((-228 . -1063) 174194) ((-40 . -301) T) ((-500 . -569) T) ((-491 . -629) 174175) ((-371 . -25) T) ((-327 . -662) 173830) ((-324 . -662) 173744) ((-371 . -21) T) ((-365 . -25) T) ((-365 . -21) T) ((-220 . -569) T) ((-357 . -25) T) ((-357 . -21) T) ((-330 . -235) 173690) ((-251 . -629) 173667) ((-139 . -629) 173648) ((-138 . -629) 173629) ((-134 . -629) 173610) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1083) T) ((-593 . -174) T) ((-577 . -174) T) ((-508 . -174) T) ((-1087 . -1242) T) ((-975 . -1242) T) ((-729 . -1242) T) ((-655 . -297) 173577) ((-674 . -626) 173559) ((-494 . -1242) T) ((-753 . -752) 173543) ((-348 . -626) 173525) ((-68 . -395) T) ((-68 . -408) T) ((-1127 . -107) 173509) ((-1087 . -905) 173491) ((-975 . -905) 173416) ((-669 . -1137) T) ((-636 . -733) 173403) ((-494 . -905) NIL) ((-1171 . -102) T) ((-1119 . -631) 173387) ((-1087 . -1063) 173369) ((-97 . -626) 173351) ((-490 . -148) T) ((-975 . -1063) 173231) ((-118 . -733) 173176) ((-728 . -923) 173083) ((-669 . -23) T) ((-494 . -1063) 172959) ((-1112 . -627) NIL) ((-1112 . -626) 172941) ((-798 . -627) NIL) ((-798 . -626) 172902) ((-796 . -627) 172536) ((-796 . -626) 172450) ((-1138 . -654) 172356) ((-815 . -868) 172335) ((-474 . -626) 172317) ((-467 . -626) 172299) ((-467 . -627) 172160) ((-1060 . -232) 172106) ((-890 . -932) 172085) ((-127 . -34) T) ((-833 . -132) T) ((-665 . -626) 172067) ((-591 . -102) T) ((-367 . -1311) 172051) ((-364 . -1311) 172035) ((-356 . -1311) 172019) ((-122 . -527) 171952) ((-128 . -527) 171885) ((-524 . -808) T) ((-524 . -811) T) ((-523 . -810) T) ((-103 . -320) 171823) ((-225 . -102) 171773) ((-715 . -174) T) ((-710 . -1125) T) ((-890 . -664) 171689) ((-65 . -396) T) ((-285 . -626) 171671) ((-65 . -408) T) ((-975 . -389) 171655) ((-888 . -301) T) ((-50 . -626) 171637) ((-1024 . -38) 171585) ((-1145 . -662) 171557) ((-594 . -626) 171539) ((-494 . -389) 171523) ((-594 . -627) 171505) ((-531 . -626) 171487) ((-933 . -1311) 171474) ((-889 . -1242) T) ((-717 . -465) T) ((-508 . -527) 171440) ((-1303 . -1242) T) ((-1302 . -1242) T) ((-500 . -375) T) ((-367 . -380) 171419) ((-364 . -380) 171398) ((-356 . -380) 171377) ((-730 . -742) T) ((-220 . -375) T) ((-117 . -465) T) ((-1315 . -1306) 171361) ((-889 . -903) 171338) ((-889 . -905) NIL) ((-987 . -865) 171237) ((-831 . -865) 171188) ((-1249 . -102) T) ((-670 . -672) 171172) ((-1228 . -34) T) ((-173 . -626) 171154) ((-1138 . -25) 170987) ((-1138 . -21) 170898) ((-889 . -1063) 170875) ((-975 . -921) 170856) ((-1265 . -47) 170833) ((-933 . -380) T) ((-606 . -868) T) ((-59 . -667) 170817) ((-529 . -667) 170801) ((-494 . -921) 170778) ((-71 . -454) T) ((-71 . -408) T) ((-509 . -667) 170762) ((-59 . -385) 170746) ((-636 . -174) T) ((-529 . -385) 170730) ((-509 . -385) 170714) ((-559 . -1242) T) ((-843 . -724) 170698) ((-1197 . -318) 170677) ((-1203 . -132) T) ((-1167 . -1076) 170661) ((-118 . -174) T) ((-1167 . -656) 170593) ((-1171 . -320) 170531) ((-171 . -1242) T) ((-1304 . -132) T) ((-1277 . -943) 170510) ((-1256 . -943) 170489) ((-1256 . -836) NIL) ((-884 . -1076) 170459) ((-648 . -760) 170443) ((-620 . -760) 170427) ((-1255 . -932) 170380) ((-1049 . -1125) T) ((-928 . -1137) T) ((-884 . -656) 170350) ((-710 . -733) 170300) ((-919 . -1242) T) ((-889 . -389) 170277) ((-889 . -350) 170254) ((-857 . -1242) T) ((-824 . -1242) T) ((-171 . -903) 170238) ((-171 . -905) 170163) ((-785 . -1242) T) ((-693 . -1242) T) ((-1292 . -527) 170096) ((-1276 . -664) 169993) ((-1105 . -235) 169866) ((-500 . -1137) T) ((-366 . -1125) T) ((-220 . -1137) T) ((-76 . -454) T) ((-76 . -408) T) ((-171 . -1063) 169762) ((-305 . -915) 169719) ((-330 . -865) T) ((-1255 . -664) 169527) ((-890 . -810) 169506) ((-890 . -807) 169485) ((-890 . -742) T) ((-500 . -23) T) ((-371 . -235) 169458) ((-365 . -235) 169431) ((-357 . -235) 169404) ((-176 . -465) T) ((-86 . -454) T) ((-225 . -320) 169342) ((-86 . -408) T) ((-226 . -626) 169324) ((-108 . -235) 169311) ((-220 . -23) T) ((-1316 . -1309) 169290) ((-693 . -1063) 169274) ((-593 . -301) T) ((-577 . -301) T) ((-508 . -301) T) ((-1265 . -1242) T) ((-137 . -483) 169229) ((-873 . -1242) T) ((-670 . -662) 169188) ((-48 . -1125) T) ((-728 . -273) 169172) ((-728 . -233) 169156) ((-889 . -921) NIL) ((-584 . -1242) T) ((-1265 . -905) NIL) ((-908 . -102) T) ((-904 . -102) T) ((-655 . -626) 169138) ((-401 . -1125) T) ((-171 . -389) 169122) ((-171 . -350) 169106) ((-1265 . -1063) 168986) ((-873 . -1063) 168882) ((-1167 . -102) T) ((-1024 . -923) 168805) ((-678 . -808) 168784) ((-669 . -132) T) ((-678 . -811) 168763) ((-118 . -527) 168671) ((-584 . -1063) 168653) ((-305 . -1299) 168623) ((-1192 . -868) NIL) ((-884 . -102) T) ((-986 . -569) 168602) ((-1236 . -1081) 168485) ((-1028 . -1076) 168430) ((-495 . -654) 168336) ((-927 . -1125) T) ((-1049 . -733) 168273) ((-727 . -1081) 168238) ((-1028 . -656) 168183) ((-630 . -102) T) ((-615 . -34) T) ((-1172 . -1242) T) ((-1236 . -111) 168052) ((-487 . -664) 167949) ((-366 . -733) 167894) ((-171 . -921) 167853) ((-715 . -301) T) ((-710 . -174) T) ((-727 . -111) 167809) ((-1321 . -1083) T) ((-1265 . -389) 167793) ((-431 . -1246) 167771) ((-1143 . -626) 167753) ((-324 . -864) NIL) ((-431 . -569) T) ((-228 . -318) T) ((-1255 . -807) 167706) ((-1255 . -810) 167659) ((-1276 . -742) T) ((-1255 . -742) T) ((-48 . -733) 167624) ((-228 . -1047) T) ((-1278 . -424) 167590) ((-1265 . -921) 167533) ((-363 . -1299) 167510) ((-1236 . -629) 167392) ((-734 . -742) T) ((-344 . -626) 167374) ((-533 . -868) 167353) ((-1138 . -235) 167244) ((-112 . -626) 167226) ((-112 . -627) 167208) ((-734 . -486) T) ((-727 . -629) 167158) ((-1315 . -1076) 167142) ((-495 . -25) 166975) ((-128 . -502) 166959) ((-122 . -502) 166943) ((-495 . -21) 166854) ((-1315 . -656) 166824) ((-636 . -301) T) ((-599 . -1081) 166799) ((-450 . -1125) T) ((-1087 . -318) T) ((-118 . -301) T) ((-1129 . -102) T) ((-1028 . -102) T) ((-599 . -111) 166767) ((-1236 . -1074) T) ((-1167 . -320) 166705) ((-1087 . -1047) T) ((-1079 . -25) T) ((-66 . -1242) T) ((-911 . -1242) T) ((-1079 . -21) T) ((-727 . -1074) T) ((-397 . -21) T) ((-397 . -25) T) ((-710 . -527) NIL) ((-1049 . -174) T) ((-727 . -249) T) ((-1087 . -558) T) ((-728 . -662) 166615) ((-519 . -102) T) ((-515 . -102) T) ((-366 . -174) T) ((-355 . -626) 166597) ((-420 . -1076) 166549) ((-407 . -626) 166531) ((-1145 . -864) T) ((-487 . -742) T) ((-911 . -1063) 166499) ((-420 . -656) 166451) ((-108 . -865) T) ((-674 . -1081) 166435) ((-500 . -132) T) ((-1278 . -1083) T) ((-220 . -132) T) ((-1182 . -102) 166385) ((-99 . -1125) T) ((-246 . -868) 166336) ((-251 . -682) 166320) ((-251 . -667) 166304) ((-674 . -111) 166283) ((-599 . -629) 166267) ((-327 . -424) 166251) ((-251 . -385) 166235) ((-1184 . -241) 166182) ((-1024 . -273) 166166) ((-1024 . -233) 166150) ((-74 . -1242) T) ((-48 . -174) T) ((-717 . -400) T) ((-717 . -144) T) ((-1315 . -102) T) ((-1223 . -1242) T) ((-1222 . -629) 166132) ((-1113 . -1242) T) ((-1112 . -1081) 165975) ((-1101 . -1242) T) ((-274 . -932) 165954) ((-254 . -932) 165933) ((-798 . -1081) 165756) ((-796 . -1081) 165599) ((-621 . -1242) T) ((-1189 . -626) 165581) ((-1112 . -111) 165410) ((-1071 . -102) T) ((-488 . -1242) T) ((-474 . -1081) 165381) ((-467 . -1081) 165224) ((-680 . -664) 165208) ((-889 . -318) T) ((-798 . -111) 165017) ((-796 . -111) 164846) ((-367 . -664) 164798) ((-364 . -664) 164750) ((-356 . -664) 164702) ((-274 . -664) 164591) ((-254 . -664) 164480) ((-1183 . -865) T) ((-1113 . -1063) 164464) ((-1101 . -1063) 164441) ((-1029 . -868) T) ((-1025 . -34) T) ((-474 . -111) 164402) ((-467 . -111) 164231) ((-996 . -868) T) ((-989 . -626) 164213) ((-986 . -1137) T) ((-981 . -1242) T) ((-127 . -1035) 164197) ((-866 . -1242) T) ((-889 . -1047) NIL) ((-751 . -1137) T) ((-731 . -1137) T) ((-674 . -629) 164115) ((-1292 . -502) 164099) ((-1209 . -1242) T) ((-1208 . -1242) T) ((-1167 . -38) 164059) ((-986 . -23) T) ((-933 . -664) 164024) ((-883 . -1125) T) ((-859 . -102) T) ((-833 . -21) T) ((-648 . -1076) 164008) ((-620 . -1076) 163992) ((-833 . -25) T) ((-751 . -23) T) ((-731 . -23) T) ((-648 . -656) 163976) ((-110 . -677) T) ((-620 . -656) 163960) ((-594 . -1081) 163925) ((-531 . -1081) 163870) ((-230 . -57) 163828) ((-466 . -23) T) ((-420 . -102) T) ((-1207 . -1242) T) ((-271 . -102) T) ((-110 . -113) T) ((-710 . -301) T) ((-884 . -38) 163798) ((-1112 . -629) 163534) ((-594 . -111) 163490) ((-531 . -111) 163419) ((-431 . -1137) T) ((-327 . -1083) 163309) ((-324 . -1083) T) ((-129 . -1242) T) ((-131 . -1242) T) ((-798 . -629) 163057) ((-796 . -629) 162823) ((-674 . -1074) T) ((-1321 . -1125) T) ((-467 . -629) 162608) ((-171 . -318) 162539) ((-431 . -23) T) ((-40 . -626) 162521) ((-40 . -627) 162505) ((-108 . -1017) 162487) ((-117 . -887) 162471) ((-665 . -629) 162455) ((-48 . -527) 162421) ((-1228 . -1035) 162405) ((-1206 . -626) 162372) ((-1214 . -34) T) ((-977 . -626) 162338) ((-944 . -626) 162320) ((-1138 . -865) 162271) ((-787 . -626) 162253) ((-688 . -626) 162235) ((-530 . -1242) T) ((-1265 . -318) 162214) ((-1182 . -320) 162152) ((-1166 . -34) T) ((-492 . -34) T) ((-1117 . -1242) T) ((-490 . -465) T) ((-1059 . -1242) T) ((-1112 . -1074) T) ((-50 . -629) 162121) ((-798 . -1074) T) ((-796 . -1074) T) ((-663 . -241) 162105) ((-645 . -241) 162051) ((-1203 . -21) T) ((-594 . -629) 162001) ((-531 . -629) 161931) ((-495 . -235) 161822) ((-1203 . -25) T) ((-1112 . -337) 161783) ((-467 . -1074) T) ((-1112 . -239) 161762) ((-798 . -337) 161739) ((-798 . -239) T) ((-796 . -337) 161711) ((-747 . -1246) 161690) ((-532 . -34) T) ((-338 . -667) 161674) ((-529 . -34) T) ((-59 . -34) T) ((-510 . -34) T) ((-509 . -34) T) ((-467 . -337) 161653) ((-338 . -385) 161637) ((-373 . -1242) T) ((-333 . -1242) T) ((-1028 . -1177) NIL) ((-747 . -569) 161568) ((-648 . -102) T) ((-620 . -102) T) ((-367 . -742) T) ((-364 . -742) T) ((-356 . -742) T) ((-274 . -742) T) ((-254 . -742) T) ((-391 . -1242) T) ((-1304 . -21) T) ((-1071 . -320) 161476) ((-1304 . -25) T) ((-924 . -1125) 161454) ((-834 . -235) 161441) ((-50 . -1074) T) ((-1199 . -569) 161420) ((-1198 . -1246) 161399) ((-1198 . -569) 161350) ((-1192 . -1246) 161329) ((-1192 . -569) 161280) ((-1049 . -301) T) ((-594 . -1074) T) ((-531 . -1074) T) ((-1028 . -38) 161225) ((-373 . -1063) 161209) ((-333 . -1063) 161193) ((-1024 . -662) 161116) ((-391 . -905) 161098) ((-852 . -1242) T) ((-843 . -1242) T) ((-841 . -1242) T) ((-815 . -1137) T) ((-933 . -742) T) ((-594 . -249) T) ((-594 . -239) T) ((-531 . -239) T) ((-531 . -249) T) ((-1151 . -569) 161077) ((-366 . -301) T) ((-663 . -711) 161061) ((-391 . -1063) 161021) ((-305 . -1076) 160942) ((-351 . -915) 160921) ((-1145 . -1083) T) ((-103 . -126) 160905) ((-305 . -656) 160847) ((-815 . -23) T) ((-1314 . -1309) 160823) ((-1312 . -1309) 160802) ((-1292 . -297) 160754) ((-1278 . -1125) T) ((-420 . -320) 160719) ((-1167 . -923) 160642) ((-888 . -626) 160624) ((-852 . -1063) 160593) ((-655 . -1081) 160577) ((-205 . -803) T) ((-204 . -803) T) ((-203 . -803) T) ((-202 . -803) T) ((-201 . -803) T) ((-200 . -803) T) ((-199 . -803) T) ((-198 . -803) T) ((-197 . -803) T) ((-196 . -803) T) ((-560 . -626) 160559) ((-508 . -1027) T) ((-284 . -855) T) ((-283 . -855) T) ((-282 . -855) T) ((-281 . -855) T) ((-48 . -301) T) ((-280 . -855) T) ((-279 . -855) T) ((-278 . -855) T) ((-195 . -803) T) ((-655 . -111) 160538) ((-625 . -865) T) ((-670 . -424) 160522) ((-686 . -238) 160473) ((-226 . -629) 160435) ((-110 . -865) T) ((-669 . -21) T) ((-669 . -25) T) ((-1315 . -38) 160405) ((-118 . -297) 160356) ((-1292 . -19) 160340) ((-1256 . -868) NIL) ((-1292 . -617) 160317) ((-1305 . -1125) T) ((-363 . -1076) 160262) ((-1102 . -1125) T) ((-1012 . -1125) T) ((-986 . -132) T) ((-833 . -235) 160249) ((-753 . -1125) T) ((-363 . -656) 160194) ((-751 . -132) T) ((-731 . -132) T) ((-524 . -809) T) ((-524 . -810) T) ((-466 . -132) T) ((-420 . -1177) 160172) ((-226 . -1074) T) 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159078) ((-1197 . -943) 159057) ((-747 . -1137) T) ((-651 . -102) T) ((-528 . -1242) T) ((-523 . -1242) T) ((-521 . -1242) T) ((-363 . -102) T) ((-1241 . -1108) T) ((-1145 . -860) T) ((-834 . -865) T) ((-747 . -23) T) ((-355 . -1081) 159002) ((-1172 . -107) 158986) ((-1293 . -626) 158968) ((-653 . -1242) T) ((-1199 . -23) T) ((-1199 . -1137) T) ((-1198 . -1137) T) ((-1198 . -23) T) ((-528 . -1063) 158952) ((-1192 . -1137) T) ((-1151 . -1137) T) ((-355 . -111) 158881) ((-1029 . -1246) T) ((-127 . -1242) T) ((-937 . -1246) T) ((-1192 . -23) T) ((-1167 . -273) 158865) ((-710 . -297) NIL) ((-730 . -1242) T) ((-1167 . -233) 158849) ((-1151 . -23) T) ((-1100 . -1125) T) ((-1029 . -569) T) ((-937 . -569) T) ((-256 . -1242) T) ((-189 . -1242) T) ((-163 . -1242) T) ((-158 . -1242) T) ((-255 . -626) 158831) ((-831 . -238) 158728) ((-815 . -132) T) ((-726 . -626) 158710) ((-327 . -733) 158620) ((-324 . -733) 158549) ((-715 . -626) 158531) ((-715 . -627) 158476) ((-420 . -413) 158460) ((-451 . -1125) T) ((-500 . -25) T) ((-500 . -21) T) ((-1145 . -1125) T) ((-220 . -25) T) ((-220 . -21) T) ((-728 . -424) 158444) ((-730 . -1063) 158413) ((-1292 . -626) 158325) ((-1292 . -627) 158286) ((-1278 . -174) T) ((-1215 . -626) 158268) ((-251 . -34) T) ((-355 . -629) 158198) ((-407 . -629) 158180) ((-949 . -999) T) ((-1228 . -1242) T) ((-678 . -807) 158159) ((-678 . -810) 158138) ((-411 . -408) T) ((-536 . -102) 158088) ((-1248 . -1242) T) ((-1060 . -1125) T) ((-420 . -923) 158011) ((-225 . -1020) 157995) ((-854 . -1242) T) ((-517 . -102) T) ((-636 . -626) 157977) ((-45 . -865) NIL) ((-636 . -627) 157954) ((-1060 . -623) 157929) ((-924 . -527) 157862) ((-330 . -238) 157814) ((-355 . -1074) T) ((-118 . -627) NIL) ((-118 . -626) 157796) ((-890 . -1242) T) ((-686 . -430) 157780) ((-686 . -1148) 157725) ((-513 . -152) 157707) ((-355 . -239) T) ((-355 . -249) T) ((-40 . -1081) 157652) ((-890 . -903) 157636) ((-890 . -905) 157561) ((-728 . -1083) T) ((-710 . -1027) NIL) ((-1276 . -47) 157531) ((-1255 . -47) 157508) ((-1166 . -1035) 157479) ((-1145 . -733) 157466) ((-3 . |UnionCategory|) T) ((-1130 . -626) 157448) ((-1105 . -148) 157427) ((-1105 . -146) 157378) ((-1029 . -375) T) ((-989 . -629) 157362) ((-228 . -943) T) ((-40 . -111) 157291) ((-890 . -1063) 157155) ((-1028 . -233) 157132) ((-1028 . -273) 157109) ((-717 . -1076) 157096) ((-937 . -375) T) ((-717 . -656) 157083) ((-330 . -1230) 157049) ((-391 . -318) T) ((-330 . -1227) 157015) ((-327 . -174) 156994) ((-324 . -174) T) ((-621 . -1218) 156970) ((-594 . -1311) 156957) ((-531 . -1311) 156934) ((-117 . -1076) 156921) ((-371 . -148) 156900) ((-371 . -146) 156851) ((-365 . -148) 156830) ((-365 . -146) 156781) ((-357 . -148) 156760) ((-117 . -656) 156747) ((-357 . -146) 156698) ((-330 . -35) 156664) ((-488 . -1218) 156643) ((0 . |EnumerationCategory|) T) ((-330 . -95) 156609) ((-391 . -1047) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -241) 156559) ((-670 . -1125) T) ((-621 . -107) 156506) ((-498 . -132) T) 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-662) 155423) ((-937 . -1137) T) ((-937 . -23) T) ((-890 . -921) 155382) ((-363 . -38) 155347) ((-888 . -1081) 155334) ((-342 . -868) T) ((-82 . -626) 155316) ((-40 . -1074) T) ((-888 . -111) 155301) ((-734 . -1242) T) ((-717 . -102) T) ((-710 . -626) 155283) ((-615 . -1242) T) ((-609 . -569) 155262) ((-440 . -1137) T) ((-351 . -1076) 155246) ((-215 . -1125) T) ((-176 . -1076) 155178) ((-487 . -47) 155148) ((-40 . -239) 155120) ((-40 . -249) T) ((-135 . -102) T) ((-117 . -102) T) ((-608 . -569) 155099) ((-351 . -656) 155083) ((-710 . -627) 154991) ((-327 . -527) 154957) ((-176 . -656) 154889) ((-324 . -527) 154781) ((-500 . -235) 154768) ((-1276 . -1063) 154752) ((-1255 . -1063) 154538) ((-1024 . -424) 154522) ((-220 . -235) 154509) ((-440 . -23) T) ((-1145 . -174) T) ((-1278 . -301) T) ((-670 . -733) 154479) ((-145 . -1125) T) ((-48 . -1027) T) ((-420 . -273) 154463) ((-420 . -233) 154447) ((-306 . -241) 154397) ((-889 . -943) T) ((-889 . -836) NIL) ((-888 . -629) 154369) ((-259 . -868) 154320) ((-258 . -868) 154271) ((-882 . -865) T) ((-1255 . -350) 154241) ((-1255 . -389) 154211) ((-1105 . -238) 154090) ((-225 . -1146) 154074) ((-305 . -923) 154033) ((-1292 . -299) 154010) ((-371 . -238) 153989) ((-365 . -238) 153968) ((-487 . -1242) T) ((-357 . -238) 153947) ((-108 . -238) T) ((-1236 . -664) 153872) ((-1028 . -662) 153802) ((-986 . -21) T) ((-986 . -25) T) ((-751 . -21) T) ((-751 . -25) T) ((-731 . -21) T) ((-731 . -25) T) ((-727 . -664) 153767) ((-466 . -21) T) ((-466 . -25) T) ((-351 . -102) T) ((-176 . -102) T) ((-1024 . -1083) T) ((-888 . -1074) T) ((-790 . -102) T) ((-1277 . -375) 153746) ((-1276 . -921) 153652) ((-1256 . -375) 153631) ((-1255 . -921) 153482) ((-1201 . -1242) T) ((-1049 . -626) 153464) ((-420 . -844) 153417) ((-1199 . -506) 153383) ((-171 . -943) 153314) ((-1198 . -506) 153280) ((-1192 . -506) 153246) ((-728 . -1125) T) ((-1151 . -506) 153212) ((-593 . -1081) 153199) ((-577 . -1081) 153186) ((-508 . -1081) 153151) ((-327 . -301) 153130) 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-107) 151851) ((-937 . -132) T) ((-928 . -865) 151802) ((-717 . -1177) T) ((-715 . -111) 151758) ((-859 . -662) 151675) ((-609 . -1137) T) ((-608 . -1137) T) ((-728 . -733) 151504) ((-727 . -742) T) ((-815 . -25) T) ((-815 . -21) T) ((-500 . -865) T) ((-610 . -1242) T) ((-609 . -23) T) ((-598 . -1242) T) ((-220 . -865) T) ((-420 . -662) 151441) ((-593 . -1074) T) ((-577 . -1074) T) ((-549 . -1242) T) ((-508 . -1074) T) ((-355 . -1311) 151418) ((-330 . -465) 151397) ((-351 . -320) 151384) ((-608 . -23) T) ((-440 . -132) T) ((-674 . -664) 151358) ((-251 . -1035) 151342) ((-890 . -318) T) ((-1316 . -1306) 151326) ((-787 . -808) T) ((-787 . -811) T) ((-717 . -38) 151313) ((-577 . -239) T) ((-508 . -249) T) ((-508 . -239) T) ((-1305 . -502) 151297) ((-1288 . -1242) T) ((-1175 . -241) 151247) ((-1112 . -932) 151226) ((-117 . -38) 151213) ((-211 . -816) T) ((-210 . -816) T) ((-209 . -816) T) ((-208 . -816) T) ((-890 . -1047) 151191) ((-680 . -1242) T) ((-661 . -1242) T) ((-798 . -932) 151170) 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148543) ((-254 . -921) 148520) ((-118 . -1074) T) ((-1112 . -742) T) ((-832 . -1137) T) ((-835 . -868) T) ((-636 . -239) 148499) ((-634 . -102) T) ((-524 . -1242) T) ((-520 . -1242) T) ((-798 . -742) T) ((-796 . -742) T) ((-1247 . -865) T) ((-426 . -1137) T) ((-118 . -249) T) ((-40 . -380) NIL) ((-118 . -239) NIL) ((-399 . -868) 148478) ((-467 . -742) T) ((-832 . -23) T) ((-747 . -25) T) ((-747 . -21) T) ((-686 . -915) 148399) ((-1102 . -297) 148378) ((-78 . -409) T) ((-78 . -408) T) ((-546 . -783) 148360) ((-228 . -868) T) ((-710 . -1081) 148310) ((-1317 . -102) T) ((-1284 . -132) T) ((-1277 . -132) T) ((-1256 . -132) T) ((-1199 . -25) T) ((-1167 . -424) 148294) ((-648 . -379) 148226) ((-620 . -379) 148158) ((-1182 . -1174) 148142) ((-103 . -1125) 148120) ((-1199 . -21) T) ((-1198 . -21) T) ((-883 . -626) 148102) ((-1024 . -733) 148050) ((-226 . -664) 148017) ((-710 . -111) 147951) ((-50 . -742) T) ((-1198 . -25) T) ((-363 . -361) T) ((-1192 . -21) T) ((-1105 . -465) 147902) ((-1192 . -25) T) ((-728 . -527) 147849) ((-594 . -742) T) ((-531 . -742) T) ((-1151 . -21) T) ((-1151 . -25) T) ((-609 . -132) T) ((-608 . -132) T) ((-305 . -662) 147584) ((-495 . -238) 147481) ((-371 . -465) T) ((-365 . -465) T) ((-357 . -465) T) ((-487 . -318) 147460) ((-1250 . -102) T) ((-324 . -297) 147395) ((-108 . -465) T) ((-79 . -454) T) ((-79 . -408) T) ((-490 . -102) T) ((-707 . -629) 147379) ((-1321 . -626) 147361) ((-1321 . -627) 147343) ((-1105 . -415) 147322) ((-1060 . -502) 147253) ((-655 . -664) 147237) ((-137 . -297) 147214) ((-577 . -811) T) ((-577 . -808) T) ((-1088 . -241) 147160) ((-1087 . -868) T) ((-729 . -868) T) ((-371 . -415) 147111) ((-365 . -415) 147062) ((-357 . -415) 147013) ((-1307 . -1137) T) ((-1316 . -1076) 146997) ((-393 . -1076) 146981) ((-1316 . -656) 146951) ((-834 . -238) T) ((-393 . -656) 146921) ((-710 . -629) 146856) ((-1307 . -23) T) ((-1294 . -102) T) ((-351 . -923) 146837) ((-177 . -626) 146819) ((-1167 . -1083) T) ((-560 . -380) T) ((-686 . -760) 146803) ((-1203 . -146) 146782) ((-1203 . -148) 146761) ((-1171 . -1125) T) ((-1171 . -1096) 146730) ((-69 . -1242) T) ((-1049 . -1081) 146667) ((-363 . -662) 146597) ((-884 . -1083) T) ((-246 . -654) 146503) ((-710 . -1074) T) ((-366 . -1081) 146448) ((-61 . -1242) T) ((-1049 . -111) 146364) ((-924 . -626) 146275) ((-710 . -249) T) ((-710 . -239) NIL) ((-859 . -864) 146254) ((-715 . -811) T) ((-715 . -808) T) ((-1028 . -424) 146231) ((-366 . -111) 146160) ((-391 . -943) T) ((-420 . -864) 146139) ((-728 . -301) 146050) ((-226 . -742) T) ((-1284 . -506) 146016) ((-1277 . -506) 145982) ((-1256 . -506) 145948) ((-591 . -1125) T) ((-327 . -1027) 145927) ((-225 . -1125) 145905) ((-1249 . -860) T) ((-330 . -998) 145867) ((-105 . -102) T) ((-48 . -1081) 145832) ((-889 . -868) NIL) ((-1316 . -102) T) ((-393 . -102) T) ((-1278 . -626) 145814) ((-1158 . -1159) 145798) ((-1029 . -654) 145780) ((-894 . -1242) T) ((-48 . -111) 145736) ((-697 . -1242) T) ((-692 . -1242) T) ((-678 . -1242) T) ((-831 . -915) 145603) ((-491 . -1242) T) ((-251 . -1242) T) ((-544 . -102) T) ((-513 . -102) T) ((-153 . -1299) 145587) ((-139 . -1242) T) ((-138 . -1242) T) ((-134 . -1242) T) ((-1241 . -102) T) ((-1049 . -629) 145524) ((-833 . -238) T) ((-1197 . -1246) 145503) ((-217 . -380) T) ((-366 . -629) 145433) ((-1150 . -1246) 145412) ((-246 . -25) 145245) ((-246 . -21) 145156) ((-128 . -120) 145140) ((-122 . -120) 145124) ((-44 . -760) 145108) ((-1197 . -569) 145019) ((-1150 . -569) 144950) ((-1249 . -1125) T) ((-559 . -868) T) ((-1060 . -297) 144925) ((-1191 . -1108) T) ((-1019 . -1108) T) ((-832 . -132) T) ((-118 . -811) NIL) ((-118 . -808) NIL) ((-367 . -318) T) ((-364 . -318) T) ((-356 . -318) T) ((-1119 . -1242) 144903) ((-259 . -1137) 144881) ((-258 . -1137) 144859) ((-1049 . -1074) T) ((-1028 . -1083) T) ((-48 . -629) 144792) ((-355 . -664) 144737) ((-1305 . -626) 144699) ((-1305 . -627) 144660) ((-634 . -38) 144644) ((-1199 . -235) 144597) ((-1198 . -235) 144543) ((-1102 . -626) 144525) 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T) ((-1107 . -102) T) ((-88 . -1242) T) ((-513 . -320) NIL) ((-1025 . -107) 143423) ((-908 . -1125) T) ((-904 . -1125) T) ((-1292 . -667) 143407) ((-1292 . -385) 143391) ((-338 . -1242) T) ((-606 . -865) T) ((-1167 . -1125) T) ((-1167 . -1078) 143331) ((-103 . -527) 143264) ((-950 . -626) 143246) ((-355 . -742) T) ((-30 . -626) 143228) ((-884 . -1125) T) ((-859 . -1083) 143207) ((-40 . -664) 143114) ((-228 . -1246) T) ((-420 . -1083) T) ((-1183 . -152) 143096) ((-1024 . -301) 143047) ((-892 . -1242) T) ((-630 . -1125) T) ((-228 . -569) T) ((-330 . -1273) 143031) ((-330 . -1270) 143001) ((-717 . -662) 142973) ((-1214 . -1218) 142952) ((-1100 . -626) 142934) ((-1214 . -107) 142884) ((-663 . -152) 142868) ((-645 . -152) 142814) ((-117 . -662) 142786) ((-492 . -1218) 142765) ((-500 . -148) T) ((-500 . -146) NIL) ((-1145 . -627) 142680) ((-451 . -626) 142662) ((-220 . -148) T) ((-220 . -146) NIL) ((-1145 . -626) 142644) ((-130 . -102) T) ((-52 . -102) T) ((-1256 . -654) 142596) ((-492 . -107) 142546) ((-1018 . -23) T) ((-1316 . -38) 142516) ((-1197 . -1137) T) ((-1150 . -1137) T) ((-1087 . -1246) T) ((-246 . -235) 142407) ((-322 . -102) T) ((-872 . -1137) T) ((-975 . -1246) 142386) ((-494 . -1246) 142365) ((-1087 . -569) T) ((-975 . -569) 142296) ((-1197 . -23) T) ((-1176 . -1108) T) ((-1150 . -23) T) ((-872 . -23) T) ((-494 . -569) 142227) ((-1167 . -733) 142159) ((-686 . -1076) 142143) ((-1171 . -527) 142076) ((-686 . -656) 142060) ((-1060 . -627) NIL) ((-1060 . -626) 142042) ((-96 . -1108) T) ((-1321 . -1081) 142029) ((-884 . -733) 141999) ((-1321 . -111) 141984) ((-1236 . -47) 141953) ((-1192 . -865) NIL) ((-259 . -132) T) ((-258 . -132) T) ((-1129 . -1125) T) ((-1028 . -1125) T) ((-62 . -626) 141935) ((-1105 . -915) 141804) ((-1049 . -808) T) ((-1049 . -811) T) ((-1284 . -25) T) ((-1284 . -21) T) ((-1277 . -21) T) ((-1277 . -25) T) ((-888 . -664) 141791) ((-1256 . -21) T) ((-1256 . -25) T) ((-1052 . -152) 141775) ((-1029 . -235) 141762) ((-890 . -836) 141741) 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T) ((-833 . -465) 141152) ((-153 . -1076) 141136) ((-1071 . -1096) 141065) ((-1052 . -1001) 141034) ((-835 . -1137) T) ((-1028 . -733) 140979) ((-153 . -656) 140963) ((-399 . -1137) T) ((-489 . -1001) 140932) ((-476 . -1001) 140901) ((-1208 . -868) T) ((-110 . -152) 140883) ((-73 . -626) 140865) ((-912 . -626) 140847) ((-1207 . -868) T) ((-1105 . -740) 140826) ((-1321 . -1074) T) ((-832 . -654) 140774) ((-305 . -1083) 140716) ((-171 . -1246) 140621) ((-228 . -1137) T) ((-335 . -23) T) ((-1192 . -1017) 140573) ((-1278 . -1081) 140478) ((-859 . -1125) T) ((-129 . -868) T) ((-1151 . -756) 140457) ((-1276 . -943) 140436) ((-1255 . -943) 140415) ((-888 . -742) T) ((-171 . -569) 140326) ((-593 . -664) 140313) ((-577 . -664) 140285) ((-420 . -1125) T) ((-271 . -1125) T) ((-215 . -626) 140267) ((-508 . -664) 140217) ((-228 . -23) T) ((-1255 . -836) 140170) ((-1314 . -102) T) ((-504 . -1242) T) ((-366 . -1311) 140147) ((-1312 . -102) T) ((-1278 . -111) 140039) ((-1138 . -915) 139906) ((-831 . -1076) 139807) ((-831 . -656) 139729) ((-145 . -626) 139711) ((-1018 . -132) T) ((-44 . -102) T) ((-246 . -865) 139662) ((-599 . -1242) T) ((-1265 . -1246) 139641) ((-103 . -502) 139625) ((-1315 . -733) 139595) ((-1112 . -47) 139556) ((-1087 . -1137) T) ((-975 . -1137) T) ((-128 . -34) T) ((-122 . -34) T) ((-1265 . -569) 139467) ((-798 . -47) 139444) ((-796 . -47) 139416) ((-1222 . -1242) T) ((-1197 . -132) T) ((-366 . -380) T) ((-494 . -1137) T) ((-1150 . -132) T) ((-889 . -375) T) ((-467 . -47) 139395) ((-872 . -132) T) ((-333 . -868) 139374) ((-153 . -102) T) ((-1087 . -23) T) ((-975 . -23) T) ((-584 . -569) T) ((-832 . -25) T) ((-832 . -21) T) ((-1167 . -527) 139307) ((-605 . -1108) T) ((-599 . -1063) 139291) ((-1278 . -629) 139165) ((-494 . -23) T) ((-363 . -1083) T) ((-391 . -868) T) ((-1236 . -921) 139146) ((-686 . -320) 139084) ((-1284 . -235) 139037) ((-1138 . -1299) 139007) ((-715 . -664) 138972) ((-1029 . -865) T) ((-1028 . -174) T) ((-986 . -146) 138951) ((-648 . -1125) T) ((-620 . -1125) T) ((-986 . -148) 138930) ((-751 . -148) 138909) ((-751 . -146) 138888) ((-674 . -1242) T) ((-996 . -865) T) ((-1277 . -235) 138834) ((-1256 . -235) 138651) ((-849 . -662) 138568) ((-487 . -943) 138547) ((-348 . -1242) T) ((-330 . -1076) 138382) ((-327 . -1081) 138292) ((-324 . -1081) 138221) ((-1024 . -297) 138179) ((-420 . -733) 138131) ((-330 . -656) 137972) ((-608 . -235) 137925) ((-717 . -864) T) ((-1278 . -1074) T) ((-327 . -111) 137821) ((-324 . -111) 137734) ((-97 . -1242) T) ((-987 . -102) T) ((-831 . -102) 137466) ((-728 . -627) NIL) ((-728 . -626) 137448) ((-1278 . -337) 137392) ((-674 . -1063) 137288) ((-1112 . -1242) T) ((-1060 . -299) 137263) ((-593 . -742) T) ((-577 . -810) T) ((-171 . -375) 137214) ((-577 . -807) T) ((-577 . -742) T) ((-508 . -742) T) ((-798 . -1242) T) ((-796 . -1242) T) ((-1171 . -502) 137198) ((-474 . -1242) T) ((-467 . -1242) T) ((-1314 . -1313) 137174) ((-1112 . -905) NIL) ((-889 . -1137) T) ((-118 . -932) NIL) ((-1312 . -1313) 137153) ((-665 . -1242) T) ((-798 . -905) NIL) ((-796 . -905) 137012) ((-1307 . -25) T) ((-1307 . -21) T) ((-1239 . -102) 136990) ((-1131 . -408) T) ((-636 . -664) 136977) ((-467 . -905) NIL) ((-691 . -102) 136927) ((-1112 . -1063) 136754) ((-889 . -23) T) ((-798 . -1063) 136613) ((-796 . -1063) 136470) ((-118 . -664) 136415) ((-467 . -1063) 136291) ((-285 . -1242) T) ((-327 . -629) 135855) ((-324 . -629) 135738) ((-50 . -1242) T) ((-403 . -662) 135707) ((-665 . -1063) 135691) ((-640 . -102) T) ((-594 . -1242) T) ((-531 . -1242) T) ((-225 . -502) 135675) ((-1292 . -34) T) ((-634 . -662) 135634) ((-300 . -1076) 135621) ((-137 . -629) 135605) ((-300 . -656) 135592) ((-648 . -733) 135576) ((-620 . -733) 135560) ((-686 . -38) 135520) ((-330 . -102) T) ((-1145 . -1081) 135507) ((-85 . -626) 135489) ((-50 . -1063) 135473) ((-1112 . -389) 135457) ((-798 . -389) 135441) ((-715 . -742) T) ((-715 . -810) T) ((-715 . -807) T) ((-60 . -57) 135403) ((-594 . -1063) 135390) ((-531 . -1063) 135367) ((-173 . -1242) T) ((-335 . -132) T) ((-327 . -1074) 135257) ((-324 . -1074) T) ((-171 . -1137) T) ((-796 . -389) 135241) ((-45 . -152) 135191) ((-1029 . -1017) 135173) ((-467 . -389) 135157) ((-420 . -174) T) ((-327 . -249) 135136) ((-324 . -249) T) ((-324 . -239) NIL) ((-305 . -1125) 134918) ((-228 . -132) T) ((-1145 . -111) 134903) ((-171 . -23) T) ((-815 . -148) 134882) ((-815 . -146) 134861) ((-259 . -654) 134767) ((-258 . -654) 134673) ((-330 . -295) 134639) ((-1182 . -527) 134572) ((-490 . -662) 134522) ((-651 . -860) T) ((-495 . -915) 134389) ((-1158 . -1125) T) ((-228 . -1085) T) ((-831 . -320) 134327) ((-1112 . -921) 134262) ((-798 . -921) 134205) ((-796 . -921) 134189) ((-1314 . -38) 134159) ((-1312 . -38) 134129) ((-1265 . -1137) T) ((-873 . -1137) T) ((-467 . -921) 134106) ((-876 . -1125) T) ((-1265 . -23) T) ((-1145 . -629) 134078) ((-1087 . -132) T) ((-873 . -23) T) ((-584 . -1137) T) ((-636 . -742) T) ((-523 . -868) T) ((-367 . -943) T) ((-364 . -943) T) ((-300 . -102) T) ((-356 . -943) T) ((-995 . -1108) T) ((-975 . -132) T) ((-832 . -235) 134023) ((-118 . -810) NIL) ((-118 . -807) NIL) ((-118 . -742) T) ((-1071 . -527) 133924) ((-710 . -932) NIL) ((-584 . -23) T) ((-494 . -132) T) ((-431 . -238) 133875) ((-691 . -320) 133813) ((-226 . -1242) T) ((-651 . -1125) T) ((-648 . -777) T) ((-620 . -777) T) ((-1256 . -865) NIL) ((-1105 . -1076) 133723) ((-1028 . -301) T) ((-710 . -664) 133673) ((-259 . -25) T) ((-363 . -1125) T) ((-259 . -21) T) ((-258 . -25) T) ((-258 . -21) T) ((-153 . -38) 133657) ((-2 . -102) T) ((-933 . -943) T) ((-1105 . -656) 133525) ((-495 . -1299) 133495) ((-1145 . -1074) T) ((-727 . -318) T) ((-717 . -1083) T) ((-371 . -1076) 133447) ((-365 . -1076) 133399) ((-357 . -1076) 133351) ((-371 . -656) 133303) ((-226 . -1063) 133280) ((-365 . -656) 133232) ((-108 . -1076) 133182) ((-357 . -656) 133134) ((-305 . -733) 133076) ((-655 . -1242) T) ((-500 . -465) T) ((-420 . -527) 132988) ((-108 . -656) 132938) ((-220 . -465) T) ((-1145 . -239) T) ((-306 . -152) 132888) ((-1024 . -627) 132849) ((-1024 . -626) 132831) ((-1014 . -626) 132813) ((-117 . -1083) T) ((-670 . -1081) 132797) ((-228 . -506) T) ((-412 . -626) 132779) ((-412 . -627) 132756) ((-1079 . -1299) 132726) ((-670 . -111) 132705) ((-686 . -923) 132628) ((-1167 . -502) 132612) ((-1316 . -662) 132571) ((-393 . -662) 132540) ((-63 . -454) T) ((-63 . -408) T) ((-1184 . -102) T) ((-889 . -132) T) ((-497 . -102) 132490) ((-1143 . -1242) T) ((-1248 . -868) T) ((-1321 . -380) T) ((-1105 . -102) T) ((-1086 . -102) T) ((-363 . -733) 132435) ((-890 . -868) 132386) ((-747 . -148) 132365) ((-747 . -146) 132344) ((-670 . -629) 132262) ((-1049 . -664) 132199) ((-536 . -1125) 132177) ((-371 . -102) T) ((-365 . -102) T) ((-357 . -102) T) ((-108 . -102) T) ((-517 . -1125) T) ((-366 . -664) 132122) ((-1197 . -654) 132070) ((-1150 . -654) 132018) ((-397 . -522) 131997) ((-849 . -864) 131976) ((-710 . -742) T) ((-391 . -1246) T) ((-344 . -1242) T) ((-1256 . -1017) 131928) ((-351 . -1083) T) ((-112 . -1242) T) ((-176 . -1083) T) ((-103 . -626) 131860) ((-1199 . -146) 131839) ((-1199 . -148) 131818) ((-391 . -569) T) ((-1198 . -148) 131797) ((-1198 . -146) 131776) ((-1192 . -146) 131683) ((-420 . -301) T) ((-1192 . -148) 131590) ((-1151 . -148) 131569) ((-1151 . -146) 131548) ((-330 . -38) 131389) ((-171 . -132) T) ((-324 . -811) NIL) ((-324 . -808) NIL) ((-670 . -1074) T) ((-48 . -664) 131339) ((-1138 . -1076) 131240) ((-912 . -629) 131217) ((-1138 . -656) 131139) ((-1191 . -102) T) ((-1019 . -102) T) ((-1018 . -21) T) ((-128 . -1035) 131123) ((-122 . -1035) 131107) ((-1018 . -25) T) ((-924 . -120) 131091) ((-1183 . -102) T) ((-1265 . -132) T) ((-1255 . -868) 130990) ((-1197 . -25) T) ((-1197 . -21) T) ((-1184 . -320) 130785) ((-355 . -1242) T) ((-1150 . -25) T) ((-873 . -132) T) ((-407 . -1242) T) ((-1150 . -21) T) ((-872 . -25) T) ((-872 . -21) T) ((-798 . -318) 130764) ((-1182 . -502) 130748) ((-1175 . -152) 130698) ((-1171 . -626) 130660) ((-663 . -102) 130610) ((-645 . -102) T) ((-1171 . -627) 130571) ((-584 . -132) T) ((-634 . -864) 130550) ((-1049 . -807) T) ((-1049 . -810) T) ((-1049 . -742) T) ((-831 . -923) 130419) ((-728 . -1081) 130242) ((-615 . -868) 130221) ((-497 . -320) 130159) ((-466 . -430) 130129) ((-363 . -174) T) ((-300 . -38) 130116) ((-259 . -235) 130007) ((-258 . -235) 129898) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-355 . -1063) 129875) ((-278 . -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) ((-728 . -111) 129684) ((-366 . -742) T) ((-686 . -273) 129668) ((-686 . -233) 129652) ((-594 . -318) T) ((-531 . -318) T) ((-305 . -527) 129601) ((-1189 . -1242) T) ((-108 . -320) NIL) ((-72 . -408) T) ((-1138 . -102) 129333) ((-849 . -424) 129317) ((-1145 . -811) T) ((-1145 . -808) T) ((-717 . -1125) T) ((-591 . -626) 129299) ((-391 . -375) T) ((-171 . -506) 129277) ((-225 . -626) 129209) ((-135 . -1125) T) ((-117 . -1125) T) ((-989 . -1242) T) ((-48 . -742) T) ((-1071 . -502) 129174) ((-142 . -438) 129156) ((-142 . -380) T) ((-1052 . -102) T) ((-525 . -522) 129135) ((-728 . -629) 128891) ((-1249 . -626) 128873) ((-1206 . -1242) T) ((-1206 . -1063) 128809) ((-1199 . -238) 128768) ((-489 . -102) T) ((-476 . -102) T) ((-1198 . -238) 128720) ((-1192 . -238) 128543) ((-1059 . -1137) T) ((-330 . -923) 128449) ((-1201 . -868) T) ((-1199 . -35) 128415) ((-1199 . -95) 128381) ((-1199 . -1230) 128347) ((-1199 . -1227) 128313) ((-1198 . -1227) 128279) ((-1198 . -1230) 128245) ((-1198 . -95) 128211) ((-1198 . -35) 128177) ((-1192 . -1227) 128143) ((-1192 . -1230) 128109) ((-1183 . -320) NIL) ((-89 . -409) T) ((-89 . -408) T) ((-1105 . -1177) 128088) ((-40 . -1242) T) ((-1192 . -95) 128054) ((-1059 . -23) T) ((-1192 . -35) 128020) ((-584 . -506) T) ((-1151 . -35) 127986) ((-1151 . -95) 127952) ((-1151 . -1230) 127918) ((-1151 . -1227) 127884) ((-373 . -1137) T) ((-371 . -1177) 127863) ((-365 . -1177) 127842) ((-357 . -1177) 127821) ((-1129 . -297) 127777) ((-977 . -1242) T) ((-944 . -1242) T) ((-108 . -1177) T) ((-849 . -1083) 127756) ((-787 . -1242) T) ((-663 . -320) 127694) ((-645 . -320) 127545) ((-688 . -1242) T) ((-728 . -1074) T) ((-1087 . -654) 127527) ((-1105 . -38) 127395) ((-975 . -654) 127343) ((-1029 . -148) T) ((-1029 . -146) NIL) ((-391 . -1137) T) ((-335 . -25) T) ((-333 . -23) T) ((-966 . -865) 127322) ((-728 . -337) 127299) ((-494 . -654) 127247) ((-40 . -1063) 127135) ((-728 . -239) T) ((-717 . -733) 127122) ((-351 . -1125) T) ((-176 . -1125) T) ((-342 . -865) T) ((-431 . -465) 127072) ((-391 . -23) T) ((-371 . -38) 127037) ((-365 . -38) 127002) ((-357 . -38) 126967) ((-80 . -454) T) ((-80 . -408) T) ((-228 . -25) T) ((-228 . -21) T) ((-852 . -1137) T) ((-108 . -38) 126917) ((-843 . -1137) T) ((-790 . -1125) T) ((-117 . -733) 126904) ((-688 . -1063) 126888) ((-625 . -102) T) ((-852 . -23) T) ((-843 . -23) T) ((-1182 . -297) 126840) ((-1138 . -320) 126778) ((-495 . -1076) 126679) ((-1127 . -241) 126663) ((-64 . -409) T) ((-64 . -408) T) ((-1176 . -102) T) ((-110 . -102) T) ((-495 . -656) 126585) ((-40 . -389) 126562) ((-96 . -102) T) ((-669 . -870) 126546) ((-1197 . -235) 126533) ((-1160 . -1108) T) ((-1087 . -21) T) ((-1087 . -25) T) ((-1079 . -1076) 126517) ((-831 . -273) 126486) ((-831 . -233) 126455) ((-975 . -25) T) ((-975 . -21) T) ((-1145 . -380) T) ((-1079 . -656) 126397) ((-634 . -1083) T) ((-1052 . -320) 126335) ((-908 . -626) 126317) ((-686 . -662) 126276) ((-494 . -25) T) ((-494 . -21) T) ((-397 . -1076) 126260) ((-904 . -626) 126242) ((-888 . -1242) T) ((-536 . -527) 126175) ((-259 . -865) 126126) ((-258 . -865) 126077) ((-397 . -656) 126047) ((-889 . -654) 126024) ((-489 . -320) 125962) ((-560 . -1242) T) ((-476 . -320) 125900) ((-363 . -301) T) ((-1182 . -1280) 125884) ((-1167 . -626) 125846) ((-1167 . -627) 125807) ((-1165 . -102) T) ((-1024 . -1081) 125703) ((-40 . -921) 125655) ((-1182 . -617) 125632) ((-1321 . -664) 125619) ((-1088 . -152) 125565) ((-500 . -915) NIL) ((-884 . -503) 125542) ((-1024 . -111) 125424) ((-890 . -1246) T) ((-220 . -915) NIL) ((-351 . -733) 125408) ((-884 . -626) 125370) ((-176 . -733) 125302) ((-890 . -569) T) ((-420 . -297) 125260) ((-246 . -238) 125157) ((-108 . -413) 125139) ((-84 . -396) T) ((-84 . -408) T) ((-717 . -174) T) ((-630 . -626) 125121) ((-99 . -742) T) ((-495 . -102) 124853) ((-99 . -486) T) ((-117 . -174) T) ((-1314 . -662) 124812) ((-1312 . -662) 124771) ((-171 . -654) 124719) ((-1105 . -923) 124590) ((-1079 . -102) T) ((-1024 . -629) 124480) ((-889 . -25) T) ((-831 . -244) 124459) ((-889 . -21) T) ((-834 . -102) T) ((-1029 . -238) T) ((-44 . -662) 124402) ((-427 . -102) T) ((-397 . -102) T) ((-110 . -320) NIL) ((-230 . -102) 124352) ((-217 . -1242) T) ((-128 . -1242) T) ((-122 . -1242) T) ((-108 . -923) NIL) ((-833 . -1076) 124303) ((-59 . -868) 124282) ((-833 . -656) 124224) ((-529 . -868) 124203) ((-509 . -868) 124182) ((-1059 . -132) T) ((-686 . -379) 124166) ((-153 . -662) 124125) ((-1321 . -742) T) ((-648 . -297) 124083) ((-620 . -297) 124041) ((-1284 . -146) 124020) ((-1265 . -654) 123968) ((-1024 . -1074) T) ((-1129 . -626) 123950) ((-1028 . -626) 123932) ((-593 . -1242) T) ((-577 . -1242) T) ((-508 . -1242) T) ((-528 . -23) T) ((-523 . -23) T) ((-355 . -318) T) ((-521 . -23) T) ((-333 . -132) T) ((-3 . -1125) T) ((-1028 . -627) 123916) ((-1024 . -249) 123895) ((-1024 . -239) 123874) ((-1284 . -148) 123853) ((-1277 . -148) 123832) ((-849 . -1125) T) ((-1277 . -146) 123811) ((-1276 . -1246) 123790) ((-1256 . -146) 123697) ((-1256 . -148) 123604) ((-1255 . -1246) 123583) ((-391 . -132) T) ((-228 . -235) 123570) ((-176 . -174) T) ((-577 . -905) 123552) ((0 . -1125) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1242) T) ((-49 . -1125) T) ((-1278 . -664) 123457) ((-1276 . -569) 123408) ((-1255 . -569) 123359) ((-730 . -1137) T) ((-653 . -23) T) ((-577 . -1063) 123341) ((-608 . -148) 123320) ((-608 . -146) 123299) ((-508 . -1063) 123242) ((-1160 . -1162) T) ((-87 . -396) T) ((-87 . -408) T) ((-890 . -375) T) ((-852 . -132) T) ((-843 . -132) T) ((-987 . -662) 123186) ((-730 . -23) T) ((-519 . -626) 123152) ((-515 . -626) 123134) ((-831 . -662) 122913) ((-1316 . -1083) T) ((-391 . -1085) T) ((-1051 . -1125) 122891) ((-55 . -1063) 122873) ((-924 . -34) T) ((-495 . -320) 122811) ((-605 . -102) T) ((-1182 . -627) 122772) ((-1182 . -626) 122704) ((-1203 . -1076) 122587) ((-45 . -102) T) ((-833 . -102) T) ((-1203 . -656) 122484) ((-1293 . -1242) T) ((-1265 . -25) T) ((-1265 . -21) T) ((-1087 . -235) 122471) ((-873 . -25) T) ((-524 . -868) T) ((-255 . -1242) T) ((-44 . -379) 122455) ((-873 . -21) T) ((-747 . -465) 122406) ((-1315 . -626) 122388) ((-726 . -1242) T) ((-715 . -1242) T) ((-1304 . -1076) 122358) ((-1079 . -320) 122296) ((-687 . -1108) T) ((-619 . -1108) T) ((-403 . -1125) T) ((-584 . -25) T) ((-584 . -21) T) ((-182 . -1108) T) ((-162 . -1108) T) ((-157 . -1108) T) ((-155 . -1108) T) ((-1304 . -656) 122266) ((-634 . -1125) T) ((-715 . -905) 122248) ((-1292 . -1242) T) ((-230 . -320) 122186) ((-145 . -380) T) ((-1215 . -1242) T) ((-1071 . -627) 122128) ((-1071 . -626) 122071) ((-324 . -932) NIL) ((-1250 . -860) T) ((-1138 . -923) 121940) ((-715 . -1063) 121885) ((-727 . -943) T) ((-487 . -1246) 121864) ((-1198 . -465) 121843) ((-1192 . -465) 121822) ((-341 . -102) T) ((-890 . -1137) T) ((-330 . -662) 121704) ((-327 . -664) 121433) ((-324 . -664) 121362) ((-487 . -569) 121313) ((-351 . -527) 121279) ((-563 . -152) 121229) ((-40 . -318) T) ((-859 . -626) 121211) ((-717 . -301) T) ((-890 . -23) T) ((-391 . -506) T) ((-1105 . -273) 121181) ((-1105 . -233) 121151) ((-525 . -102) T) ((-420 . -627) 120958) ((-420 . -626) 120940) ((-271 . -626) 120922) ((-117 . -301) T) ((-1278 . -742) T) ((-636 . -1242) T) ((-1317 . -1125) T) ((-1276 . -375) 120901) ((-1255 . -375) 120880) ((-1305 . -34) T) ((-1250 . -1125) T) ((-118 . -1242) T) ((-108 . -273) 120862) ((-108 . -233) 120844) ((-1203 . -102) T) ((-490 . -1125) T) ((-536 . -502) 120828) ((-753 . -34) T) ((-669 . -1076) 120812) ((-669 . -656) 120782) ((-889 . -235) NIL) ((-142 . -34) T) ((-118 . -903) 120759) ((-118 . -905) NIL) ((-636 . -1063) 120642) ((-1304 . -102) T) ((-1284 . -238) 120601) ((-660 . -865) 120580) ((-1277 . -238) 120532) ((-1256 . -238) 120355) ((-306 . -102) T) ((-728 . -380) 120334) ((-118 . -1063) 120311) ((-403 . -733) 120295) ((-608 . -238) 120254) ((-634 . -733) 120238) ((-1130 . -1242) T) ((-45 . -320) 120042) ((-832 . -146) 120021) ((-832 . -148) 120000) ((-300 . -662) 119972) ((-1315 . -394) 119951) ((-835 . -865) T) ((-1294 . -1125) T) ((-1184 . -232) 119898) ((-399 . -865) 119877) ((-1284 . -35) 119843) ((-1284 . -1230) 119809) ((-1284 . -1227) 119775) ((-1277 . -1227) 119741) 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. -1083) T) ((-747 . -972) 116302) ((-1167 . -239) 116281) ((-366 . -1242) T) ((-1107 . -1125) T) ((-1059 . -25) T) ((-1059 . -21) T) ((-1028 . -1081) 116226) ((-338 . -868) 116205) ((-928 . -102) T) ((-884 . -1074) T) ((-710 . -921) NIL) ((-367 . -340) 116189) ((-367 . -375) T) ((-364 . -340) 116173) ((-364 . -375) T) ((-356 . -340) 116157) ((-356 . -375) T) ((-500 . -102) T) ((-1304 . -38) 116127) ((-559 . -865) T) ((-536 . -703) 116077) ((-220 . -102) T) ((-1049 . -1063) 115957) ((-1028 . -111) 115886) ((-651 . -626) 115868) ((-1199 . -998) 115837) ((-1198 . -998) 115799) ((-533 . -152) 115783) ((-1105 . -382) 115762) ((-363 . -626) 115744) ((-333 . -21) T) ((-366 . -1063) 115721) ((-333 . -25) T) ((-1192 . -998) 115690) ((-48 . -1242) T) ((-76 . -626) 115672) ((-1151 . -998) 115639) ((-715 . -318) T) ((-130 . -860) T) ((-933 . -375) T) ((-391 . -25) T) ((-391 . -21) T) ((-933 . -340) 115626) ((-86 . -626) 115608) ((-715 . -1047) T) ((-693 . -865) T) ((-401 . -1242) T) ((-1276 . 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. -569) T) ((-608 . -915) 106249) ((-327 . -903) 106233) ((-327 . -905) 106158) ((-324 . -903) 106119) ((-140 . -1242) T) ((-137 . -1242) T) ((-115 . -1242) T) ((-324 . -905) NIL) ((-815 . -320) 106084) ((-330 . -733) 105925) ((-399 . -398) 105909) ((-335 . -334) 105886) ((-498 . -102) T) ((-487 . -25) T) ((-487 . -21) T) ((-431 . -38) 105860) ((-327 . -1063) 105523) ((-228 . -1227) T) ((-228 . -1230) T) ((-3 . -626) 105505) ((-324 . -1063) 105435) ((-890 . -235) 105380) ((-2 . -1125) T) ((-2 . |RecordCategory|) T) ((-1138 . -1083) 105358) ((-849 . -626) 105340) ((-1087 . -238) T) ((-593 . -943) T) ((-577 . -836) T) ((-577 . -943) T) ((-508 . -943) T) ((-137 . -1063) 105324) ((-228 . -95) T) ((-171 . -148) 105303) ((-75 . -454) T) ((0 . -626) 105285) ((-75 . -408) T) ((-171 . -146) 105236) ((-228 . -35) T) ((-49 . -626) 105218) ((-490 . -1083) T) ((-500 . -273) 105200) ((-500 . -233) 105182) ((-497 . -993) 105166) ((-220 . -273) 105148) ((-220 . -233) 105130) ((-81 . -454) T) ((-81 . 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-408) T) ((-135 . -629) 101773) ((-117 . -629) 101745) ((-1029 . -656) 101695) ((-966 . -1005) 101679) ((-937 . -656) 101631) ((-937 . -1076) 101583) ((-933 . -21) T) ((-933 . -25) T) ((-890 . -865) 101534) ((-884 . -664) 101494) ((-727 . -1137) T) ((-727 . -23) T) ((-717 . -1074) T) ((-717 . -239) T) ((-300 . -174) T) ((-670 . -1242) T) ((-322 . -93) T) ((-663 . -1125) 101472) ((-645 . -623) 101447) ((-645 . -1125) T) ((-594 . -1246) T) ((-594 . -569) T) ((-531 . -1246) T) ((-531 . -569) T) ((-500 . -662) 101397) ((-487 . -235) 101343) ((-440 . -1076) 101327) ((-440 . -656) 101311) ((-371 . -733) 101263) ((-365 . -733) 101215) ((-351 . -1081) 101199) ((-357 . -733) 101151) ((-351 . -111) 101130) ((-176 . -1081) 101062) ((-176 . -111) 100973) ((-108 . -733) 100923) ((-220 . -662) 100873) ((-284 . -1125) T) ((-283 . -1125) T) ((-282 . -1125) T) ((-281 . -1125) T) ((-280 . -1125) T) ((-279 . -1125) T) ((-278 . -1125) T) ((-214 . -1125) T) ((-213 . -1125) T) ((-171 . -1230) 100851) ((-171 . -1227) 100829) ((-211 . -1125) T) ((-210 . -1125) T) ((-117 . -1074) T) ((-209 . -1125) T) ((-208 . -1125) T) ((-205 . -1125) T) ((-204 . -1125) T) ((-203 . -1125) T) ((-202 . -1125) T) ((-201 . -1125) T) ((-200 . -1125) T) ((-199 . -1125) T) ((-198 . -1125) T) ((-197 . -1125) T) ((-196 . -1125) T) ((-195 . -1125) T) ((-246 . -102) 100561) ((-171 . -35) 100539) ((-171 . -95) 100517) ((-670 . -1063) 100413) ((-495 . -1083) 100391) ((-1138 . -1125) 100143) ((-1167 . -34) T) ((-686 . -502) 100127) ((-73 . -1242) T) ((-105 . -626) 100109) ((-912 . -1242) T) ((-1316 . -626) 100091) ((-393 . -626) 100073) ((-351 . -629) 100025) ((-176 . -629) 99942) ((-1241 . -503) 99923) ((-747 . -38) 99772) ((-584 . -1230) T) ((-584 . -1227) T) ((-544 . -626) 99754) ((-533 . -320) 99692) ((-513 . -626) 99674) ((-513 . -627) 99656) ((-1241 . -626) 99622) ((-1192 . -1177) NIL) ((-215 . -1242) T) ((-1052 . -1096) 99591) ((-1052 . -1125) T) ((-1029 . -102) T) ((-996 . -102) T) ((-937 . -102) T) ((-912 . -1063) 99568) ((-1167 . -742) T) ((-1028 . -664) 99475) ((-489 . -1125) T) ((-476 . -1125) T) ((-599 . -23) T) ((-584 . -35) T) ((-584 . -95) T) ((-440 . -102) T) ((-1088 . -232) 99421) ((-1199 . -38) 99318) ((-1198 . -38) 99159) ((-944 . -868) T) ((-884 . -742) T) ((-787 . -868) T) ((-710 . -943) T) ((-688 . -868) T) ((-524 . -25) T) ((-520 . -21) T) ((-520 . -25) T) ((-1192 . -38) 98955) ((-351 . -1074) T) ((-145 . -1242) T) ((-1105 . -174) T) ((-176 . -1074) T) ((-1151 . -38) 98852) ((-728 . -47) 98829) ((-371 . -174) T) ((-365 . -174) T) ((-532 . -57) 98803) ((-510 . -57) 98753) ((-363 . -1311) 98730) ((-228 . -465) T) ((-330 . -301) 98681) ((-357 . -174) T) ((-176 . -249) T) ((-1255 . -865) 98580) ((-108 . -174) T) ((-890 . -1017) 98564) ((-674 . -1137) T) ((-594 . -375) T) ((-594 . -340) 98551) ((-531 . -340) 98528) ((-531 . -375) T) ((-327 . -318) 98507) ((-324 . -318) T) ((-615 . -865) 98486) ((-1138 . -733) 98428) ((-533 . -293) 98412) ((-674 . -23) T) ((-431 . -233) 98396) 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96435) ((-560 . -868) T) ((-1107 . -627) 96416) ((-420 . -932) 96395) ((-1236 . -132) T) ((-50 . -1137) T) ((-1192 . -413) 96347) ((-1049 . -943) T) ((-1028 . -742) T) ((-859 . -664) 96320) ((-728 . -905) NIL) ((-609 . -1076) 96280) ((-594 . -1137) T) ((-531 . -1137) T) ((-608 . -1076) 96163) ((-1182 . -34) T) ((-1029 . -320) NIL) ((-831 . -502) 96147) ((-609 . -656) 96120) ((-366 . -943) T) ((-608 . -656) 96017) ((-933 . -235) 96004) ((-420 . -664) 95920) ((-50 . -23) T) ((-727 . -132) T) ((-728 . -1063) 95800) ((-594 . -23) T) ((-108 . -527) NIL) ((-531 . -23) T) ((-171 . -422) 95771) ((-1165 . -1125) T) ((-1307 . -1306) 95755) ((-747 . -923) 95732) ((-717 . -811) T) ((-717 . -808) T) ((-1145 . -318) T) ((-391 . -148) T) ((-291 . -626) 95714) ((-290 . -626) 95696) ((-1255 . -1017) 95666) ((-48 . -943) T) ((-691 . -502) 95650) ((-259 . -1299) 95620) ((-258 . -1299) 95590) ((-1113 . -238) T) ((-1201 . -865) T) ((-1145 . -1047) T) ((-1071 . -34) T) ((-852 . -148) 95569) ((-852 . -146) 95548) ((-753 . -107) 95532) ((-625 . -133) T) ((-1203 . -1083) T) ((-495 . -1125) 95284) ((-1199 . -923) 95197) ((-1198 . -923) 95103) ((-1192 . -923) 94864) ((-889 . -465) T) ((-85 . -1242) T) ((-142 . -107) 94846) ((-1151 . -923) 94830) ((-728 . -389) 94814) ((-849 . -629) 94682) ((-1315 . -742) T) ((-1304 . -1083) T) ((-1284 . -102) T) ((-1277 . -102) T) ((-1145 . -558) T) ((-592 . -102) T) ((-130 . -503) 94664) ((-1197 . -972) 94633) ((-403 . -1081) 94617) ((-1150 . -972) 94584) ((-44 . -297) 94561) ((-130 . -626) 94528) ((-52 . -626) 94510) ((-217 . -868) T) ((-669 . -424) 94494) ((-1256 . -102) T) ((-1183 . -527) NIL) ((-678 . -25) T) ((-634 . -1081) 94478) ((-678 . -21) T) ((-986 . -662) 94388) ((-751 . -662) 94333) ((-731 . -662) 94305) ((-403 . -111) 94284) ((-225 . -262) 94268) ((-1079 . -1078) 94208) ((-1079 . -1125) T) ((-1029 . -1177) T) ((-834 . -1125) T) ((-466 . -662) 94123) ((-648 . -664) 94107) ((-634 . -111) 94086) ((-620 . -664) 94070) ((-355 . -1246) T) ((-609 . -102) T) ((-322 . -503) 94051) ((-599 . -132) T) ((-608 . -102) T) ((-427 . -1125) T) ((-397 . -1125) T) ((-322 . -626) 94017) ((-230 . -1125) 93995) ((-663 . -527) 93928) ((-645 . -527) 93772) ((-849 . -1074) 93751) ((-660 . -152) 93735) ((-355 . -569) T) ((-728 . -921) 93678) ((-563 . -232) 93628) ((-1284 . -295) 93594) ((-1277 . -295) 93560) ((-1105 . -301) 93511) ((-577 . -868) T) ((-500 . -864) T) ((-226 . -1137) T) ((-1256 . -295) 93477) ((-1236 . -506) 93443) ((-1029 . -38) 93393) ((-220 . -864) T) ((-431 . -662) 93352) ((-937 . -38) 93304) ((-859 . -810) 93283) ((-859 . -807) 93262) ((-859 . -742) 93241) ((-371 . -301) T) ((-365 . -301) T) ((-357 . -301) T) ((-171 . -465) 93172) ((-440 . -38) 93156) ((-226 . -23) T) ((-108 . -301) T) ((-420 . -810) 93135) ((-420 . -807) 93114) ((-420 . -742) T) ((-513 . -299) 93089) ((-490 . -1081) 93054) ((-674 . -132) T) ((-634 . -629) 93023) ((-1138 . -527) 92956) ((-348 . -132) T) ((-171 . -415) 92935) ((-495 . -733) 92877) ((-831 . -297) 92854) ((-490 . -111) 92810) ((-669 . -1083) T) ((-655 . -23) T) ((-1197 . -915) 92713) ((-1150 . -915) 92695) ((-832 . -1076) 92538) ((-1303 . -1108) T) ((-1265 . -465) 92469) ((-832 . -656) 92318) ((-1302 . -1108) T) ((-1112 . -132) T) ((-1079 . -733) 92260) ((-1052 . -527) 92193) ((-798 . -132) T) ((-796 . -132) T) ((-715 . -868) T) ((-584 . -465) T) ((-634 . -1074) T) ((-605 . -1125) T) ((-546 . -175) T) ((-474 . -132) T) ((-467 . -132) T) ((-391 . -238) T) ((-1024 . -1242) T) ((-45 . -1125) T) ((-397 . -733) 92163) ((-833 . -1125) T) ((-489 . -527) 92096) ((-476 . -527) 92029) ((-1317 . -629) 92011) ((-466 . -379) 91981) ((-45 . -623) 91960) ((-412 . -1242) T) ((-327 . -313) T) ((-1292 . -868) 91939) ((-843 . -238) 91918) ((-490 . -629) 91868) ((-1256 . -320) 91753) ((-686 . -626) 91715) ((-59 . -865) 91694) ((-1029 . -413) 91676) ((-561 . -626) 91658) ((-815 . -662) 91617) ((-831 . -617) 91594) ((-529 . -865) 91573) ((-509 . -865) 91552) ((-1024 . -1063) 91448) ((-40 . -1246) T) 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((-872 . -870) 90358) ((-1203 . -1125) T) ((-103 . -1242) T) ((-975 . -972) 90319) ((-833 . -733) 90261) ((-1256 . -1177) NIL) ((-494 . -972) 90206) ((-1087 . -144) T) ((-60 . -102) 90156) ((-44 . -626) 90138) ((-78 . -626) 90120) ((-363 . -664) 90065) ((-1304 . -1125) T) ((-524 . -865) T) ((-300 . -297) 90044) ((-355 . -1137) T) ((-306 . -1125) T) ((-1024 . -921) 90003) ((-306 . -623) 89982) ((-1316 . -629) 89931) ((-1284 . -38) 89828) ((-1277 . -38) 89669) ((-1256 . -38) 89465) ((-500 . -1083) T) ((-393 . -629) 89449) ((-220 . -1083) T) ((-355 . -23) T) ((-153 . -626) 89431) ((-849 . -811) 89410) ((-849 . -808) 89389) ((-1241 . -629) 89370) ((-609 . -38) 89343) ((-608 . -38) 89240) ((-888 . -569) T) ((-226 . -132) T) ((-330 . -1027) 89206) ((-79 . -626) 89188) ((-728 . -318) 89167) ((-305 . -742) 89069) ((-840 . -102) T) ((-882 . -860) T) ((-305 . -486) 89048) ((-1307 . -102) T) ((-40 . -375) T) ((-890 . -148) 89027) ((-498 . -662) 89009) ((-890 . -146) 88988) ((-1183 . -502) 88970) ((-1316 . -1074) T) ((-495 . -527) 88903) ((-655 . -132) T) ((-1171 . -1242) T) ((-987 . -626) 88885) ((-663 . -502) 88869) ((-645 . -502) 88800) ((-831 . -626) 88493) ((-48 . -27) T) ((-1203 . -733) 88390) ((-975 . -915) 88369) ((-669 . -1125) T) ((-879 . -878) T) ((-449 . -376) 88343) ((-747 . -662) 88253) ((-494 . -915) 88228) ((-1127 . -102) T) ((-995 . -1125) T) ((-882 . -1125) T) ((-832 . -320) 88215) ((-546 . -540) T) ((-546 . -589) T) ((-1312 . -394) 88187) ((-710 . -868) T) ((-1079 . -527) 88120) ((-1184 . -297) 88096) ((-246 . -273) 88065) ((-246 . -233) 88034) ((-259 . -1076) 87935) ((-258 . -1076) 87836) ((-1304 . -733) 87806) ((-1191 . -93) T) ((-1019 . -93) T) ((-833 . -174) 87785) ((-259 . -656) 87707) ((-258 . -656) 87629) ((-1239 . -503) 87606) ((-591 . -1242) T) ((-230 . -527) 87539) ((-634 . -811) 87518) ((-634 . -808) 87497) ((-1239 . -626) 87409) ((-225 . -1242) T) ((-691 . -626) 87341) ((-1199 . -662) 87251) ((-1182 . -1035) 87235) ((-966 . -102) 87165) ((-363 . -742) T) ((-879 . -626) 87147) ((-1198 . -662) 87029) ((-1192 . -662) 86866) ((-1151 . -662) 86776) ((-1256 . -413) 86728) ((-1138 . -502) 86712) ((-60 . -320) 86650) ((-342 . -102) T) ((-1236 . -21) T) ((-1236 . -25) T) ((-40 . -1137) T) ((-727 . -21) T) ((-640 . -626) 86632) ((-528 . -334) 86611) ((-727 . -25) T) ((-452 . -102) T) ((-108 . -297) NIL) ((-944 . -1137) T) ((-40 . -23) T) ((-787 . -1137) T) ((-577 . -1246) T) ((-508 . -1246) T) ((-1029 . -273) 86593) ((-330 . -626) 86575) ((-1029 . -233) 86557) ((-171 . -167) 86541) ((-593 . -569) T) ((-577 . -569) T) ((-508 . -569) T) ((-787 . -23) T) ((-1276 . -148) 86520) ((-1276 . -146) 86499) ((-1184 . -617) 86475) ((-1255 . -146) 86400) ((-1052 . -502) 86384) ((-1249 . -1242) T) ((-1255 . -148) 86309) ((-1307 . -1313) 86288) ((-889 . -915) NIL) ((-489 . -502) 86272) ((-476 . -502) 86256) ((-536 . -34) T) ((-669 . -733) 86226) ((-1284 . -923) 86139) ((-1277 . -923) 86045) ((-1256 . -923) 85806) ((-112 . -992) T) ((-1203 . -174) 85757) ((-678 . -865) 85736) ((-377 . -102) T) ((-608 . -923) 85649) ((-246 . -244) 85628) ((-259 . -102) T) ((-258 . -102) T) ((-1265 . -972) 85597) ((-251 . -865) 85576) ((-1049 . -868) T) ((-832 . -38) 85425) ((-45 . -527) 85217) ((-1183 . -297) 85167) ((-216 . -1125) T) ((-1175 . -1125) T) ((-890 . -238) 85118) ((-1175 . -623) 85097) ((-599 . -25) T) ((-599 . -21) T) ((-1127 . -320) 85035) ((-986 . -424) 85019) ((-715 . -1246) T) ((-645 . -297) 84972) ((-1112 . -654) 84920) ((-928 . -1125) T) ((-798 . -654) 84868) ((-796 . -654) 84816) ((-355 . -132) T) ((-300 . -626) 84798) ((-888 . -1137) T) ((-715 . -569) T) ((-130 . -629) 84780) ((-467 . -654) 84728) ((-171 . -915) 84649) ((-928 . -926) 84633) ((-391 . -465) T) ((-500 . -1125) T) ((-966 . -320) 84571) ((-717 . -664) 84543) ((-562 . -860) T) ((-220 . -1125) T) ((-327 . -943) 84522) ((-324 . -943) T) ((-324 . -836) NIL) ((-403 . -736) T) ((-888 . -23) T) ((-117 . -664) 84509) ((-487 . -146) 84488) ((-431 . -424) 84472) ((-487 . -148) 84451) ((-110 . -502) 84433) ((-322 . -629) 84414) ((-2 . -626) 84396) ((-188 . -102) T) ((-1183 . -19) 84378) ((-1183 . -617) 84353) ((-674 . -21) T) ((-674 . -25) T) ((-606 . -1169) T) ((-1138 . -297) 84330) ((-348 . -25) T) ((-348 . -21) T) ((-908 . -1242) T) ((-904 . -1242) T) ((-1314 . -1081) 84314) ((-246 . -662) 84093) ((-508 . -375) T) ((-1312 . -1081) 84077) ((-1307 . -38) 84047) ((-1276 . -1227) 84013) ((-1276 . -1230) 83979) ((-1265 . -915) 83882) ((-1197 . -1076) 83705) ((-1167 . -1242) T) ((-1150 . -1076) 83548) ((-872 . -1076) 83532) ((-645 . -617) 83507) ((-1276 . -95) 83473) ((-1276 . -238) 83425) ((-1259 . -102) 83403) ((-1197 . -656) 83232) ((-1150 . -656) 83081) ((-872 . -656) 83051) ((-1256 . -233) 83003) ((-1112 . -25) T) ((-562 . -1125) T) ((-1112 . -21) T) ((-986 . -1083) T) ((-544 . -808) T) ((-544 . -811) T) ((-118 . -1246) T) ((-884 . -1242) T) ((-636 . -569) T) ((-798 . -25) T) ((-798 . -21) T) ((-796 . -21) T) ((-796 . -25) T) ((-751 . -1083) T) ((-731 . -1083) T) ((-686 . -1081) 82987) ((-530 . -1108) T) ((-474 . -25) T) ((-118 . -569) T) ((-474 . -21) T) ((-467 . -25) T) ((-467 . -21) T) ((-1256 . -273) 82939) ((-1176 . -93) T) ((-1167 . -1063) 82835) ((-833 . -301) 82814) ((-1255 . -1227) 82780) ((-839 . -1125) T) ((-989 . -992) T) ((-686 . -111) 82759) ((-630 . -1242) T) ((-306 . -527) 82551) ((-1255 . -1230) 82517) ((-1255 . -238) 82376) ((-1250 . -380) T) ((-259 . -320) 82314) ((-258 . -320) 82252) ((-1247 . -860) T) ((-1184 . -627) NIL) ((-1184 . -626) 82234) ((-1167 . -389) 82218) ((-1145 . -836) T) ((-1145 . -943) T) ((-96 . -93) T) ((-1138 . -617) 82195) ((-1105 . -627) 82179) ((-1105 . -626) 82161) ((-1029 . -662) 82111) ((-937 . -662) 82048) ((-831 . -299) 82025) ((-497 . -626) 81957) ((-621 . -152) 81904) ((-500 . -733) 81854) ((-431 . -1083) T) ((-495 . -502) 81838) ((-440 . -662) 81797) ((-338 . -865) 81776) ((-351 . -664) 81750) ((-50 . -21) T) ((-50 . -25) T) ((-220 . -733) 81700) ((-171 . -740) 81671) ((-176 . -664) 81603) ((-594 . -21) T) ((-594 . -25) T) ((-531 . -25) T) ((-531 . -21) T) ((-488 . -152) 81553) ((-1086 . -626) 81535) ((-1018 . -102) T) ((-880 . -102) T) ((-832 . -923) 81435) ((-815 . -424) 81398) ((-40 . -132) T) ((-715 . -375) T) ((-717 . -742) T) ((-717 . -810) T) ((-717 . -807) T) ((-214 . -916) T) ((-593 . -1137) T) ((-577 . -1137) T) ((-508 . -1137) T) ((-371 . -626) 81380) ((-365 . -626) 81362) ((-357 . -626) 81344) ((-66 . -409) T) ((-66 . -408) T) ((-108 . -627) 81274) ((-108 . -626) 81216) ((-213 . -916) T) ((-981 . -152) 81200) ((-787 . -132) T) ((-686 . -629) 81118) ((-135 . -742) T) ((-117 . -742) T) ((-1276 . -35) 81084) ((-1079 . -502) 81068) ((-593 . -23) T) ((-577 . -23) T) ((-508 . -23) T) ((-1255 . -95) 81034) ((-1255 . -35) 81000) ((-1197 . -102) T) ((-1150 . -102) T) ((-872 . -102) T) ((-230 . -502) 80984) ((-1314 . -111) 80963) ((-1312 . -111) 80942) ((-44 . -1081) 80926) ((-1315 . -1242) T) ((-1314 . -629) 80872) ((-1314 . -1074) T) ((-1312 . -629) 80801) 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. -465) T) ((-928 . -297) 65638) ((-831 . -380) 65617) ((-523 . -522) 65596) ((-521 . -522) 65575) ((-890 . -915) 65496) ((-500 . -297) NIL) ((-495 . -299) 65473) ((-431 . -301) T) ((-366 . -132) T) ((-220 . -297) NIL) ((-710 . -506) NIL) ((-99 . -1137) T) ((-40 . -235) 65404) ((-171 . -38) 65232) ((-975 . -923) 65213) ((-1276 . -998) 65175) ((-1255 . -998) 65144) ((-1172 . -320) 65082) ((-494 . -923) 65059) ((-1138 . -1074) 65037) ((-933 . -415) T) ((-653 . -522) 65009) ((-1278 . -569) T) ((-1175 . -617) 64988) ((-112 . -865) T) ((-1088 . -502) 64919) ((-593 . -21) T) ((-593 . -25) T) ((-577 . -21) T) ((-577 . -25) T) ((-508 . -25) T) ((-508 . -21) T) ((-1265 . -1177) 64897) ((-1138 . -239) 64849) ((-48 . -132) T) ((-1223 . -102) T) ((-246 . -1125) 64601) ((-889 . -413) 64578) ((-1113 . -102) T) ((-1101 . -102) T) ((-912 . -868) T) ((-621 . -102) T) ((-488 . -102) T) ((-1265 . -38) 64407) ((-873 . -38) 64377) ((-1059 . -1076) 64351) ((-747 . -174) 64262) ((-669 . -626) 64244) ((-661 . 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. -320) 20349) ((-496 . -1125) T) ((-1150 . -627) 20097) ((-1059 . -174) T) ((-966 . -299) 20074) ((-221 . -1125) T) ((-872 . -626) 20056) ((-621 . -527) 19839) ((-81 . -629) 19780) ((-834 . -1063) 19764) ((-488 . -527) 19556) ((-849 . -868) 19535) ((-986 . -742) T) ((-751 . -742) T) ((-731 . -742) T) ((-363 . -1137) T) ((-1204 . -626) 19517) ((-226 . -102) T) ((-495 . -389) 19486) ((-528 . -1125) T) ((-523 . -1125) T) ((-521 . -1125) T) ((-815 . -664) 19460) ((-1049 . -465) T) ((-981 . -527) 19393) ((-363 . -23) T) ((-648 . -132) T) ((-620 . -132) T) ((-366 . -465) T) ((-246 . -380) 19372) ((-391 . -174) T) ((-1276 . -1083) T) ((-1255 . -1083) T) ((-228 . -1027) T) ((-832 . -629) 19109) ((-715 . -400) T) ((-431 . -742) T) ((-717 . -1246) T) ((-1167 . -654) 19057) ((-653 . -1125) T) ((-655 . -102) T) ((-593 . -887) 19041) ((-1307 . -1081) 19025) ((-1184 . -1218) 19001) ((-717 . -569) T) ((-127 . -1125) 18979) ((-730 . -1125) T) ((-674 . -38) 18949) ((-495 . -921) 18881) ((-256 . -1125) 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((-1307 . -629) 17388) ((-341 . -1242) T) ((-487 . -1083) T) ((-1248 . -1125) T) ((-1256 . -808) NIL) ((-1256 . -811) NIL) ((-1024 . -865) 17367) ((-884 . -21) T) ((-854 . -1125) T) ((-835 . -626) 17349) ((-884 . -25) T) ((-815 . -742) T) ((-653 . -733) 17333) ((-176 . -1246) T) ((-594 . -38) 17298) ((-531 . -38) 17263) ((-399 . -626) 17245) ((-344 . -102) T) ((-335 . -626) 17227) ((-171 . -297) 17185) ((-1250 . -868) T) ((-63 . -1242) T) ((-112 . -102) T) ((-890 . -1125) T) ((-525 . -1242) T) ((-176 . -569) T) ((-730 . -733) 17155) ((-305 . -132) 17038) ((-228 . -626) 17020) ((-228 . -627) 16950) ((-1028 . -654) 16889) ((-1307 . -1074) T) ((-1203 . -1242) T) ((-1145 . -148) T) ((-645 . -1218) 16864) ((-747 . -932) 16843) ((-606 . -34) T) ((-663 . -107) 16827) ((-645 . -107) 16773) ((-1304 . -1242) T) ((-636 . -915) 16694) ((-1265 . -297) 16621) ((-747 . -664) 16510) ((-306 . -1242) T) ((-1203 . -1063) 16406) ((-966 . -631) 16383) ((-590 . -589) T) ((-590 . -540) T) ((-542 . -540) T) 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-1230) 14519) ((-467 . -923) 14496) ((-327 . -982) 14475) ((-135 . -1137) T) ((-117 . -1137) T) ((-995 . -1242) T) ((-882 . -1242) T) ((-717 . -23) T) ((-669 . -1242) T) ((-615 . -1290) 14459) ((-615 . -1125) 14409) ((-544 . -868) T) ((-513 . -868) T) ((-327 . -95) 14388) ((-91 . -527) 14321) ((-176 . -375) T) ((-259 . -629) 14119) ((-258 . -629) 13917) ((-327 . -35) 13896) ((-621 . -502) 13830) ((-135 . -23) T) ((-117 . -23) T) ((-989 . -102) T) ((-734 . -1125) T) ((-488 . -502) 13767) ((-420 . -654) 13715) ((-669 . -1063) 13611) ((-981 . -502) 13595) ((-367 . -1083) T) ((-364 . -1083) T) ((-356 . -1083) T) ((-274 . -1083) T) ((-254 . -1083) T) ((-889 . -627) NIL) ((-889 . -626) 13577) ((-1303 . -503) 13558) ((-1302 . -503) 13539) ((-1315 . -21) T) ((-1303 . -626) 13505) ((-1302 . -626) 13471) ((-584 . -1027) T) ((-747 . -742) T) ((-1315 . -25) T) ((-259 . -1074) 13449) ((-258 . -1074) 13427) ((-72 . -1242) T) ((-1167 . -235) 13372) ((-259 . -239) 13324) ((-258 . -239) 13276) ((-1145 . -238) T) ((-40 . -102) T) ((-933 . -1083) T) ((-710 . -915) NIL) ((-1206 . -102) T) ((-129 . -502) 13258) ((-1199 . -742) T) ((-1198 . -742) T) ((-1192 . -742) T) ((-1192 . -807) NIL) ((-1192 . -810) NIL) ((-977 . -102) T) ((-944 . -102) T) ((-888 . -1076) 13245) ((-1151 . -742) T) ((-787 . -102) T) ((-688 . -102) T) ((-888 . -656) 13232) ((-559 . -626) 13214) ((-487 . -1125) T) ((-351 . -1137) T) ((-176 . -1137) T) ((-330 . -943) 13193) ((-1276 . -733) 13034) ((-890 . -174) T) ((-1255 . -733) 12848) ((-859 . -21) 12800) ((-859 . -25) 12752) ((-251 . -1174) 12736) ((-127 . -527) 12669) ((-420 . -25) T) ((-420 . -21) T) ((-351 . -23) T) ((-171 . -627) 12435) ((-171 . -626) 12417) ((-176 . -23) T) ((-660 . -299) 12394) ((-533 . -34) T) ((-919 . -626) 12376) ((-89 . -1242) T) ((-857 . -626) 12358) ((-824 . -626) 12340) ((-785 . -626) 12322) ((-693 . -626) 12304) ((-246 . -664) 12137) ((-630 . -113) T) ((-1201 . -1125) T) ((-1197 . -1081) 11960) ((-216 . -1242) T) ((-1175 . -1242) T) ((-1150 . -1081) 11803) ((-872 . -1081) 11787) ((-1107 . -868) T) ((-1259 . -631) 11771) ((-1197 . -111) 11580) ((-1150 . -111) 11409) ((-872 . -111) 11388) ((-1249 . -865) T) ((-1265 . -627) NIL) ((-1265 . -626) 11370) ((-355 . -1177) T) ((-873 . -626) 11352) ((-1101 . -297) 11331) ((-1236 . -662) 11241) ((-80 . -1242) T) ((-928 . -1242) T) ((-1228 . -527) 11174) ((-1029 . -932) NIL) ((-1112 . -273) 11158) ((-621 . -297) 11134) ((-1112 . -233) 11118) ((-500 . -1242) T) ((-584 . -626) 11100) ((-488 . -297) 11079) ((-1029 . -664) 11029) ((-530 . -93) T) ((-1028 . -235) 10960) ((-220 . -1242) T) ((-981 . -297) 10912) ((-888 . -102) T) ((-300 . -943) T) ((-833 . -318) 10891) ((-798 . -273) 10875) ((-798 . -233) 10859) ((-937 . -664) 10811) ((-727 . -662) 10761) ((-710 . -740) 10728) ((-648 . -21) T) ((-648 . -25) T) ((-620 . -21) T) ((-560 . -102) T) ((-355 . -38) 10693) ((-500 . -903) 10675) ((-500 . -905) 10657) ((-487 . -733) 10498) ((-64 . -1242) T) ((-220 . -903) 10480) ((-220 . -905) 10462) ((-620 . -25) T) ((-440 . -664) 10436) ((-1197 . -629) 10205) ((-500 . -1063) 10165) ((-890 . -527) 10077) ((-1150 . -629) 9869) ((-872 . -629) 9787) ((-220 . -1063) 9747) ((-246 . -34) T) ((-1025 . -1125) 9725) ((-593 . -1076) 9712) ((-577 . -1076) 9699) ((-508 . -1076) 9664) ((-1276 . -174) 9595) ((-1255 . -174) 9526) ((-593 . -656) 9513) ((-577 . -656) 9500) ((-508 . -656) 9465) ((-728 . -146) 9444) ((-728 . -148) 9423) ((-130 . -868) T) ((-717 . -132) T) ((-562 . -1242) T) ((-137 . -478) 9400) ((-1172 . -626) 9332) ((-674 . -672) 9316) ((-129 . -297) 9266) ((-117 . -132) T) ((-490 . -1246) T) ((-621 . -617) 9242) ((-488 . -617) 9221) ((-610 . -1125) T) ((-348 . -347) 9190) ((-598 . -1125) T) ((-549 . -1125) T) ((-490 . -569) T) ((-1197 . -1074) T) ((-1150 . -1074) T) ((-872 . -1074) T) ((-839 . -1242) T) ((-246 . -810) 9169) ((-246 . -809) 9148) ((-1197 . -337) 9125) ((-246 . -742) 9103) ((-981 . -19) 9087) ((-500 . -389) 9069) ((-500 . -350) 9051) ((-1150 . -337) 9023) ((-366 . -1299) 9000) ((-220 . -389) 8982) ((-220 . -350) 8964) ((-981 . -617) 8941) ((-1197 . -239) T) ((-1288 . -1125) T) ((-1214 . -1125) T) ((-680 . -1125) T) ((-661 . -1125) T) ((-1112 . -261) 8878) ((-599 . -662) 8838) ((-367 . -1125) T) ((-364 . -1125) T) ((-356 . -1125) T) ((-274 . -1125) T) ((-254 . -1125) T) ((-84 . -1242) T) ((-217 . -102) T) ((-128 . -102) 8788) ((-122 . -102) 8738) ((-1255 . -527) 8598) ((-1214 . -623) 8577) ((-1166 . -1125) T) ((-1140 . -629) 8558) ((-1105 . -943) 8509) ((-492 . -1125) T) ((-1029 . -810) T) ((-1029 . -807) T) ((-492 . -623) 8488) ((-259 . -811) 8467) ((-259 . -808) 8446) ((-258 . -811) 8425) ((-40 . -1177) NIL) ((-258 . -808) 8404) ((-1029 . -742) T) ((-129 . -19) 8386) ((-996 . -810) T) ((-715 . -1076) 8351) ((-937 . -742) T) ((-933 . -1125) T) ((-911 . -626) 8333) ((-129 . -617) 8308) ((-715 . -656) 8273) ((-91 . -502) 8257) ((-500 . -921) NIL) ((-890 . -301) T) ((-228 . -1081) 8222) ((-852 . -297) 8201) ((-220 . -921) NIL) ((-849 . -1137) 8180) ((-59 . -1125) 8130) ((-532 . -1125) 8108) ((-529 . -1125) 8058) ((-510 . -1125) 8036) ((-509 . -1125) 7986) ((-593 . -102) T) ((-577 . -102) T) ((-508 . -102) T) ((-487 . -174) 7917) ((-371 . -943) T) ((-365 . -943) T) ((-357 . -943) T) ((-228 . -111) 7873) ((-849 . -23) 7825) ((-440 . -742) T) ((-108 . -943) T) ((-40 . -38) 7770) ((-108 . -836) T) ((-594 . -361) T) ((-531 . -361) T) ((-674 . -662) 7729) ((-327 . -465) 7708) ((-324 . -465) T) ((-615 . -527) 7641) ((-420 . -235) 7586) ((-351 . -132) T) ((-176 . -132) T) ((-305 . -25) 7450) ((-305 . -21) 7333) ((-45 . -1218) 7312) ((-66 . -626) 7294) ((-55 . -102) T) ((-348 . -662) 7276) ((-1293 . -102) T) ((-1292 . -102) 7206) ((-1284 . -664) 7131) ((-1277 . -664) 7028) ((-45 . -107) 6978) ((-835 . -629) 6962) ((-1256 . -664) 6814) ((-1256 . -932) NIL) ((-1247 . -1242) T) ((-1223 . -626) 6796) ((-1215 . -102) T) ((-1127 . -438) 6780) ((-1127 . -380) 6759) ((-399 . -629) 6743) ((-335 . -629) 6727) ((-1121 . -93) T) ((-1112 . -662) 6637) ((-1088 . -1242) T) ((-1087 . -1081) 6624) ((-1087 . -111) 6609) ((-975 . -111) 6438) ((-975 . -1081) 6281) ((-798 . -662) 6191) ((-796 . -662) 6101) ((-680 . -733) 6085) ((-636 . -1076) 6072) ((-636 . -656) 6059) ((-561 . -868) T) ((-494 . -1081) 5902) ((-490 . -375) T) ((-474 . -662) 5858) ((-467 . -662) 5768) ((-228 . -629) 5718) ((-367 . -733) 5670) ((-364 . -733) 5622) ((-118 . -1076) 5567) ((-356 . -733) 5519) ((-274 . -733) 5368) ((-254 . -733) 5217) ((-1115 . -93) T) ((-1098 . -93) T) ((-118 . -656) 5162) ((-1091 . -93) T) ((-966 . -667) 5146) ((-1082 . -1125) 5124) ((-494 . -111) 4953) ((-1061 . -93) T) ((-1044 . -93) T) ((-966 . -385) 4937) ((-255 . -102) T) ((-986 . -47) 4916) ((-74 . -626) 4898) ((-728 . -238) T) ((-726 . -102) T) ((-715 . -102) T) ((-1 . -1125) T) ((-634 . -1137) T) ((-1113 . -626) 4880) ((-639 . -93) T) ((-1101 . -626) 4862) ((-933 . -733) 4827) ((-127 . -502) 4811) ((-496 . -93) T) ((-634 . -23) T) ((-403 . -23) T) ((-87 . -1242) T) ((-221 . -93) T) ((-621 . -626) 4793) ((-621 . -627) NIL) ((-488 . -627) NIL) ((-488 . -626) 4775) ((-363 . -25) T) ((-363 . -21) T) ((-50 . -662) 4734) ((-524 . -1125) T) ((-520 . -1125) T) ((-122 . -320) 4672) ((-128 . -320) 4610) ((-609 . -664) 4584) ((-608 . -664) 4509) ((-594 . -662) 4459) ((-228 . -1074) T) ((-531 . -662) 4389) ((-1087 . -629) 4361) ((-391 . -1027) T) ((-228 . -249) T) ((-228 . -239) T) ((-866 . -503) 4345) ((-1087 . -631) 4326) ((-981 . -627) 4287) ((-981 . -626) 4199) ((-975 . -629) 3988) ((-866 . -626) 3936) ((-888 . -38) 3923) ((-729 . -629) 3873) ((-1276 . -301) 3824) ((-1255 . -301) 3775) ((-494 . -629) 3560) ((-1145 . -465) T) ((-515 . -865) T) ((-327 . -1164) 3539) ((-1126 . -1242) T) ((-1024 . -148) 3518) ((-1024 . -146) 3497) ((-508 . -320) 3484) ((-1209 . -626) 3466) ((-306 . -1218) 3445) ((-1208 . -626) 3427) ((-1160 . -1242) T) ((-1207 . -626) 3409) ((-889 . -1081) 3354) ((-490 . -1137) T) ((-140 . -851) 3336) ((-115 . -851) 3317) ((-1228 . -502) 3301) ((-1087 . -1074) T) ((-636 . -102) T) ((-986 . -1242) T) ((-975 . -1074) T) ((-259 . -380) 3280) ((-258 . -380) 3259) ((-889 . -111) 3188) ((-306 . -107) 3138) ((-131 . -626) 3120) ((-129 . -627) NIL) ((-129 . -626) 3064) ((-118 . -102) T) ((-751 . -1242) T) ((-731 . -1242) T) ((-490 . -23) T) ((-466 . -1242) T) ((-494 . -1074) T) ((-1087 . -239) T) ((-975 . -337) 3033) ((-40 . -923) 2942) ((-494 . -337) 2899) ((-367 . -174) T) ((-364 . -174) T) ((-356 . -174) T) ((-274 . -174) 2810) ((-254 . -174) 2721) ((-986 . -1063) 2617) ((-530 . -503) 2598) ((-751 . -1063) 2569) ((-530 . -626) 2535) ((-431 . -1242) T) ((-1130 . -102) T) ((-1117 . -626) 2494) ((-1059 . -626) 2476) ((-710 . -1076) 2426) ((-1305 . -152) 2410) ((-1303 . -629) 2391) ((-1302 . -629) 2372) ((-1297 . -626) 2354) ((-1284 . -742) T) ((-710 . -656) 2304) ((-1277 . -742) T) ((-1256 . -807) NIL) ((-1256 . -810) NIL) ((-171 . -1081) 2214) ((-933 . -174) T) ((-889 . -629) 2144) ((-1256 . -742) T) ((-1028 . -354) 2118) ((-226 . -662) 2070) ((-1025 . -527) 2003) ((-859 . -865) 1982) ((-577 . -1177) T) ((-487 . -301) 1933) ((-609 . -742) T) ((-373 . -626) 1915) ((-333 . -626) 1897) ((-431 . -1063) 1793) ((-608 . -742) T) ((-420 . -865) 1744) ((-171 . -111) 1640) ((-849 . -132) 1592) ((-1292 . -320) 1530) ((-753 . -152) 1514) ((-987 . -868) 1413) ((-831 . -868) 1364) ((-500 . -318) T) ((-391 . -626) 1331) ((-533 . -1035) 1315) ((-391 . -627) 1229) ((-220 . -318) T) ((-142 . -152) 1211) ((-730 . -297) 1190) ((-500 . -1047) T) ((-593 . -38) 1177) ((-577 . -38) 1164) ((-508 . -38) 1129) ((-655 . -662) 1098) ((-220 . -1047) T) ((-889 . -1074) T) ((-852 . -626) 1080) ((-843 . -626) 1062) ((-841 . -626) 1044) ((-832 . -932) 1023) ((-1316 . -1137) T) ((-323 . -1242) T) ((-1265 . -1081) 846) ((-873 . -1081) 830) ((-889 . -249) T) ((-889 . -239) NIL) ((-705 . -1242) T) ((-1316 . -23) T) ((-832 . -664) 719) ((-563 . -1242) T) ((-431 . -350) 703) ((-584 . -1081) 690) ((-1265 . -111) 499) ((-717 . -654) 481) ((-873 . -111) 460) ((-393 . -23) T) ((-171 . -629) 238) ((-1214 . -527) 30) ((-894 . -1125) T) ((-697 . -1125) T) ((-692 . -1125) T) ((-678 . -1125) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 8a7823a2..8fd5f037 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3486967785)            
-(4469 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3487133925)            
+(4473 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -61,7 +61,7 @@
  |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType|
  |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType|
  |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage|
- |d03eefAnnaType| |d03fafAnnaType| |DataArray| |Database|
+ |d03eefAnnaType| |d03fafAnnaType| |DataArray| |Database| |DualBasis|
  |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion|
  |DefinitionAst| |ElementaryFunctionDefiniteIntegration|
  |RationalFunctionDefiniteIntegration| |DegreeReductionPackage|
@@ -230,11 +230,11 @@
  |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory|
  |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&|
  |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage|
- |RationalFunctionLimitPackage| |LinearDependence| |LinearElement|
- |LinearlyExplicitRingOver| |LinearSet| |ListToMap| |ListFunctions2|
- |ListFunctions3| |List| |Literal| |LeftLinearSet|
- |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&|
- |LinearAggregate| |ElementaryFunctionLODESolver|
+ |RationalFunctionLimitPackage| |LinearBasis| |LinearDependence|
+ |LinearElement| |LinearlyExplicitRingOver| |LinearForm| |LinearSet|
+ |ListToMap| |ListFunctions2| |ListFunctions3| |List| |Literal|
+ |LeftLinearSet| |ListMultiDictionary| |LeftModule| |ListMonoidOps|
+ |LinearAggregate&| |LinearAggregate| |ElementaryFunctionLODESolver|
  |LinearOrdinaryDifferentialOperator1|
  |LinearOrdinaryDifferentialOperator2|
  |LinearOrdinaryDifferentialOperatorCategory&|
@@ -488,662 +488,663 @@
  |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram|
  |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
  |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |computeCycleEntry| |stoseIntegralLastSubResultant|
- |lambert| |insertTop!| |arg2| |f02agf| |stronglyReduce|
- |viewWriteAvailable| |string| |trunc| |integralAtInfinity?|
- |makeResult| |upperCase!| |minimalPolynomial|
- |semiResultantEuclidean2| |subResultantGcdEuclidean| |showAllElements|
- |nand| |readLineIfCan!| |exportedOperators| |writable?| |say|
- |nullSpace| |scalarMatrix| |constantToUnaryFunction| |imagE|
- |allRootsOf| |solveLinear| |conditions| |matrixConcat3D|
- |setVariableOrder| |linearAssociatedExp| |exponential1|
- |basisOfCommutingElements| |palgRDE0| |d02bbf|
- |solveLinearPolynomialEquation| |getIdentifier| |complementaryBasis|
- |title| |f02aef| |match| |OMopenString| |insertMatch|
- |primitiveElement| |reset| |raisePolynomial| |birth| |swapColumns!|
- |rk4a| |arguments| |dot| |maximumExponent| |e02ajf| |mainContent|
- |univariatePolynomialsGcds| |digamma| |inc| |permutationGroup|
- |twoFactor| |setLabelValue| |dequeue!| |backOldPos| |idealiserMatrix|
- |lighting| |s18acf| |lex| |leadingSupport| |write| |isTimes|
- |showClipRegion| |testModulus| |hessian| |denominator| |e| |iilog|
- |isNot| |save| |f02akf| |adaptive| |s17acf| |critT|
- |extractSplittingLeaf| |e01bhf| |split| |ddFact| |mapExpon| |nothing|
- |diff| |radicalEigenvalues| |cycles| |mindegTerm| |e04ucf| |argscript|
- |iflist2Result| |pmintegrate| |f01rdf| |iiacsc| |binding| |signAround|
- |var1Steps| |reseed| |leftTrace| |beauzamyBound| |rightDiscriminant|
- |trailingCoefficient| |maxColIndex| |indices| |complete| |f04adf|
- |top| |nextIrreduciblePoly| |Vectorise| |safetyMargin| |divideIfCan!|
- |leastPower| |pow| |linearDependenceOverZ| |continue| |e02akf|
- |fortranLogical| |zeroDim?| |generalizedEigenvectors| |e01sff|
- |readUInt8!| |linearDependence| |palginfieldint| |content|
- |setStatus!| |sn| |extensionDegree| |se2rfi| |revert| |principal?|
- |integralMatrixAtInfinity| |parts| |f02aaf| |splitDenominator|
- |enterPointData| |shiftLeft| |printTypes| |typeForm| |mdeg| |reopen!|
- |pureLex| |palgextint0| |d01aqf| ** |hash| |functionIsFracPolynomial?|
- |thetaCoord| |horizConcat| |s18adf| |newLine| |universe|
- |nonLinearPart| |squareFreeLexTriangular| |doubleRank|
- |numberOfComposites| |count| |linearElement| |viewpoint|
- |separateFactors| |createThreeSpace| |singleFactorBound| |datalist|
- |makeTerm| |fortranComplex| |lagrange| |bandedHessian| |determinant|
- |divisor| |cdr| |copy!| |f04atf| |rightRecip| |primlimintfrac|
- |bipolar| |OMputBVar| |radPoly| |getDatabase| |dictionary|
- |ip4Address| |squareTop| |laguerre| |Frobenius| |constant|
- |getGoodPrime| |green| |weierstrass| |tablePow| |ParCondList| |entry?|
- |dimensionsOf| |iifact| |commutativeEquality| |chebyshevT|
- |integralBasisAtInfinity| |returnTypeOf| |mantissa| |OMreadStr|
- |endSubProgram| |multiplyExponents| |outputList| |traceMatrix|
- |chiSquare1| |leftOne| |addBadValue| |degreeSubResultantEuclidean|
- |stripCommentsAndBlanks| |lazyEvaluate| |sts2stst| |makeFR| |sign|
- |c06fpf| |romberg| |numberOfFactors| |printHeader| |primaryDecomp|
- |rank| |clipBoolean| |RittWuCompare| |c06gcf| |e01saf| |lexGroebner|
- |extendIfCan| |asimpson| |maxdeg| |brillhartIrreducible?| |implies|
- |showTheRoutinesTable| |check| |quotedOperators| |SturmHabicht|
- |completeEchelonBasis| |subResultantGcd| |OMsend|
- |monicDecomposeIfCan| |neglist| |open?| |morphism| |basisOfCentroid|
- |legendre| |reflect| |OMputEndBVar| |sorted?| |resetNew| |component|
- F2FG |decreasePrecision| |f02ajf| |subResultantChain|
- |rightRegularRepresentation| |chebyshevU| |logical?| |red| GF2FG
- |normalizedDivide| |checkPrecision| |hasPredicate?| |noKaratsuba|
- |fortranLiteral| |firstDenom| |quadraticNorm| |diagonals| |heapSort|
- |f01qdf| |cPower| |commonDenominator| |arrayStack| |isOp| |separant|
- |nthr| |quartic| |leader| |e02bdf| |integralRepresents| |getBadValues|
- |dual| UP2UTS |nthRootIfCan| |selectFiniteRoutines| |frst| |swapRows!|
- |clip| |oddInfiniteProduct| |setEmpty!| |solid| |max| |rename!|
- |integralBasis| |binarySearchTree| |categories|
- |wordsForStrongGenerators| |cfirst| |coerceS| |lexico| |padicFraction|
- |numer| |laplace| |lists| |retractIfCan| |usingTable?| |trivialIdeal?|
- |member?| |possiblyInfinite?| |fintegrate| |associatorDependence|
- |changeMeasure| |totalDifferential| |child?| |cRationalPower| |denom|
- |s14baf| |complexEigenvalues| |extension|
- |semiResultantReduitEuclidean| |elementary| |rightTrace| |polar|
- |startTableInvSet!| |gcdcofact| |legendreP| |blue| |mathieu11|
- |atrapezoidal| |OMgetObject| |algint| |trigs2explogs|
- |createMultiplicationMatrix| |pushucoef| |createPrimitiveNormalPoly|
- |setMaxPoints| |nsqfree| |pi| |in?| |closeComponent|
- |absolutelyIrreducible?| |secIfCan| |euclideanGroebner| |closedCurve?|
- |collectUnder| |toseLastSubResultant| |infinity| |rename| |jacobi|
- |complexNumericIfCan| |s21baf| |clearDenominator| |critMonD1|
- |genericLeftDiscriminant| |concat| |step| |cyclotomicFactorization|
- |numericalIntegration| |iisqrt3| |factorSquareFree| |exprToXXP|
- |clipParametric| |unaryFunction| |nextPrimitiveNormalPoly|
- |semiResultantEuclideannaif| |range| |unrankImproperPartitions0|
- |droot| |roughSubIdeal?| |bernoulliB| |continuedFraction|
- |mainPrimitivePart| |coordinate| |internalIntegrate|
- |nextLatticePermutation| |hdmpToP| |removeIrreducibleRedundantFactors|
- |useEisensteinCriterion?| |denomRicDE| |kernel| |node?| |discriminant|
- |simpleBounds?| |rightTraceMatrix| |pquo| |internalInfRittWu?| |init|
- |nextSublist| |key?| |f04mbf| |list| |bumptab1| |ptree|
- |topFortranOutputStack| |removeConstantTerm| |viewport2D| |number?|
- |Beta| |lhs| |balancedBinaryTree| |showFortranOutputStack| |rk4|
- |draw| |callForm?| |polyRDE| |leadingBasisTerm| |s15adf| |clearCache|
- |bringDown| |fullDisplay| |rhs| |f01ref| |nthExpon| |iteratedInitials|
- |linears| |rootProduct| |deleteRoutine!| |SturmHabichtSequence|
- |derivative| |adaptive3D?| |isAnd| |constantKernel| |qroot|
- |integral?| |semiResultantEuclidean1| |ratDsolve| |mainVariables|
- |currentEnv| |systemSizeIF| |aLinear| |tableau| |stirling1|
- |operation| |traverse| |zeroVector| |makeViewport3D|
- |SturmHabichtMultiple| |shallowCopy| |resultantnaif| |charClass|
- |irreducibleFactors| |makeObject| |gbasis| |parametersOf|
- |solveRetract| |initials| |computeBasis| |gramschmidt| |middle|
- |directory| |degree| |coef| |sizePascalTriangle| |exactQuotient|
- |stoseSquareFreePart| |totalDegree| |getOperator| |expintfldpoly|
- |powerAssociative?| |userOrdered?| |primeFrobenius| |pointPlot|
- |relerror| |hcrf| |operators| |harmonic| |restorePrecision|
- |schwerpunkt| |fortranCharacter| |wholeRadix| |reducedQPowers|
- |stoseInvertible?sqfreg| |abs| |limitedint| |pushNewContour|
- |bubbleSort!| |inconsistent?| |ode2| |df2st| |torsionIfCan|
- |reciprocalPolynomial| |exponent| |kind| |evaluate| |setErrorBound|
- |viewSizeDefault| |rightMinimalPolynomial|
- |primPartElseUnitCanonical!| |exprHasWeightCosWXorSinWX|
- |sylvesterSequence| |numericIfCan| |stosePrepareSubResAlgo| |op|
- |minPoints3D| |colorFunction| |iiasinh| |dark| |kernels|
- |branchPointAtInfinity?| |lastSubResultantEuclidean|
- |resultantEuclideannaif| |cCsc| |presuper| |OMUnknownSymbol?| |minset|
- |lquo| |move| |physicalLength| |c05adf| |cAsech| |leftFactorIfCan|
- |LazardQuotient2| |operator| |more?| |constantOpIfCan| |outputGeneral|
- |binaryTree| |expenseOfEvaluation| SEGMENT |notelem| |s18aef|
- |countRealRootsMultiple| |sech2cosh| |quoted?| |singularAtInfinity?|
- |plotPolar| |cCosh| |dflist| |nativeModuleExtension| |univariate|
- |sort| |OMputFloat| |antisymmetricTensors| |nil?| |taylorIfCan|
- |lieAdmissible?| |dn| |generalizedEigenvector| |child| |sh|
- |pleskenSplit| |radicalEigenvectors| |dec| |algebraic?|
- |virtualDegree| |unitsColorDefault| |readByte!| |iicot|
- |wordInStrongGenerators| |hasTopPredicate?| |numberOfComputedEntries|
- |OMgetFloat| |mathieu12| |LyndonWordsList| |mirror| |rightMult|
- |union| |iprint| |normalized?| |create| |divisorCascade| |routines|
- |getProperties| |randomR| |c05nbf| |factor| |round| |eulerE|
- |showIntensityFunctions| |lfintegrate| |readInt8!| |viewWriteDefault|
- |random| |ceiling| |mesh| |pastel| |sqrt| |unary?| |OMgetEndError|
- |getCurve| |s17ajf| |comp| |pack!| |extendedResultant| |lifting|
- |generalInfiniteProduct| |trim| |real| |oblateSpheroidal| |fi2df|
- |e01bff| |zeroOf| |rotatex| |useSingleFactorBound?|
- |nthFractionalTerm| |OMconnOutDevice| |imag| |linearlyDependentOverZ?|
- |properties| |seriesToOutputForm| |univariatePolynomials|
- |cycleSplit!| |doubleDisc| |copy| |directProduct| |rur| |OMgetBVar|
- |modifyPointData| |unitNormalize| |radix| |super| |ocf2ocdf|
- |getGraph| |translate| |OMgetEndBVar| |padicallyExpand| |rotatey|
- |readable?| |drawCurves| |Aleph| |f02aff| |iiasech| |fortranTypeOf|
- |depth| |wronskianMatrix| |setEpilogue!| |knownInfBasis|
- |clipPointsDefault| |abelianGroup| |push!| |alternative?| |brace|
- |symmetricSquare| |factorList| |decompose| |perfectSqrt|
- |noLinearFactor?| |quasiComponent| |d01alf| |complexNormalize|
- |characteristic| |destruct| |erf| |trapezoidalo| |critpOrder| |e02dff|
- |noValueMode| |outputFixed| |algintegrate| |minordet| |OMlistSymbols|
- |invertibleElseSplit?| |match?| |upperCase| |normal?| |simpsono|
- |numberOfHues| |autoCoerce| |rewriteIdealWithRemainder| |writeBytes!|
- |currentScope| |fractionFreeGauss!| |d03edf| |nextPartition|
- |interactiveEnv| |basis| |children| |fill!| |nextSubsetGray|
- |endOfFile?| |upperBound| |cyclicEqual?| |dilog| |rangeIsFinite|
- |complex?| |s17dgf| |mathieu23| |digit| |leftZero| |expand|
- |goodnessOfFit| |boundOfCauchy| |irreducible?| |monomial| |sin|
- |constant?| |ranges| |radicalSimplify| |multiplyCoefficients|
- |physicalLength!| |rowEchelonLocal| |filterWhile| |root|
- |makingStats?| |multivariate| |stoseInvertibleSetreg| |close| |cos|
- |lazyPseudoRemainder| |create3Space| |quasiRegular?| |accuracyIF| F
- |rightUnit| |filterUntil| |karatsubaDivide| |leftDivide|
- |discriminantEuclidean| |fractRagits| |variables| |tan| |normalForm|
- |commutative?| |toseSquareFreePart| |euclideanSize| |select|
- |PDESolve| |binaryFunction| |deepestTail| |scopes| |HenselLift|
- |display| |cot| |optional?| |binary| |setlast!| |before?| |points|
- |rootRadius| |diagonal?| |setleaves!| |innerint| |sec| |iicos|
- |UnVectorise| |pushup| |defineProperty| |sumOfKthPowerDivisors|
- |createZechTable| |parent| |exprToGenUPS| |symmetricRemainder| |csc|
- |expenseOfEvaluationIF| |toroidal| |minus!| |OMgetEndBind| |factors|
- |edf2df| |shrinkable| |members| |tensorProduct| |asin| |removeZero|
- |critMTonD1| |pop!| |interpretString| |setAttributeButtonStep|
- |alphabetic| |getPickedPoints| |qualifier| |debug| |nthRoot| |qelt|
- |taylor| |acos| |predicate| |perfectNthPower?| |fTable|
- |createGenericMatrix| |createPrimitiveElement| |binaryTournament|
- |startPolynomial| |qsetelt| |vedf2vef| |irDef| |expt| D |laurent|
- |input| |atan| |fortranInteger| |antiAssociative?| |ode| |f02xef|
- |primitive?| |cAtan| |schema| |complexForm| |xRange| |nextColeman|
- |puiseux| |library| |acot| |copyInto!| |OMencodingXML| |newTypeLists|
- |fibonacci| EQ |modTree| |removeRoughlyRedundantFactorsInPol| |write!|
- |groebnerFactorize| |youngGroup| |yRange| |asec| |jokerMode| |returns|
- |primeFactor| |leftExactQuotient| |setFieldInfo| |fortranLinkerArgs|
- |tube| |primitivePart!| |inv| |pToHdmp| |zRange| |acsc| |setProperty|
- |box| |c05pbf| |totalGroebner| |bipolarCylindrical|
- |extendedEuclidean| |read!| |cAcos| |ground?| |any?| |map!|
- |OMreceive| |sinh| |OMgetString| |sPol| |transpose| |cAcsc|
- |dualSignature| |dihedral| |e01daf| |qsetelt!| |elem?| |ground|
- |resetBadValues| |set| |cosh| |leftRankPolynomial|
- |internalIntegrate0| |semiDegreeSubResultantEuclidean| |alphanumeric?|
- |double| |mapDown!| |rightExtendedGcd| |complexZeros| |sincos|
- |intermediateResultsIF| |leadingMonomial| |transcendent?| |tanh|
- |compBound| |unravel| |partition| |BumInSepFFE| |yellow| |scaleRoots|
- |mapGen| |fixedPoint| |OMputEndAttr| |leadingCoefficient|
- |outputSpacing| |coth| |expextendedint| |makeSeries| |normal01|
- |localUnquote| |size| |permutation| |realRoots| |argument| |subset?|
- |rubiksGroup| |primitiveMonomials| |parameters| |sech| |leftFactor|
- |setright!| |s20acf| |lowerCase?| |mkcomm| |block| |groebgen| |d01anf|
- |print| |chiSquare| |reductum| |csch| |mapBivariate| |e02daf|
- |evaluateInverse| |typeLists| |finiteBound| |intPatternMatch|
- |curryLeft| |resolve| |subCase?| |cSech| |acsch| |asinh|
- |gcdPolynomial| |fglmIfCan| |cyclicEntries| |orbit| |skewSFunction|
- |fortranDouble| |OMReadError?| |invmod| |norm| |acosh| |true|
- |quoByVar| |Gamma| |besselJ| |category| |seed| |iiabs| |constDsolve|
- |halfExtendedSubResultantGcd2| |limitedIntegrate| |f07aef| |f04asf|
- |basisOfNucleus| |domain| |over| |optional| |dmp2rfi| |declare!|
- |cot2tan| |deepestInitial| |insertionSort!| |coth2trigh| |factorset|
- |epilogue| |linearPolynomials| |clikeUniv| |OMcloseConn| |integers|
- |package| |iisec| |vectorise| |whileLoop| |OMgetAttr| |aromberg|
- |infinite?| |insert| |maxIndex| |reindex| |exists?| |eyeDistance|
- |readInt32!| |extract!| |cosSinInfo| |imagk| |recoverAfterFail| |show|
- |iiacsch| |exprHasAlgebraicWeight| |discreteLog| |outputArgs|
- |singularitiesOf| |search| |f04qaf| |dmpToP| |lazyVariations|
- |lazyPremWithDefault| |rewriteSetWithReduction| |stopTableInvSet!|
- UTS2UP |sinIfCan| |node| |solid?| |symmetricTensors| |rquo|
- |pointColor| |c06fuf| |trace| |fmecg| |cTanh| |setAdaptive3D|
- |conical| |has?| |partialQuotients| |cothIfCan| |iisech|
- |zeroDimensional?| |capacity| |coefficient| |region| |degreePartition|
- |iomode| |OMencodingBinary| |mapdiv| |e01sbf| |odd?| |stop| |ratpart|
- |adaptive?| |segment| |monicCompleteDecompose| |sylvesterMatrix|
- |nonSingularModel| |idealSimplify| |ListOfTerms| |setTex!| |OMputApp|
- |alternating| |extractIfCan| |prologue| |quotient| |voidMode|
- |setsubMatrix!| |prefixRagits| |listOfLists| |formula| |flatten|
- |latex| |tanintegrate| |setScreenResolution3D| |lazyGintegrate|
- |paraboloidal| |rootNormalize| |charpol| |d02gaf| |lllip| |subMatrix|
- |extractBottom!| |mainVariable| |rightFactorIfCan| |reducedForm|
- |graeffe| |isQuotient| |monicRightFactorIfCan| |writeInt8!| |getlo|
- |doubleComplex?| |lepol| |sinhIfCan| |zero?| |trace2PowMod|
- |zeroDimPrime?| |s18aff| |ideal| |dioSolve| |reify| |lyndon| |cAsec|
- |pole?| |elliptic?| |augment| |purelyAlgebraic?| |nrows|
- |OMUnknownCD?| |genericLeftTraceForm| |entries| |updatD|
- |lastSubResultant| |axes| |exprHasLogarithmicWeights| |OMputVariable|
- |lazyPrem| |ncols| |UP2ifCan| |c06fqf| |leftRecip| |controlPanel|
- |changeBase| |incrementKthElement| |simplify| |conjugates|
- |setIntersection| |ScanFloatIgnoreSpacesIfCan| |distdfact| |nullary?|
- |ignore?| |mapUnivariateIfCan| |fortranCarriageReturn| |gcdcofactprim|
- |height| |units| |log10| |mesh?| |setTopPredicate| |factorSFBRlcUnit|
- |rewriteIdealWithHeadRemainder| |equation| |drawToScale| |s17aef|
- |expIfCan| |null?| |mindeg| |basisOfLeftNucloid| |bitand| |cup|
- |rationalPoints| |univariatePolynomial| |OMserve| |optpair| |leaves|
- |outerProduct| |deriv| |bitior| |d02ejf| |setOrder| |addmod|
- |genericLeftNorm| |pseudoQuotient| |roughUnitIdeal?| |shape|
- |toseInvertible?| |radicalRoots| |triangSolve| |Ci| |cLog|
- |divergence| |shallowExpand| |jacobian| |macroExpand|
- |leftCharacteristicPolynomial| |distribute| |Is| |anticoord|
- |elements| |bumptab| |linSolve| |closedCurve| |replaceKthElement|
- |subNodeOf?| |readBytes!| |rightDivide|
- |generalizedContinuumHypothesisAssumed?| |explimitedint|
- |startTableGcd!| |numberOfVariables| |compdegd| |clearTheSymbolTable|
- |df2fi| |inGroundField?| |iitanh| |tubeRadius| |hasHi| |besselI|
- |insert!| |createNormalPoly| |pascalTriangle| |f02adf| |getOperands|
- |rule| |tryFunctionalDecomposition?| |fprindINFO| |declare| |makeCrit|
- |inRadical?| |resize| |ellipticCylindrical| |splitSquarefree| |common|
- |rootBound| |linearlyDependent?| |mainMonomial| |atanIfCan|
- |asinhIfCan| |mapUp!| |imaginary| |writeLine!| |minRowIndex|
- |factorials| |exptMod| |d02gbf| |zoom| |hexDigit| |euler|
- |numberOfPrimitivePoly| |PollardSmallFactor| |interReduce| |c06ecf|
- |symmetricGroup| |deleteProperty!| |realEigenvectors| |lintgcd|
- |zCoord| |lazy?| |elRow2!| |branchIfCan| |partialDenominators|
- |iiasin| |leadingExponent| |d02kef| |matrix| |symbol?|
- |domainTemplate| |HermiteIntegrate| |twist| |algSplitSimple| |Nul|
- |edf2ef| |readUInt16!| |partitions| |removeCoshSq| |ord| |e02adf|
- |var2StepsDefault| |Si| |isOpen?| |quotientByP| |ratDenom| |prevPrime|
- |createPrimitivePoly| |groebner?| |dequeue| |generators|
- |squareFreeFactors| Y |trapezoidal| |acosIfCan| |tanSum| |sec2cos|
- |elseBranch| |extendedIntegrate| |isEquiv| |limitPlus| |linearPart|
- |label| |internalLastSubResultant| |diagonalProduct| |ef2edf| |inR?|
- |associatedEquations| |safeFloor| |makeGraphImage| |B1solve| |df2mf|
- |escape| |sin2csc| |stiffnessAndStabilityFactor| |components|
- |leastAffineMultiple| |deepCopy| |coerceP|
- |numberOfImproperPartitions| |mainDefiningPolynomial|
- |rangePascalTriangle| |pair?| |palgint0| |minPol|
- |basisOfMiddleNucleus| |rightRankPolynomial| |univariateSolve|
- |composites| |result| |zeroDimPrimary?| |iidsum| |listOfMonoms|
- |categoryMode| |univariate?| |extendedint| |mkIntegral| |cSec|
- |taylorRep| |d02raf| |vark| |enterInCache| |associatedSystem|
- |laplacian| |rightExactQuotient| |noncommutativeJordanAlgebra?|
- |f02fjf| |expint| |changeNameToObjf| |validExponential| |fixedDivisor|
- |d01bbf| |bernoulli| |gcdprim| |showAll?| |setButtonValue| |cyclic|
- |setCondition!| |constantOperator| |s17dhf| |setLength!|
- |hypergeometric0F1| |constructor| |rightPower| |inverseIntegralMatrix|
- |readIfCan!| |graphState| |represents| |approximants| |normalElement|
- |substitute| |OMgetEndApp| |hexDigit?| |sum| |iibinom| |totalLex|
- |bindings| |cTan| |option| |f04faf| |showSummary| |symbolTable|
- |makeCos| |e02ddf| |e04gcf| |basicSet| |OMputSymbol| |leaf?|
- |sechIfCan| |rdHack1| |GospersMethod| |curveColorPalette|
- |squareFreePart| |getMatch| |front| |squareFreePrim| |symFunc|
- |multiEuclideanTree| |s19acf| |elliptic| |pushFortranOutputStack|
- |showAttributes| |lp| |d01gaf| |poisson| |badValues| |deref|
- |getVariableOrder| |newSubProgram| |elaborateFile| |moduleSum|
- |makeRecord| |regime| |popFortranOutputStack| |sturmSequence| |lllp|
- |tab1| |realSolve| |complexSolve| |imagI| |saturate| |cAsin| |atom?|
- |outputAsFortran| |insertRoot!| |vertConcat| |alphanumeric|
- |prinpolINFO| |duplicates?| |OMgetInteger| |name| |bitLength| |d01asf|
- |genericRightDiscriminant| |mergeDifference| |setMinPoints3D|
- |parabolicCylindrical| |matrixGcd| |currentCategoryFrame| |rightTrim|
- |redpps| |body| |prinb| |selectAndPolynomials| |indicialEquations|
- |duplicates| |subresultantSequence| |kroneckerDelta| |e02zaf|
- |OMgetError| |leftTrim| |untab| |high| |outputAsTex|
- |bezoutDiscriminant| |null| |binomThmExpt| |karatsubaOnce| |e04fdf|
- |shufflein| |solveLinearPolynomialEquationByRecursion| |stack|
- |rootsOf| |linGenPos| |quasiAlgebraicSet| |iicosh| |not| |janko2|
- |lazyIrreducibleFactors| |cAtanh| |s19abf| |homogeneous?| BY |cn|
- |top!| |subtractIfCan| |ODESolve| |maxPoints| |and| |solve1|
- |removeSuperfluousQuasiComponents| |setProperties| |weights| |d02cjf|
- |simplifyPower| |categoryFrame| |diagonal| |monicLeftDivide| |or|
- |getSyntaxFormsFromFile| |mpsode| |identitySquareMatrix| |curryRight|
- |infix| |overset?| |eigenvalues| |magnitude| |opeval| |xor| |pdf2df|
- |viewDefaults| |normFactors| |youngDiagram| |innerEigenvectors|
- |s13aaf| |besselK| |numerator| |signature| |primextintfrac| |dim|
- |case| |spherical| |OMgetEndAtp| |assert| |factorByRecursion| |hasoln|
- |po| |port| |infiniteProduct| |leftUnits| |s13adf| |makeMulti|
- |pattern| |Zero| |iiasec| |orthonormalBasis| |identification| |presub|
- |integral| |rationalIfCan| |SFunction| |simpson| |csubst| |One|
- |rationalApproximation| |lazyPseudoDivide| |patternMatchTimes|
- |asechIfCan| |subscriptedVariables| |t| |selectNonFiniteRoutines|
- |s13acf| |ScanRoman| |basisOfRightNucleus| |shift| NOT
- |LyndonWordsList1| |FormatArabic| |shiftRight| |coordinates| |output|
- |palglimint0| |powmod| |f04maf| |chainSubResultants| |nodeOf?| OR
- |vector| |leadingIndex| |messagePrint| |eq?| |bracket|
- |irreducibleFactor| |df2ef| |polyred| |expandLog| |problemPoints|
- |message| AND |differentiate| |mapCoef| |integerIfCan| |getZechTable|
- |multiset| |mergeFactors| |genus| |OMgetSymbol| |setrest!| |unit|
- |cAcoth| |lazyPquo| |initTable!| |positive?| |fortran| |curry| |delay|
- |iiexp| |initiallyReduce| |reduceLODE| |elt| |overlabel| |tanNa|
- |hMonic| |henselFact| |tan2trig| |mainSquareFreePart| |finiteBasis|
- |headReduce| |fixPredicate| |iFTable| |replace| |An|
- |addMatchRestricted| |level| |indiceSubResultantEuclidean|
- |generalSqFr| |coerceListOfPairs| |closed?| |LyndonCoordinates|
- |outputBinaryFile| |zeroSetSplitIntoTriangularSystems| |startStats!|
- |concat!| |colorDef| |numericalOptimization|
- |factorSquareFreePolynomial| |enqueue!| |prod| |sizeLess?|
- |removeSuperfluousCases| |branchPoint?| |palgintegrate| |coord| |cons|
- |selectOptimizationRoutines| |double?| |sumSquares| |normDeriv2|
- |addPoint2| |mainExpression| |s01eaf| |nodes| |htrigs| |cond|
- |completeHermite| |negative?| |quadratic| |setValue!| |retract|
- |leftNorm| |terms| |paren| |asinIfCan| |completeHensel| |makeSUP|
- |clipSurface| |cSinh| |groebnerIdeal| |leftScalarTimes!|
- |extractProperty| |subspace| |support| |interpolate| |prime|
- |fractionPart| |point?| |second| * |s17akf| |subResultantsChain|
- |multisect| |graphCurves| |var2Steps| |ridHack1| |invertIfCan| |row|
- |addPoint| |third| |inrootof| |bfEntry| |basisOfRightNucloid| |nary?|
- |identityMatrix| |tryFunctionalDecomposition| |setleft!| |reduction|
- |typeList| |decrease| |putProperty| |semiSubResultantGcdEuclidean1|
- |source| |void| |pushdown| |conditionsForIdempotents| |gensym|
- |sortConstraints| |explogs2trigs| = |printStats!| |enumerate|
- |dominantTerm| |stoseLastSubResultant| |e04dgf| |makeop| |mix|
- |multiEuclidean| |createLowComplexityNormalBasis|
- |numberOfIrreduciblePoly| |chvar| |symmetricPower| |script|
- |rightCharacteristicPolynomial| |modulus| |mappingMode| |maxrank|
- |find| |rationalPoint?| |readUInt32!| < |completeEval| |collectUpper|
- |findConstructor| |plusInfinity| |initializeGroupForWordProblem|
- |char| |deepExpand| |iCompose| > |iitan| |d02bhf| |minusInfinity|
- |isOr| |s17def| |cotIfCan| |systemCommand| |alternatingGroup|
- |totolex| <= |isPlus| |whatInfinity| |viewPhiDefault| |tex| |target|
- |OMencodingUnknown| |qinterval| |inverseColeman| |s17aff|
- |setchildren!| |rightRank| >= |imagJ| |ffactor| |factorPolynomial|
- |pr2dmp| |newReduc| |retractable?| |pointColorPalette|
- |zeroSquareMatrix| |expr| |roughBase?| |car| |eulerPhi| |mkPrim|
- |isExpt| |normal| |changeVar| |s17ahf| |reduceByQuasiMonic|
- |ramified?| |permutationRepresentation| |xCoord| |lookup| |isAtom|
- |linear| |constantRight| |complexRoots| + |evenInfiniteProduct|
- |partialNumerators| |createIrreduciblePoly| |type| |getOrder|
- |firstNumer| |exactQuotient!| |exQuo| |s18dcf| - |float| |subPolSet?|
- |mathieu22| |certainlySubVariety?| |nthFactor| |rootKerSimp| |f02bjf|
- |polynomial| |leadingIdeal| |variable| |repSq| / |phiCoord| |solve|
- |roughBasicSet| |postfix| |algebraicVariables| |oddlambert|
- |iterators| |divisors| |pdct| |inputBinaryFile| |viewDeltaXDefault|
- |rightGcd| |fullPartialFraction| |subresultantVector| |sin?| |inspect|
- |maxint| |push| |solveLinearlyOverQ| |tanIfCan| |headAst| |readLine!|
- |f02axf| |OMputEndBind| |coshIfCan| |tubePoints| |element?|
- |mightHaveRoots| |sumOfDivisors| |s21bdf| |polarCoordinates| |id|
- |copies| |hconcat| |fortranReal| |contours| |value| |triangular?|
- |merge| |comparison| |generateIrredPoly| |updatF| |symbol| |lo|
- |jordanAdmissible?| |modularFactor| |OMputEndAtp| |startTable!|
- |SturmHabichtCoefficients| |compiledFunction| |removeSquaresIfCan|
- |atanhIfCan| |f02wef| |expression| |lieAlgebra?| |rightUnits| |bit?|
- |denomLODE| |multinomial| |s19aaf| |OMwrite| |charthRoot| |calcRanges|
- |integer| |integer?| |nthExponent| |leftReducedSystem| GE |hex|
- |minrank| |supDimElseRittWu?| |removeZeroes| |intersect| |medialSet|
- |setPoly| |unitVector| |contains?| |rational?| GT |bitTruth|
- |showRegion| |lSpaceBasis| |f01qcf| |principalAncestors|
- |variationOfParameters| |hermite| |style| |eigenvectors| LE |pomopo!|
- |e02gaf| |bivariate?| |createRandomElement| |zerosOf|
- |createLowComplexityTable| |reduceBasisAtInfinity| |setelt!|
- |reverseLex| LT |rotatez| |stopMusserTrials| |distFact|
- |decomposeFunc| |extractTop!| |getMultiplicationTable| |crest|
- |socf2socdf| |iterationVar| |c06gsf| |list?| |UpTriBddDenomInv|
- |connect| |nor| |squareMatrix| |invertibleSet|
- |numberOfFractionalTerms| |curve?| |computeCycleLength| |pile|
- |integralMatrix| |OMbindTCP| |denominators| |monomial?|
- |transcendenceDegree| |keys| |edf2efi| |expressIdealMember| |select!|
- |bombieriNorm| |bothWays| |cos2sec| |unknownEndian| |unitNormal|
- |separateDegrees| |numberOfOperations| |OMgetApp| |lyndonIfCan|
- |singRicDE| |linearAssociatedLog| |cycleRagits| |leviCivitaSymbol|
- |OMgetVariable| |primlimitedint| |index| |makeEq| |definingPolynomial|
- |numberOfComponents| |order| |triangularSystems| |OMencodingSGML|
- |repeatUntilLoop| |square?| |nextNormalPoly| |numeric| |s17dlf|
- |shuffle| |cCoth| |polygon| |pushdterm| |hdmpToDmp| |rightNorm|
- |gderiv| |redPo| |radical| |OMputBind| |patternMatch| |removeCosSq|
- |fixedPointExquo| |resultant| |fortranDoubleComplex| |bivariateSLPEBR|
- |reduced?| |rightQuotient| |pair| |open| |tree| |positiveRemainder|
- |primPartElseUnitCanonical| |structuralConstants| |outlineRender|
- |curve| |kmax| |bright| |setImagSteps| |rst| |graphStates| |tanQ|
- |numberOfChildren| |thenBranch| |currentSubProgram|
- |LowTriBddDenomInv| |plus!| |fortranCompilerName| |FormatRoman|
- |useEisensteinCriterion| |critB| |eof?| |getRef| |algDsolve| |e04jaf|
- |printingInfo?| |eval| |makeFloatFunction| |ode1|
- |removeRoughlyRedundantFactorsInContents| |setUnion| |stFunc1|
- |vspace| |scale| |indicialEquationAtInfinity| |writeByte!|
- |expintegrate| |adjoint| |splitNodeOf!| |operations| |mapMatrixIfCan|
- |selectOrPolynomials| |checkForZero| |normalizeAtInfinity| |torsion?|
- |largest| |lfunc| |internalDecompose| |lowerBound| |bandedJacobian|
- |e04mbf| |solveid| |OMreadFile| |interpret| |conjunction| |error|
- |midpoints| |complexExpand| |selectIntegrationRoutines| |imagK|
- |airyBi| |clearTable!| |f2df| |aQuartic| |ref| |setStatus| |groebner|
- |normalize| |quadratic?| |lexTriangular| |pointSizeDefault|
- |sayLength| |direction| |optimize| |standardBasisOfCyclicSubmodule|
- |algebraicOf| |insertBottom!| |perspective| |sequence| |logGamma|
- |function| |stoseInvertibleSet| |symmetricProduct| |OMmakeConn|
- |oneDimensionalArray| |cAcsch| |rightOne| |symbolTableOf|
- |createNormalElement| |lflimitedint| |tubeRadiusDefault| |subHeight|
- |autoReduced?| |symbolIfCan| |matrixDimensions| |seriesSolve|
- |reducedSystem| |llprop| |width| |ramifiedAtInfinity?|
- |inputOutputBinaryFile| |makeUnit| |cyclicGroup| |lookupFunction|
- |iiacoth| |rules| |topPredicate| |monicDivide| |aspFilename|
- |primintegrate| |cubic| |dihedralGroup| |rectangularMatrix| |critM|
- |explicitEntries?| |unitCanonical| |maxrow| |pseudoRemainder|
- |rightRemainder| |divideIfCan| |sumOfSquares| |cCot|
- |getMultiplicationMatrix| |tubePlot| |degreeSubResultant|
- |extendedSubResultantGcd| |e02bbf| |bezoutResultant| |baseRDEsys|
- |tracePowMod| |setMaxPoints3D| |OMconnectTCP| |countRealRoots|
- |solveLinearPolynomialEquationByFractions|
- |unprotectedRemoveRedundantFactors| |smith|
- |leftRegularRepresentation| |queue| |someBasis| |logpart| |printCode|
- |mr| |subscript| |selectsecond| |sinh2csch| |genericRightTrace|
- |real?| |characteristicSerie| |length| |leftGcd| |redmat| |float?|
- |upperCase?| |sort!| |rootPoly| |xn| |changeWeightLevel| |ratPoly|
- |changeThreshhold| |scripts| |irreducibleRepresentation| |preprocess|
- |prem| |rem| |purelyTranscendental?| |removeRedundantFactors|
- |string?| |euclideanNormalForm| |npcoef| |numberOfNormalPoly|
- |definingEquations| |scanOneDimSubspaces| |cycle| |selectPDERoutines|
- |upDateBranches| |quo| |weakBiRank| |empty?| |argumentList!|
- |buildSyntax| |cCos| |varList| |uniform01| |removeSinhSq|
- |lfextlimint| |infieldIntegrate| |e02ahf| |intcompBasis| |mainKernel|
- |every?| |LiePoly| |wreath| |lcm| |tanhIfCan| |headRemainder|
- |normalise| |lineColorDefault| |div| |inf| |delete| |BasicMethod|
- |vconcat| |isList| |external?| |graphs| |genericRightTraceForm|
- |clearTheFTable| |stoseInvertible?reg| |exquo| |relativeApprox|
- |digit?| |algebraicCoefficients?| |drawComplex| |bigEndian| |append|
- |minPoints| |normalDeriv| |floor| |pointData| ~= |monicRightDivide|
- |minGbasis| |composite| |wholeRagits| |irVar| |imagj| |gcd|
- |OMlistCDs| |laurentIfCan| |representationType| |#| |subNode?|
- |s15aef| |semiSubResultantGcdEuclidean2| |factorGroebnerBasis|
- |OMputEndApp| |perfectSquare?| |false| |status| |delete!|
- |factorOfDegree| |extractClosed| ~ |readInt16!| |realEigenvalues|
- |aCubic| |mappingAst| |genericPosition| |randnum| |collectQuasiMonic|
- |btwFact| |cross| |reorder| |hspace| |bumprow| |ravel| |rowEchLocal|
- |att2Result| |complexEigenvectors| |realElementary| |cosIfCan|
- |e02agf| |zeroSetSplit| |rk4f| |roman| |reshape| |oddintegers|
- |sqfrFactor| |e02dcf| |setprevious!| |airyAi| |stirling2| |/\\| |bat|
- |laguerreL| |selectODEIVPRoutines| |processTemplate| |f04axf|
- |functorData| |moebiusMu| |plenaryPower| |modularGcdPrimitive|
- |stopTableGcd!| |logIfCan| |\\/| |constantCoefficientRicDE|
- |rootPower| |genericRightMinimalPolynomial| |innerSolve1|
- |viewPosDefault| |apply| |coerce| |genericLeftMinimalPolynomial|
- |flexibleArray| |s17adf| |equality| |tRange| |closed| |OMclose|
- |d01fcf| |first| |construct| |setLegalFortranSourceExtensions|
- |varselect| |idealiser| |internalSubPolSet?| |mainForm|
- |prepareDecompose| |listexp| |f04mcf| |printInfo!| |stFunc2| |rest|
- |cap| |contractSolve| |anfactor| |f07fdf| |rdregime| |showArrayValues|
- |regularRepresentation| |character?| |ParCond| |extractIndex| |plus|
- |update| |irCtor| |atoms| |inverseLaplace| |mkAnswer| |unvectorise|
- |coHeight| |inHallBasis?| |dmpToHdmp| |groebSolve| |commutator|
- |functionIsContinuousAtEndPoints| |critBonD| |meshPar1Var|
- |completeSmith| |conjugate| |componentUpperBound| |algebraicSort|
- |bytes| |computePowers| |exponential| |redPol| |palglimint|
- |showTheSymbolTable| |d03faf| |isPower| |quote| |plot| |times|
- |selectMultiDimensionalRoutines| |rootOf| |slex| |parents|
- |lfextendedint| |c06ekf| |rspace| |bfKeys|
- |selectSumOfSquaresRoutines| |leftMult| |addPointLast| |scalarTypeOf|
- |f07adf| |tubePointsDefault| |expandPower| |submod| |sparsityIF|
- |iiatan| |empty| |position| |subQuasiComponent?| |csch2sinh|
- |printStatement| |s18def| |polygon?| |rationalFunction|
- |numberOfDivisors| |rowEchelon| |listBranches|
- |tableForDiscreteLogarithm| |even?| |radicalSolve|
- |expandTrigProducts| |recur| |eigenMatrix| |OMunhandledSymbol|
- |antiCommutator| |cycleTail| |doublyTransitive?|
- |internalZeroSetSplit| |crushedSet| |collect| |split!| |reverse!|
- |monom| |rootSplit| |lift| |conditionP| |sequences| |leftRank| |tab|
- |failed?| |subSet| |getMeasure| |imports| |toseInvertibleSet|
- |sdf2lst| |loadNativeModule| |fillPascalTriangle| |reduce| |power!|
- |point| |exteriorDifferential| |powern| |mvar| |cyclic?|
- |areEquivalent?| |iiatanh| |generalTwoFactor| |close!|
- |strongGenerators| |polCase| |part?| |simplifyExp| |getConstant|
- |rootOfIrreduciblePoly| |qqq| |integralCoordinates| |lazyResidueClass|
- |yCoordinates| |moreAlgebraic?| |remainder| |nonQsign| |frobenius|
- |remove!| |OMputEndError| |positiveSolve|
- |semiIndiceSubResultantEuclidean| |tan2cot| |blankSeparate|
- |mapUnivariate| |f04jgf| |generalPosition| |zeroMatrix| |gethi|
- |comment| |padecf| |series| |factorAndSplit| |nullity|
- |removeRedundantFactorsInContents| |partialFraction| |center| |f02awf|
- |removeRedundantFactorsInPols| |integerBound| |infieldint| |log|
- |pushuconst| |coerceImages| |expPot| |lastSubResultantElseSplit|
- |associative?| |numFunEvals| |complement| |cExp| |OMputAttr|
- |specialTrigs| |subTriSet?| |setelt| |nlde| |internal?| |powerSum|
- |rewriteIdealWithQuasiMonicGenerators| |s17dcf| |isConnected?|
- |OMputEndObject| |setClipValue| |extractPoint| |nthFlag| |quatern|
- |leftUnit| |module| |swap| |selectPolynomials| |freeOf?|
- |mainCoefficients| |singular?| |changeName| |contract| |minimize|
- |maxRowIndex| |bottom!| |resultantReduitEuclidean| |min|
- |outputFloating| |halfExtendedResultant1| |palgLODE| |nextPrime|
- |hasSolution?| |ipow| |leadingCoefficientRicDE| |infinityNorm|
- |outputForm| |setFormula!| |yCoord| |c02agf| |fixedPoints|
- |createMultiplicationTable| |lazyIntegrate| |appendPoint| |monomials|
- |cyclicParents| |setColumn!| |createNormalPrimitivePoly|
- |measure2Result| |jacobiIdentity?| |flagFactor| |moduloP|
- |listRepresentation| |sup| |setvalue!| |totalfract| |exprToUPS|
- |bivariatePolynomials| |rootSimp| |iicsc| |figureUnits| |f01bsf|
- |factorSquareFreeByRecursion| |property| |transcendentalDecompose|
- |unmakeSUP| |unexpand| |f01maf| |d03eef| |numberOfCycles| |mat|
- |prindINFO| |byte| |goodPoint| |generalizedInverse| |showScalarValues|
- |omError| |separate| |badNum| |meatAxe| |OMputObject| |acothIfCan|
- |errorInfo| |setref| |rootDirectory| |zero| |setRealSteps| |mulmod|
- |reverse| |sinhcosh| |minColIndex| |algebraicDecompose| |mainValue|
- |acschIfCan| |call| |prinshINFO| |myDegree| |pToDmp| |product|
- |setRow!| |ldf2vmf| |KrullNumber| |rotate| |polyPart| |setOfMinN| |li|
- |OMputError| |iisin| |difference| |OMopenFile| |multiple?| |And|
- |viewport3D| |size?| |alphabetic?| |imagi| |mapSolve| |unparse|
- |Lazard2| |unknown| |geometric| |makeVariable| |setScreenResolution|
- |increasePrecision| |rCoord| |Or| |besselY| |reducedContinuedFraction|
- |sturmVariationsOf| |mapmult| |rightZero| |screenResolution3D| |exp1|
- |primitivePart| |elaborate| |column| |rightScalarTimes!| |findCycle|
- |Not| |generalLambert| |bezoutMatrix| |build| |approxSqrt| |makeprod|
- |signatureAst| |finite?| |leftRemainder| |identity| |cycleElt|
- |mainMonomials| |setPredicates| |firstUncouplingMatrix| |pointLists|
- |complexLimit| |d01ajf| |position!| |superscript| |getStream|
- |midpoint| FG2F |weighted| |modifyPoint| |bsolve| |recip| |localReal?|
- |int| |cschIfCan| |scripted?| |color| |coth2tanh| |listYoungTableaus|
- |superHeight| |factorFraction| |minIndex| |root?| |cylindrical|
- |OMputString| |basisOfLeftNucleus| |localAbs| |realZeros|
- |useSingleFactorBound| |f01mcf| |gradient| |dimension| |symmetric?|
- |decimal| |iisqrt2| |e02baf| |resultantReduit| |attributeData|
- |innerSolve| |binomial| |cSin| |supRittWu?| |f02abf| |OMParseError?|
- |repeating| |rk4qc| |Lazard| |trueEqual| |OMread|
- |shanksDiscLogAlgorithm| |iiGamma| |distance| |stopTable!|
- |loopPoints| |interval| |stoseInternalLastSubResultant| |test|
- |exponents| |getProperty| |quickSort| |elaboration| |graphImage|
- |cyclotomicDecomposition| |remove| |fortranLiteralLine| |power|
- |nextNormalPrimitivePoly| |musserTrials| |host| |primes|
- |argumentListOf| |probablyZeroDim?| |bat1| |factorsOfDegree| |kovacic|
- |factorial| |functionIsOscillatory| |zag| |genericLeftTrace| |cAcosh|
- |tanAn| |inverse| |removeDuplicates| |cartesian|
- |quasiMonicPolynomials| |dAndcExp| |addMatch| |getButtonValue| |last|
- |OMgetAtp| |patternVariable| |ksec| |reducedDiscriminant| |e04naf|
- |extend| |cyclicSubmodule| |differentialVariables| |clearTheIFTable|
- |nextPrimitivePoly| |wholePart| |assoc| |credPol| |coefChoose|
- |errorKind| |normalDenom| |c06gbf| |leftLcm| |assign| |c02aff|
- |ReduceOrder| |rewriteSetByReducingWithParticularGenerators|
- |condition| |divide| |dimensions| |tower|
- |generalizedContinuumHypothesisAssumed| |isobaric?|
- |removeRoughlyRedundantFactorsInPols| |writeUInt8!| |parametric?|
- |palgRDE| |rightFactorCandidate| |basisOfLeftAnnihilator|
- |primintfldpoly| |whitePoint| |parabolic| |infLex?| |iiperm| |bits|
- |e01sef| |light| |indiceSubResultant| |acscIfCan| |headReduced?|
- |prefix| |nilFactor| |bounds| |stoseInvertibleSetsqfreg| |limit|
- |s20adf| |uniform| |cyclicCopy| |const| |wrregime| |putProperties|
- |generic| |leftExtendedGcd| |parseString| |setClosed| |polyRicDE|
- |axesColorDefault| |weight| |localIntegralBasis| |tValues|
- |laurentRep| |obj| |derivationCoordinates| |eq| |orbits|
- |genericRightNorm| |meshFun2Var| |arbitrary| |putGraph| |coerceL|
- |e02bef| |option?| |pade| |conjug| |cache| |monomialIntegrate| |iter|
- |isMult| |setDifference| |flexible?| |Ei| |complexNumeric|
- |lowerPolynomial| |e01baf| |variable?| |aQuadratic| |listLoops|
- |setfirst!| |maxPoints3D| |infRittWu?| |linkToFortran| |solveInField|
- |heap| |nextItem| |lfinfieldint| |stronglyReduced?| |forLoop|
- |sizeMultiplication| |irForm| |shiftRoots| |perfectNthRoot|
- |cycleLength| |e02aef| |permutations| |coleman| |RemainderList|
- |withPredicates| |merge!| |firstSubsetGray| |compose| |fracPart|
- |coefficients| |nullary| |digits| |isAbsolutelyIrreducible?|
- |associates?| |f07fef| |screenResolution| |f01rcf| |normalizeIfCan|
- |LiePolyIfCan| |eisensteinIrreducible?| |OMputInteger| |generic?|
- |radicalEigenvector| |surface| |acotIfCan| |uncouplingMatrices|
- |subst| |f2st| |mapExponents| |rightLcm| |roughEqualIdeals?| |low|
- |substring?| |setAdaptive| |internalAugment| |leadingTerm| |monic?|
- |packageCall| |ricDsolve| |exp| |debug3D| |iipow| |s19adf|
- |applyRules| |exprex| |nthCoef| |quadraticForm| |froot| |acoshIfCan|
- |clipWithRanges| |resetVariableOrder| |bag| |shellSort| |d01amf| |hue|
- |map| |nextsousResultant2| |suffix?| |possiblyNewVariety?|
- |cycleEntry| |s14abf| |mainVariable?| |ScanArabic| |environment|
- |lifting1| |lyndon?| |one?| |table| |Hausdorff| |generator|
- |palgLODE0| |getExplanations| |OMgetBind| |simplifyLog|
- |commaSeparate| |nil| |explicitlyEmpty?| |semicolonSeparate|
- |wordInGenerators| |asecIfCan| |integralLastSubResultant| |new|
- |atanh| |basisOfCenter| |prefix?| |OMsupportsCD?| |encodingDirectory|
- |antiCommutative?| |OMgetType| |compile| |complexIntegrate| |rischDE|
- |principalIdeal| |quasiMonic?| |s21bbf| |OMconnInDevice| |acoth|
- |linear?| |repeating?| |LyndonBasis| |e04ycf| |sncndn| |objects|
- |iiacos| |directSum| |c06gqf| |normInvertible?| |predicates|
- |fractRadix| |asech| |brillhartTrials| |randomLC| |supersub|
- |halfExtendedSubResultantGcd1| |pdf2ef| |base| |approximate| |space|
- |constantIfCan| |tanh2trigh| |convert| |leastMonomial|
- |prolateSpheroidal| |polynomialZeros| |countable?| |minPoly| |just|
- |complex| |coercePreimagesImages| |computeInt| |monomRDEsys| |belong?|
- |d01gbf| |multiple| |drawComplexVectorField| |univcase| |makeSin|
- |dimensionOfIrreducibleRepresentation| |d01akf| |lprop| |increment|
- |cAcot| |optAttributes| |hostByteOrder| |applyQuote|
- |factorsOfCyclicGroupSize| |mathieu24| |rroot| |monicModulo| |failed|
- |particularSolution| |testDim| |overlap| |baseRDE|
- |characteristicPolynomial| |invertible?| |infix?| |palgint|
- |cosh2sech| |csc2sin| |gcdPrimitive| |refine| |integrate| |iisinh|
- |cyclePartition| |balancedFactorisation| |compactFraction| |mask|
- |satisfy?| |intensity| |radicalOfLeftTraceForm| |leftAlternative?|
- |viewDeltaYDefault| |var1StepsDefault| |elRow1!| |compound?| |ruleset|
- |incr| |setPosition| |cyclotomic| |biRank| |measure| |quasiRegular|
- |purelyAlgebraicLeadingMonomial?| |transform| |OMgetEndAttr| |c06eaf|
- |f01qef| |hi| |pmComplexintegrate| |hitherPlane|
- |basisOfRightAnnihilator| |selectfirst| |s14aaf| |normalizedAssociate|
- |chineseRemainder| |left| |stoseInvertible?| |convergents| |qPot|
- |LazardQuotient| |head| |removeSinSq| |rotate!| |outputMeasure|
- |updateStatus!| |leftMinimalPolynomial| |sqfree| |right| |suchThat|
- |eigenvector| |rational| |sub| |stFuncN| |index?| |rischDEsys|
- |palgextint| |primextendedint| |doubleFloatFormat| |monomRDE| |rowEch|
- |nextsubResultant2| |squareFreePolynomial| |shade| |ran|
- |rationalPower| |associator| |OMgetEndObject| |outputAsScript|
- |prime?| |safeCeiling| |relationsIdeal| |previous| |less?| |delta|
- |invmultisect| |curveColor| |integralDerivationMatrix| |consnewpol|
- |pseudoDivide| |clearFortranOutputStack| |leftQuotient|
- |rischNormalize| |halfExtendedResultant2| |resultantEuclidean|
- |edf2fi| |rightAlternative?| |cAsinh| |initial| |diagonalMatrix|
- |drawStyle| |iiacosh| |s17agf| |pol| |cscIfCan| |next|
- |pointColorDefault| |goto| |explicitlyFinite?| |monomialIntPoly|
- |precision| |central?| |s21bcf| |key| |hyperelliptic|
- |listConjugateBases| |iidprod| |removeDuplicates!| |cot2trig| |f02bbf|
- |putColorInfo| |antisymmetric?| |approxNthRoot| |slash|
- |exponentialOrder| |intChoose| |makeYoungTableau| |prepareSubResAlgo|
- |unit?| |choosemon| |taylorQuoByVar| |times!| |filename| |c06ebf|
- |viewThetaDefault| |swap!| |psolve| |inverseIntegralMatrixAtInfinity|
- |hostPlatform| |hclf| |dfRange| |companionBlocks| |powers|
- |mainCharacterization| |splitLinear| |corrPoly| |e01bgf| |returnType!|
- |qfactor| |setPrologue!| |connectTo| |f01brf| |evenlambert|
- |combineFeatureCompatibility| |diag| |parse| |numberOfMonomials|
- |arity| |littleEndian| |divideExponents| |recolor| |lambda|
- |semiLastSubResultantEuclidean| |iicoth| |indicialEquation| |code|
- |rombergo| |generate| |cardinality| |modularGcd| |byteBuffer|
- |linearAssociatedOrder| |showTheFTable| |unrankImproperPartitions1|
- |setMinPoints| |diophantineSystem| |setnext!| |trigs|
- |symmetricDifference| |addiag| |log2| |sample| |OMsupportsSymbol?|
- |highCommonTerms| |back| |karatsuba| |iroot| |initiallyReduced?|
- |incrementBy| |getCode| |overbar| |checkRur| |disjunction|
- |ScanFloatIgnoreSpaces| |numerators| |OMsetEncoding| |truncate|
- |factor1| |e01bef| |lazyPseudoQuotient| |lowerCase| |isImplies|
- |lowerCase!| |tanh2coth| |permanent| |externalList| |viewZoomDefault|
- |constantLeft| |OMputAtp| |resetAttributeButtons| |elColumn2!|
- |numFunEvals3D| |findBinding| |printInfo| |multMonom| |ldf2lst|
- |doubleResultant| |splitConstant| |jordanAlgebra?| |d01apf| |rarrow|
- |polygamma| |makeSketch| |cCsch| |squareFree| |ptFunc| |leftPower|
- |complexElementary| |octon| |hermiteH| |leftDiscriminant| LODO2FUN
- |stiffnessAndStabilityOfODEIF| |iiacot| |is?| |linearMatrix|
- |useNagFunctions| |minimumExponent| |e02bcf| |scan| |options|
- |increase| |equiv| |meshPar2Var| |makeViewport2D| |summation| |tail|
- |dom| |any| |leftTraceMatrix| |triangulate| RF2UTS |bitCoef| |moebius|
- |toScale| |definingInequation| |e02def| |characteristicSet|
- |minimumDegree| |iicsch| |arg1| |c06frf| |entry| |f04arf| |iExquo|
- |showTheIFTable| |internalSubQuasiComponent?| |LagrangeInterpolation|
- |semiDiscriminantEuclidean| |nil| |infinite| |arbitraryExponent|
+ |Record| |Union| |LyndonCoordinates| |rename!| |setClosed|
+ |elementary| |pointLists| |arg2| |f04asf| |youngGroup| |radicalRoots|
+ |string| |mapDown!| |reduceBasisAtInfinity| |constantCoefficientRicDE|
+ |LyndonBasis| |mainValue| |tube| |alternating| |makeGraphImage|
+ |lexGroebner| |f04atf| |contractSolve| |say| |normalizeAtInfinity|
+ |changeVar| |zeroDimensional?| |mainDefiningPolynomial| |unitVector|
+ |cyclic| |conditions| |graphImage| |totalGroebner| |f04axf|
+ |decomposeFunc| |complementaryBasis| |ratDsolve| |fglmIfCan|
+ |mainForm| |cosSinInfo| |dihedral| |title| |groebSolve| |match|
+ |f04faf| |expressIdealMember| |unvectorise| |reset| |integral?|
+ |indicialEquationAtInfinity| |groebner| |rischDE| |arguments|
+ |loopPoints| |cap| |testDim| |principalIdeal| |f04jgf| |bubbleSort!|
+ |inc| |integralAtInfinity?| |reduceLODE| |lexTriangular| |rischDEsys|
+ |generalTwoFactor| |cup| |genericPosition| |f04maf|
+ |LagrangeInterpolation| |insertionSort!| |write|
+ |integralBasisAtInfinity| |singRicDE| |squareFreeLexTriangular|
+ |monomRDE| |generalSqFr| |e| |wreath| |save| |lfunc| |psolve| |f04mbf|
+ |check| |ramified?| |polyRicDE| |belong?| |baseRDE| |twoFactor|
+ |SFunction| |inHallBasis?| |nothing| |wrregime| |f04mcf| |lprop|
+ |ramifiedAtInfinity?| |ricDsolve| |Ci| |polyRDE| |setOrder|
+ |skewSFunction| |reorder| |rdregime| |f04qaf| |llprop| |singular?|
+ |triangulate| |Si| |monomRDEsys| |getOrder| |cyclotomicDecomposition|
+ |headAst| |bsolve| |top| |f07adf| |lllp| |singularAtInfinity?|
+ |solveInField| |Ei| |baseRDEsys| |less?| |cyclotomicFactorization|
+ |continue| |heap| |dmp2rfi| |f07aef| |lllip| |branchPoint?|
+ |wronskianMatrix| |linGenPos| |weighted| |userOrdered?|
+ |rangeIsFinite| |sn| |gcdprim| |se2rfi| |f07fdf| |mesh?| |parts|
+ |branchPointAtInfinity?| |variationOfParameters| |groebgen| |rdHack1|
+ |largest| |functionIsContinuousAtEndPoints| |typeForm| |gcdcofact|
+ |pr2dmp| |f07fef| |mesh| ** |hash| |rationalPoint?| |lexico| |totolex|
+ |midpoint| |more?| |functionIsOscillatory| |gcdcofactprim| |hasoln|
+ |s01eaf| |polygon?| |count| |absolutelyIrreducible?| |OMmakeConn|
+ |minPol| |midpoints| |setVariableOrder| |datalist| |changeName|
+ |lintgcd| |ParCondList| |s13aaf| |polygon| |genus| |OMcloseConn|
+ |computeBasis| |realZeros| |getVariableOrder|
+ |exprHasWeightCosWXorSinWX| |hex| |redpps| |s13acf| |closedCurve?|
+ |getZechTable| |OMconnInDevice| |coord| |mainCharacterization|
+ |resetVariableOrder| |constant| |exprHasAlgebraicWeight| |every?|
+ |B1solve| |s13adf| |closedCurve| |createZechTable| |OMconnOutDevice|
+ |anticoord| |algebraicOf| |prime?| |exprHasLogarithmicWeights| |any?|
+ |mantissa| |factorset| |s14aaf| |curve?| |outputList|
+ |createMultiplicationTable| |OMconnectTCP| |intcompBasis|
+ |ReduceOrder| |sample| |combineFeatureCompatibility| |host| |maxrank|
+ |s14abf| |curve| |createMultiplicationMatrix| |OMbindTCP| |choosemon|
+ |setref| |rationalFunction| |rank| |setProperty| |sparsityIF|
+ |trueEqual| |minrank| |s14baf| |point?| |createLowComplexityTable|
+ |OMopenFile| |transform| |deref| |taylorIfCan|
+ |stiffnessAndStabilityFactor| |factorList| |minset| |s15adf|
+ |enterPointData| |createLowComplexityNormalBasis| |OMopenString|
+ |pack!| |ref| |removeZeroes| |deleteProperty!|
+ |stiffnessAndStabilityOfODEIF| |listConjugateBases| |nextSublist|
+ |s15aef| |composites| |representationType| |OMclose| |complexLimit|
+ |radicalEigenvectors| |taylorRep| |has?| |systemSizeIF| |matrixGcd|
+ |overset?| |s17acf| |components| |checkPrecision|
+ |createPrimitiveElement| |OMsetEncoding| |limit| |radicalEigenvector|
+ |factorSquareFree| |expenseOfEvaluationIF| |divideIfCan!| |ParCond|
+ |s17adf| |numberOfComposites| |tableForDiscreteLogarithm| |OMputApp|
+ |linearlyDependent?| |radicalEigenvalues| |henselFact| |accuracyIF|
+ |leader| |leastPower| |redmat| |s17aef| |numberOfComponents|
+ |factorsOfCyclicGroupSize| |OMputAtp| |linearDependence| |eigenMatrix|
+ |hasHi| |resetAttributeButtons| |intermediateResultsIF| |idealiser|
+ |regime| |s17aff| |create3Space| |getButtonValue| |sizeMultiplication|
+ |categories| |OMputAttr| |solveLinear| |normalise| |numer| |fmecg|
+ |decrease| |lists| |subscriptedVariables| |retractIfCan|
+ |idealiserMatrix| |sqfree| |s17agf| |outputAsScript|
+ |getMultiplicationMatrix| |OMputBind| |linearElement| |gramschmidt|
+ |denom| |commonDenominator| |increase| |central?| |moduleSum|
+ |inconsistent?| |s17ahf| |outputAsTex| |getMultiplicationTable|
+ |OMputBVar| |reducedSystem| |orthonormalBasis| |clearDenominator|
+ |elliptic?| |mapUnivariate| |numFunEvals| |s17ajf| |abs| |primitive?|
+ |OMputError| |leftReducedSystem| |antisymmetricTensors| |pi|
+ |splitDenominator| |mapUnivariateIfCan| |setAdaptive| |s17akf| |Beta|
+ |numberOfIrreduciblePoly| |OMputObject| |linearForm|
+ |createGenericMatrix| |infinity| |monicRightFactorIfCan|
+ |associatedSystem| |charClass| |mapMatrixIfCan| |adaptive?| |s17dcf|
+ |digamma| |concat| |step| |numberOfPrimitivePoly| |OMputEndApp|
+ |setDifference| |symmetricTensors| |rightFactorIfCan|
+ |uncouplingMatrices| |alphanumeric?| |mapBivariate|
+ |setScreenResolution| |s17def| |polygamma| |numberOfNormalPoly|
+ |OMputEndAtp| |setIntersection| |tensorProduct| |leftFactorIfCan|
+ |lowerCase?| |fullDisplay| |screenResolution| |s17dgf| |Gamma|
+ |setUnion| |permutationRepresentation| |kernel| |monicDecomposeIfCan|
+ |upperCase?| |relationsIdeal| |setMaxPoints| |s17dhf| |besselJ| |init|
+ |edf2ef| |substitute| |list| |completeEchelonBasis|
+ |monicCompleteDecompose| |ptree| |alphabetic?| |saturate| |maxPoints|
+ |s17dlf| |besselY| |lhs| |vedf2vef| |duplicates?|
+ |createRandomElement| |draw| |divideIfCan| |hexDigit?| |groebner?|
+ |setMinPoints| |clearCache| |s18acf| |besselI| |rhs| |df2st| |mapGen|
+ |cyclicSubmodule| |noKaratsuba| |digit?| |s18adf| |besselK| |f2st|
+ |mapExpon| |standardBasisOfCyclicSubmodule| |karatsubaOnce| |escape|
+ |degreePartition| |quoted?| |s18aef| |airyAi| |currentEnv| |ldf2lst|
+ |integerBound| |commutativeEquality| |areEquivalent?| |karatsuba|
+ |ord| |operation| |factorOfDegree| |inR?| |s18aff| |airyBi| |sdf2lst|
+ |setright!| |leftMult| |isAbsolutelyIrreducible?| |makeObject|
+ |separate| |mkIntegral| |factorsOfDegree| |isList| |s18dcf| |subNode?|
+ |getlo| |setleft!| |directory| |pseudoDivide| |coef| |radPoly|
+ |pascalTriangle| |isOp| |s18def| |infLex?| |gethi| |approxSqrt|
+ |shade| |brillhartIrreducible?| |pseudoQuotient| |rootPoly|
+ |rangePascalTriangle| |satisfy?| |s19aaf| |setEmpty!| |outputMeasure|
+ |generateIrredPoly| |nthRootIfCan| |brillhartTrials| |composite|
+ |goodPoint| |sizePascalTriangle| |addBadValue| |s19abf| |setStatus!|
+ |measure2Result| |complexExpand| |expIfCan| |noLinearFactor?|
+ |subResultantGcd| |chvar| |fillPascalTriangle| |badValues| |kind|
+ |att2Result| |complexIntegrate| |logIfCan| |insertRoot!| |resultant|
+ |removeDuplicates| |safeCeiling| |retractable?| |d02gbf| |subTriSet?|
+ |iflist2Result| |op| |dimensionOfIrreducibleRepresentation| |sinIfCan|
+ |binarySearchTree| |discriminant| |find| |kernels| |safeFloor|
+ |ListOfTerms| |d02kef| |subPolSet?| |pdf2ef|
+ |irreducibleRepresentation| |cosIfCan| |nor| |pseudoRemainder|
+ |clipParametric| |safetyMargin| |d02raf| |PDESolve|
+ |internalSubPolSet?| |operator| |pdf2df| |checkRur| |tanIfCan| |nand|
+ |basisOfCommutingElements| |clipWithRanges| SEGMENT |sumSquares|
+ |leftFactor| |d03edf| |internalInfRittWu?| |df2ef| |cAcsch| |cotIfCan|
+ |binaryTournament| |cyclicEntries| |basisOfLeftAnnihilator|
+ |numberOfHues| |euclideanNormalForm| |sort| |d03eef|
+ |rightFactorCandidate| |univariate| |internalSubQuasiComponent?|
+ |unary?| |fi2df| |cAsech| |secIfCan| |binaryTree| |cyclicCopy|
+ |yellow| |euclideanGroebner| |dec| |measure| |d03faf|
+ |subQuasiComponent?| |mat| |cAcoth| |cscIfCan| |setLength!| |cyclic?|
+ |iifact| |factorGroebnerBasis| |coerceImages| |e01baf|
+ |removeSuperfluousQuasiComponents| |neglist| |union| |cAtanh|
+ |asinIfCan| |capacity| |complexNormalize| |iibinom|
+ |groebnerFactorize| |e01bef| |fixedPoints| |subCase?| |factor|
+ |multiEuclidean| |cAcosh| |acosIfCan| |byteBuffer| |complexElementary|
+ |iiperm| |credPol| |random| |e01bff| |odd?| |sqrt|
+ |removeSuperfluousCases| |extendedEuclidean| |cAsinh| |atanIfCan|
+ |unknownEndian| |trigs| |comp| |iipow| |redPol| |e01bgf| |even?|
+ |prepareDecompose| |real| |euclideanSize| |cCsch| |acotIfCan|
+ |bigEndian| |real?| |iidsum| |gbasis| |e01bhf| |numberOfCycles|
+ |branchIfCan| |imag| |properties| |sizeLess?| |cSech| |asecIfCan|
+ |littleEndian| |complexForm| |copy| |iidprod| |directProduct| |critT|
+ |cyclePartition| |e01daf| |startTableGcd!| |super| |simplifyPower|
+ |cCoth| |translate| |acscIfCan| |subtractIfCan| |UpTriBddDenomInv|
+ |ipow| |critM| |coerceListOfPairs| |e01saf| |stopTableGcd!| |number?|
+ |cTanh| |depth| |sinhIfCan| |setPosition| |LowTriBddDenomInv|
+ |factorial| |critB| |e01sbf| |coercePreimagesImages| |brace|
+ |startTableInvSet!| |seriesSolve| |cCosh| |coshIfCan|
+ |generalizedContinuumHypothesisAssumed| |simplify| |multinomial|
+ |critBonD| |e01sef| |listRepresentation| |destruct| |stopTableInvSet!|
+ |erf| |constantToUnaryFunction| |cSinh| |tanhIfCan|
+ |generalizedContinuumHypothesisAssumed?| |htrigs| |permutation|
+ |critMTonD1| |permanent| |e01sff| |stosePrepareSubResAlgo| |match?|
+ |tubePlot| |cAcsc| |cothIfCan| |countable?| |simplifyExp| |autoCoerce|
+ |stirling1| |critMonD1| |cycles| |e02adf|
+ |stoseInternalLastSubResultant| |exponentialOrder| |cAsec| |sechIfCan|
+ |Aleph| |simplifyLog| |stirling2| |redPo| |cycle| |e02aef|
+ |stoseIntegralLastSubResultant| |dilog| |completeEval| |cAcot|
+ |cschIfCan| |unravel| |expandPower| |summation| |hMonic| |expand|
+ |e02agf| |initializeGroupForWordProblem| |monomial|
+ |stoseLastSubResultant| |sin| |lowerPolynomial| |cAtan| |asinhIfCan|
+ |leviCivitaSymbol| |expandLog| |factorials| |updatF| |filterWhile|
+ |e02ahf| |support| |multivariate| |stoseInvertible?sqfreg| |close|
+ |cos| |kroneckerDelta| |raisePolynomial| |cAcos| |acoshIfCan| F
+ |cos2sec| |mkcomm| |sPol| |filterUntil| |e02ajf| |wordInGenerators|
+ |variables| |stoseInvertibleSetsqfreg| |tan| |normalDeriv| |cAsin|
+ |atanhIfCan| |reindex| |cosh2sech| |polarCoordinates| |select|
+ |updatD| |wordInStrongGenerators| |e02akf| |stoseInvertible?reg|
+ |display| |cot| |ran| |cCsc| |acothIfCan| |principalAncestors|
+ |cot2trig| |imaginary| |minGbasis| |orbits| |e02baf|
+ |stoseInvertibleSetreg| |sec| |highCommonTerms| |cSec| |asechIfCan|
+ |exportedOperators| |coth2trigh| |elaborateFile| |lepol| |orbit|
+ |e02bbf| |stoseInvertible?| |csc| |mapCoef| |cCot| |acschIfCan|
+ |alphanumeric| |csc2sin| |elaborate| |prinshINFO| |permutationGroup|
+ |e02bcf| |stoseInvertibleSet| |asin| |nthCoef| |cTan| |pushdown|
+ |alphabetic| |csch2sinh| |solid| |prindINFO| |e02bdf|
+ |wordsForStrongGenerators| |debug| |qelt| |stoseSquareFreePart|
+ |taylor| |acos| |predicate| |binomThmExpt| |cCos| |pushup| |hexDigit|
+ |sec2cos| |solid?| |qsetelt| |fprindINFO| |e02bef| |strongGenerators|
+ D |coleman| |laurent| |input| |atan| |pomopo!| |cSin|
+ |reducedDiscriminant| |digit| |sech2cosh| |denominators| |prinpolINFO|
+ |e02daf| |generators| |xRange| |inverseColeman| |puiseux| |library|
+ |acot| |mapExponents| |cLog| |idealSimplify| |sin2csc| EQ |numerators|
+ |prinb| |e02dcf| |bivariateSLPEBR| |yRange| |listYoungTableaus| |asec|
+ |linearAssociatedLog| |cExp| |definingInequation| |sinh2csch|
+ |convergents| |critpOrder| |e02ddf|
+ |solveLinearPolynomialEquationByRecursion| |inv| |zRange|
+ |makeYoungTableau| |acsc| |linearAssociatedOrder| |cRationalPower|
+ |definingEquations| |tan2trig| |approximants| |ground?| |makeCrit|
+ |map!| |factorByRecursion| |e02def| |nextColeman| |sinh|
+ |linearAssociatedExp| |cPower| |setStatus| |tanh2trigh| |reducedForm|
+ |qsetelt!| |ground| |virtualDegree| |factorSquareFreeByRecursion|
+ |e02dff| |nextLatticePermutation| |set| |cosh| |createNormalElement|
+ |seriesToOutputForm| |quasiAlgebraicSet| |double| |tan2cot|
+ |partialQuotients| |conditionsForIdempotents| |e02gaf| |randomR|
+ |leadingMonomial| |nextPartition| |balancedBinaryTree| |tanh|
+ |setLabelValue| |iCompose| |radicalSimplify| |tanh2coth|
+ |partialDenominators| |genericRightDiscriminant| |e02zaf|
+ |factorSFBRlcUnit| |leadingCoefficient| |numberOfImproperPartitions|
+ |sylvesterMatrix| |coth| |getCode| |taylorQuoByVar| |denominator|
+ |cot2tan| |size| |partialNumerators| |genericRightTraceForm| |e04dgf|
+ |charthRoot| |primitiveMonomials| |subSet| |parameters| |sech|
+ |printCode| |iExquo| |numerator| |coth2tanh|
+ |reducedContinuedFraction| |genericLeftDiscriminant| |e04fdf|
+ |conditionP| |print| |unrankImproperPartitions0| |reductum| |csch|
+ |printStatement| |box| |getStream| |quadraticForm| |removeCosSq|
+ |push| |genericLeftTraceForm| |resolve| |e04gcf|
+ |solveLinearPolynomialEquation| |unrankImproperPartitions1| |acsch|
+ |asinh| |block| |getRef| |back| |removeSinSq| |cartesian|
+ |genericRightNorm| |factorSquareFreePolynomial| |e04jaf|
+ |subresultantSequence| |acosh| |returns| |true| |makeSeries| |front|
+ |category| |removeCoshSq| |polar| |genericRightTrace|
+ |factorPolynomial| |e04mbf| |SturmHabichtSequence| |bezoutMatrix|
+ |domain| |call| |mappingMode| |optional| |rotate!| |declare!|
+ |removeSinhSq| |cylindrical| |genericRightMinimalPolynomial|
+ |squareFreePolynomial| |e04naf| |SturmHabichtCoefficients|
+ |bezoutResultant| |goto| |categoryMode| |dequeue!| |package|
+ |expandTrigProducts| |spherical| |rightRankPolynomial| |gcdPolynomial|
+ |e04ucf| |SturmHabicht| |insert| |repeatUntilLoop| |voidMode|
+ |enqueue!| |fintegrate| |parabolic| |genericLeftNorm| |torsion?|
+ |e04ycf| |countRealRoots| |show| |whileLoop| |noValueMode| |quatern|
+ |coefficient| |basisOfRightAnnihilator| |genericLeftTrace| |search|
+ |torsionIfCan| |f01brf| |SturmHabichtMultiple| |forLoop| |jokerMode|
+ |imagK| |coHeight| |node| |basisOfLeftNucleus|
+ |genericLeftMinimalPolynomial| |getGoodPrime| |f01bsf|
+ |countRealRootsMultiple| |trace| |sin?| GF2FG |imagJ| |extendIfCan|
+ |basisOfRightNucleus| |leftRankPolynomial| |badNum| |f01maf|
+ |signatureAst| |zeroVector| FG2F |imagI| |algebraicVariables|
+ |basisOfMiddleNucleus| |generic| |mix| |f01mcf| |pop!| |stop| F2FG
+ |conjugate| |zeroSetSplitIntoTriangularSystems| |segment|
+ |basisOfNucleus| |rightUnits| |doubleDisc| |f01qcf| |push!|
+ |validExponential| |explogs2trigs| |queue| |zeroSetSplit|
+ |basisOfCenter| |leftUnits| |polyred| |f01qdf| |minordet| |formula|
+ |flatten| |rootNormalize| |trigs2explogs| |nthRoot|
+ |reduceByQuasiMonic| |basisOfLeftNucloid| |compBound| |padicFraction|
+ |f01qef| |determinant| |tanQ| |swap!| |fractRadix| |collectQuasiMonic|
+ |basisOfRightNucloid| |f01rcf| |isQuotient| |diagonalProduct|
+ |callForm?| |fill!| |wholeRadix| |removeZero| |exprToUPS| |slash|
+ |basisOfCentroid| |f01rdf| |diagonal| |getIdentifier| |minIndex|
+ |cycleRagits| |initiallyReduce| |exprToGenUPS| |over|
+ |radicalOfLeftTraceForm| |f01ref| |diagonalMatrix| |nrows| |variable?|
+ |maxIndex| |prefixRagits| |headReduce| |localAbs| |zag| |applyRules|
+ |f02aaf| |scalarMatrix| |ncols| |getConstant| |stronglyReduce|
+ |universe| |postfix| |localUnquote| |f02abf| |hermite| |environment|
+ |palgint| |rewriteIdealWithRemainder| |rewriteSetWithReduction|
+ |arbitrary| |complement| |infix| |f02adf| |height| |completeHermite|
+ |units| |irForm| |log10| |palgextint| |rewriteIdealWithHeadRemainder|
+ |autoReduced?| |equation| |cardinality| |vconcat| |setColumn!|
+ |f02aef| |smith| |elaboration| |bitand| |palglimint| |remainder|
+ |initiallyReduced?| |internalIntegrate0| |hconcat| |leaves|
+ |outerProduct| |select!| |bitior| |palgRDE| |headRemainder|
+ |headReduced?| |makeCos| |rspace| |rightPower|
+ |lastSubResultantElseSplit| |delete!| |palgLODE| |roughUnitIdeal?|
+ |stronglyReduced?| |makeSin| |vspace| |derivationCoordinates|
+ |invertibleSet| |macroExpand| |dn| |splitConstant| |roughEqualIdeals?|
+ |reduced?| |iiGamma| |hspace| |one?| |invertible?|
+ |bezoutDiscriminant| |sncndn| |pmComplexintegrate| |roughSubIdeal?|
+ |iiabs| |superHeight| |splitSquarefree| |invertibleElseSplit?|
+ |bfEntry| |categoryFrame| |pmintegrate| |roughBase?| |compound?|
+ |bringDown| |subHeight| |normalDenom|
+ |purelyAlgebraicLeadingMonomial?| |interactiveEnv| |infieldint|
+ |trivialIdeal?| |getOperands| |rule| |newReduc| |declare|
+ |doubleFloatFormat| |totalfract| |algebraicCoefficients?|
+ |putProperties| |extendedint| |collectUpper| |common| |getOperator|
+ |logical?| |messagePrint| |pushdterm| |purelyTranscendental?|
+ |getProperties| |limitedint| |collect| |nil?| |character?| |members|
+ |pushucoef| |purelyAlgebraic?| |var2StepsDefault| |putProperty|
+ |integerIfCan| |collectUnder| |buildSyntax| |doubleComplex?| |padecf|
+ |pushuconst| |prepareSubResAlgo| |tubePointsDefault| |getProperty|
+ |internalIntegrate| |mainVariable?| |solve| |complex?|
+ |numberOfMonomials| |pade| |matrix| |internalLastSubResultant|
+ |tubeRadiusDefault| |scopes| |infieldIntegrate| |mainVariables|
+ |triangularSystems| |double?| |root| |multiset|
+ |integralLastSubResultant| |dimension| |eigenvalues|
+ |limitedIntegrate| |removeSquaresIfCan| |nativeModuleExtension|
+ |ffactor| |quotientByP| |mergeDifference| |toseLastSubResultant|
+ |crest| |eigenvector| |extendedIntegrate|
+ |unprotectedRemoveRedundantFactors| |hostByteOrder| Y |qfactor|
+ |moduloP| |squareFreePrim| |toseInvertible?| |cfirst|
+ |generalizedEigenvector| |varselect| |removeRedundantFactors| |label|
+ |hostPlatform| |UP2ifCan| |modulus| |compdegd| |toseInvertibleSet|
+ |sts2stst| |generalizedEigenvectors| |kmax| |certainlySubVariety?|
+ |rootDirectory| |anfactor| |digits| |univcase| |toseSquareFreePart|
+ |clikeUniv| |eigenvectors| |ksec| |possiblyNewVariety?| |bumprow|
+ |fortranCharacter| |continuedFraction| |consnewpol| |quotedOperators|
+ |weierstrass| |factorAndSplit| |vark| |probablyZeroDim?| |result|
+ |bumptab| |fortranDoubleComplex| |light| |nsqfree| |rur| |qqq|
+ |rightOne| |removeConstantTerm| |selectPolynomials| |bumptab1|
+ |fortranComplex| |pastel| |intChoose| |create| |integralBasis|
+ |leftOne| |mkPrim| |selectOrPolynomials| |untab| |fortranLogical|
+ |dark| |coefChoose| |enterInCache| |localIntegralBasis| |rightZero|
+ |intPatternMatch| |selectAndPolynomials| |bat1| |fortranInteger|
+ |getSyntaxFormsFromFile| |myDegree| |currentCategoryFrame|
+ |constructor| |qualifier| |leftZero| |primintegrate|
+ |quasiMonicPolynomials| |bat| |fortranDouble| |surface| |normDeriv2|
+ |currentScope| |mainExpression| |sum| |bindings| |swap| |expintegrate|
+ |univariate?| |option| |tab1| |showSummary| |symbolTable|
+ |fortranReal| |coordinate| |plenaryPower| |pushNewContour|
+ |changeWeightLevel| |minPoly| |tanintegrate| |univariatePolynomials|
+ |tab| |external?| |conjugates| |c02aff| |findBinding|
+ |characteristicSerie| |freeOf?| |primextendedint| |linear?| |lex|
+ |pushFortranOutputStack| |scalarTypeOf| |lp| |showAttributes|
+ |shuffle| |c02agf| |contours| |characteristicSet| |operators|
+ |expextendedint| |linearPolynomials| |makeRecord| |slex|
+ |popFortranOutputStack| |fortranCarriageReturn| |shufflein| |c05adf|
+ |structuralConstants| |medialSet| |mainKernel| |primlimitedint|
+ |bivariate?| |inverse| |outputAsFortran| |fortranLiteral| |sequences|
+ |c05nbf| |coordinates| |Hausdorff| |distribute| |name| |explimitedint|
+ |bivariatePolynomials| |maxrow| |fortranLiteralLine| |permutations|
+ |c05pbf| |bounds| |Frobenius| |rightTrim| |functionIsFracPolynomial?|
+ |body| |primextintfrac| |removeRoughlyRedundantFactorsInPols|
+ |tableau| |processTemplate| |makeResult| |c06eaf| |high|
+ |transcendenceDegree| |leftTrim| |problemPoints| |primlimintfrac|
+ |removeRoughlyRedundantFactorsInPol| |listOfLists| |null| |makeFR|
+ |is?| |c06ebf| |low| |stack| |extensionDegree| |zerosOf|
+ |primintfldpoly| |interReduce| |tanSum| |not| |musserTrials| |Is|
+ |c06ecf| |subset?| |inGroundField?| BY |cn| |singularitiesOf|
+ |expintfldpoly| |roughBasicSet| |tanAn| |and| |stopMusserTrials|
+ |addMatchRestricted| |c06ekf| |symmetricDifference| |transcendent?|
+ |polynomialZeros| |monomialIntegrate| |crushedSet| |tanNa| |or|
+ |numberOfFactors| |insertMatch| |c06fpf| |difference| |algebraic?|
+ |f2df| |monomialIntPoly|
+ |rewriteSetByReducingWithParticularGenerators| |initTable!| |xor|
+ |modularFactor| |addMatch| |c06fqf| |intersect| |sh| |ef2edf|
+ |inverseLaplace| |rewriteIdealWithQuasiMonicGenerators| |signature|
+ |dim| |printInfo!| |case| |useSingleFactorBound?| |getMatch| |assert|
+ |c06frf| |part?| |mirror| |ocf2ocdf| |port| |inputOutputBinaryFile|
+ |squareFreeFactors| |pattern| |startStats!| |Zero|
+ |useSingleFactorBound| |failed?| |c06fuf| |latex| |monomial?|
+ |socf2socdf| |closed| |univariatePolynomialsGcds| |printStats!| |One|
+ |useEisensteinCriterion?| |optpair| |c06gbf| |member?| |rquo| |df2fi|
+ |t| |bothWays| |removeRoughlyRedundantFactorsInContents| |shift|
+ |clearTable!| NOT |useEisensteinCriterion| |c06gcf| |getBadValues|
+ |enumerate| |output| |lquo| |edf2fi| |bytes|
+ |removeRedundantFactorsInContents| |usingTable?| OR |vector|
+ |eisensteinIrreducible?| |resetBadValues| |c06gqf| |setOfMinN|
+ |mindegTerm| |edf2df| |ip4Address| |removeRedundantFactorsInPols|
+ |message| |printingInfo?| AND |differentiate|
+ |tryFunctionalDecomposition?| |hasTopPredicate?| |c06gsf| |elements|
+ |product| |expenseOfEvaluation| |iprint| |irreducibleFactors|
+ |makingStats?| |tryFunctionalDecomposition| |d01ajf| |topPredicate|
+ |replaceKthElement| |fortran| |LiePolyIfCan| |numberOfOperations|
+ |elem?| |lazyIrreducibleFactors| |extractIfCan| |elt| |btwFact|
+ |setTopPredicate| |d01akf| |incrementKthElement| |trunc| |edf2efi|
+ |notelem| |removeIrreducibleRedundantFactors| |insert!|
+ |beauzamyBound| |patternVariable| |d01alf| |cdr| |level| |degree|
+ |dfRange| |logpart| |normalForm| |interpretString| |bombieriNorm|
+ |withPredicates| |d01amf| |car| |quasiRegular| |dflist| |ratpart|
+ |changeBase| |stripCommentsAndBlanks| |rootBound| |setPredicates|
+ |d01anf| |float?| |cons| |quasiRegular?| |df2mf| |mkAnswer|
+ |companionBlocks| |setPrologue!| |singleFactorBound| |predicates|
+ |d01apf| |integer?| |constant?| |ldf2vmf| |cond| |irDef| |xCoord|
+ |setTex!| |retract| |quadraticNorm| |hasPredicate?| |d01aqf| |symbol?|
+ |mindeg| |irCtor| |yCoord| |setEpilogue!| |infinityNorm| |optional?|
+ |d01asf| |string?| |maxdeg| |style| |irVar| |zCoord| |prologue|
+ |second| * |scaleRoots| |multiple?| |d01bbf| |list?| |RemainderList|
+ |toScale| |perfectNthPower?| |rCoord| |epilogue| |third| |shiftRoots|
+ |generic?| |d01fcf| |pair?| |unexpand| |pointColorPalette|
+ |perfectNthRoot| |thetaCoord| |endOfFile?| |d01gaf| |atom?| |source|
+ |void| |shape| |curveColorPalette| |approxNthRoot| |phiCoord|
+ |readIfCan!| |exp1| = |evaluateInverse| |d01gbf| |null?|
+ |youngDiagram| |var1Steps| |perfectSquare?| |color| |readLineIfCan!|
+ |log2| |evaluate| |d02bbf| |startTable!| |script| |triangSolve|
+ |var2Steps| |perfectSqrt| |hue| |readLine!| |rationalApproximation| <
+ |conjug| |d02bhf| |stopTable!| |univariateSolve| |space|
+ |plusInfinity| |writeLine!| |char| |relerror| > |adjoint| |d02cjf|
+ |supDimElseRittWu?| |realSolve| |tubePoints| |minusInfinity|
+ |innerSolve1| |prevPrime| |systemCommand| |sign| |complexSolve| <=
+ |arity| |d02ejf| |algebraicSort| |tex| |target| |positiveSolve|
+ |tubeRadius| |innerSolve| |primes| |mapUp!| |nonQsign| |complexRoots|
+ >= |getDatabase| |d02gaf| |moreAlgebraic?| |squareFree| |weight|
+ |makeEq| |selectsecond| |setleaves!| |direction| |expr| |realRoots|
+ |numericalOptimization| |linearlyDependentOverZ?| |makeVariable|
+ |modularGcdPrimitive| |selectfirst| |normal| |createThreeSpace|
+ |leadingTerm| |goodnessOfFit| |invertIfCan| |changeThreshhold|
+ |linearDependenceOverZ| |finiteBound| |modularGcd| |makeprod| |linear|
+ |cyclicParents| |overlap| + |whatInfinity| |copy!|
+ |selectMultiDimensionalRoutines| |solveLinearlyOverQ|
+ |sortConstraints| |type| |reduction| |property| |cyclicEqual?| |hcrf|
+ - |infinite?| |float| |plus!| |selectNonFiniteRoutines| |sumOfSquares|
+ |signAround| |disjunction| |polynomial| |hclf| |variable| / |finite?|
+ |minus!| |selectSumOfSquaresRoutines| |splitLinear| |invmod|
+ |conjunction| |mapdiv| |iterators| |writable?| |pureLex|
+ |leftScalarTimes!| |selectFiniteRoutines| |simpleBounds?| |powmod|
+ |isEquiv| |lazyGintegrate| |readable?| |totalLex| |rightScalarTimes!|
+ |selectODEIVPRoutines| |linearMatrix| |mulmod| |isImplies| |power|
+ |exists?| |reverseLex| |times!| |selectPDERoutines| |linearPart|
+ |submod| |isOr| |sincos| |id| |extension| |leftLcm| |power!|
+ |selectOptimizationRoutines| |value| |dot| |nonLinearPart| |addmod|
+ |isAnd| |symbol| |sinhcosh| |lo| |shallowExpand| |rightExtendedGcd|
+ |just| |selectIntegrationRoutines| |scan| |quadratic?|
+ |symmetricRemainder| |isNot| |expression| |subresultantVector|
+ |deepExpand| |rightGcd| |gradient| |routines| |graphCurves|
+ |setButtonValue| |changeNameToObjf| |positiveRemainder| |isAtom|
+ |integer| |primitivePart| |clearFortranOutputStack|
+ |rightExactQuotient| GE |divergence| |mainSquareFreePart| |drawCurves|
+ |optAttributes| |bit?| |atoms| |setAttributeButtonStep| |pointData|
+ |showFortranOutputStack| |rightRemainder| GT |laplacian|
+ |mainPrimitivePart| |scale| |Nul| |algint| |dual| |parent|
+ |topFortranOutputStack| |rightQuotient| LE |hessian| |mainContent|
+ |connect| |exponents| |algintegrate| |equiv| |extractProperty|
+ |setFormula!| |rightLcm| LT |bandedHessian| |primitivePart!| |region|
+ |iisqrt2| |palgintegrate| |implies| |extractClosed| |linkToFortran|
+ |leftExtendedGcd| |jacobian| |nextsubResultant2| |points| |iisqrt3|
+ |palginfieldint| |merge!| |extractIndex|
+ |setLegalFortranSourceExtensions| |leftGcd| |bandedJacobian|
+ |LazardQuotient2| |getGraph| |iiexp| |bitLength| |max| |extractPoint|
+ |keys| |fracPart| |leftExactQuotient| |duplicates| |LazardQuotient|
+ |putGraph| |iilog| |bitCoef| |resultantEuclidean| |traverse|
+ |polyPart| |leftRemainder| |removeDuplicates!| |subResultantChain|
+ |graphs| |iisin| |bitTruth| |semiResultantEuclidean2| |defineProperty|
+ |index| |fullPartialFraction| |leftQuotient| |linears|
+ |halfExtendedSubResultantGcd2| |graphStates| |iicos| |contains?|
+ |semiResultantEuclidean1| |numeric| |closeComponent| |primeFrobenius|
+ |monicLeftDivide| |ddFact| |halfExtendedSubResultantGcd1| |graphState|
+ |iitan| |inf| |indiceSubResultant| |radical| |modifyPoint|
+ |discreteLog| |monicRightDivide| |separateFactors|
+ |extendedSubResultantGcd| |makeViewport2D| |iicot| |qinterval|
+ |indiceSubResultantEuclidean| |addPointLast| |pair| |open| |tree|
+ |decreasePrecision| |leftDivide| |exptMod| |exactQuotient!|
+ |viewport2D| |iisec| |bright| |interval|
+ |semiIndiceSubResultantEuclidean| |addPoint2| |increasePrecision|
+ |rightDivide| |meshPar2Var| |exactQuotient| |getPickedPoints| |iicsc|
+ |unit?| |degreeSubResultant| |addPoint| |bits| |hermiteH|
+ |meshFun2Var| |primPartElseUnitCanonical!| |colorDef| |iiasin| |eval|
+ |associates?| |degreeSubResultantEuclidean| |merge| |unitNormalize|
+ |laguerreL| |meshPar1Var| |primPartElseUnitCanonical| |intensity|
+ |iiacos| |unitCanonical| |semiDegreeSubResultantEuclidean| |deepCopy|
+ |operations| |unit| |legendreP| |ptFunc| |lazyResidueClass| |lighting|
+ |iiatan| |unitNormal| |lastSubResultantEuclidean| |shallowCopy|
+ |flagFactor| |writeBytes!| |minimumExponent| |monicModulo| |interpret|
+ |clipSurface| |iiacot| |error| |lfextendedint|
+ |semiLastSubResultantEuclidean| |numberOfChildren| |sqfrFactor|
+ |writeUInt8!| |maximumExponent| |lazyPseudoDivide| |showClipRegion|
+ |iiasec| |lflimitedint| |subResultantGcdEuclidean| |children|
+ |primeFactor| |writeInt8!| |rowEch| |lazyPremWithDefault| |optimize|
+ |showRegion| |iiacsc| |lfinfieldint| |semiSubResultantGcdEuclidean2|
+ |child| |nthFlag| |function| |writeByte!| |rowEchLocal| |lazyPquo|
+ |hitherPlane| |iisinh| |lfintegrate| |semiSubResultantGcdEuclidean1|
+ |birth| |nthExponent| |isOpen?| |rowEchelonLocal| |lazyPrem|
+ |eyeDistance| |iicosh| |lfextlimint| |discriminantEuclidean|
+ |internal?| |width| |irreducibleFactor| |outputBinaryFile|
+ |normalizedDivide| |pquo| |perspective| |iitanh| |BasicMethod| |rules|
+ |semiDiscriminantEuclidean| |root?| |factors| |blankSeparate| |maxint|
+ |prem| |zoom| |iicoth| |PollardSmallFactor| |chainSubResultants|
+ |leaf?| |nilFactor| |semicolonSeparate| |binaryFunction| |supRittWu?|
+ |rotate| |iisech| |showTheFTable| |schema| |outputForm|
+ |regularRepresentation| |commaSeparate| |makeFloatFunction|
+ |RittWuCompare| |drawStyle| |iicsch| |clearTheFTable|
+ |resultantReduit| |argscript| |traceMatrix| |pile| |unaryFunction|
+ |mainMonomials| |mr| |outlineRender| |iiasinh| |fTable|
+ |resultantReduitEuclidean| |superscript| |randomLC| |paren| |length|
+ |compiledFunction| |mainCoefficients| |diagonals| |morphism| |iiacosh|
+ |palgint0| |semiResultantReduitEuclidean| |subscript| |minimize|
+ |bracket| |scripts| |corrPoly| |leastMonomial| |axes|
+ |balancedFactorisation| |rem| |setRow!| |iiatanh| |palgextint0|
+ |divide| |scripted?| |module| |prod| |lifting| |mainMonomial|
+ |controlPanel| |quo| |oneDimensionalArray| |iiacoth| |palglimint0|
+ |Lazard| |resetNew| |varList| |rightRegularRepresentation| |overlabel|
+ |lifting1| |quasiMonic?| |viewpoint| |iiasech| |palgRDE0| |Lazard2|
+ |symFunc| |leftRegularRepresentation| |lcm| |overbar| |exprex|
+ |monic?| |dimensions| |div| |iiacsch| |delete| |palgLODE0|
+ |nextsousResultant2| |symbolTableOf| |rightTraceMatrix| |prime|
+ |coerceL| |deepestInitial| |resize| |exquo| |specialTrigs|
+ |chineseRemainder| |resultantnaif| |argumentListOf| |leftTraceMatrix|
+ |append| |quote| |coerceS| |iteratedInitials| |move| ~= |localReal?|
+ |divisors| |resultantEuclideannaif| |returnTypeOf| |rightDiscriminant|
+ |supersub| |gcd| |frobenius| |deepestTail| |modifyPointData| |#|
+ |rischNormalize| |eulerPhi| |semiResultantEuclideannaif| |printHeader|
+ |comparison| |leftDiscriminant| |presuper| |false| |computePowers|
+ |head| |subspace| ~ |realElementary| |fibonacci| |pdct| |returnType!|
+ |equality| |represents| |presub| |pow| |mdeg| |makeViewport3D|
+ |harmonic| |powers| |ravel| |argumentList!| |mergeFactors| |sub| |An|
+ |mvar| |viewport3D| |doubleResultant| |jacobi| |partitions| |reshape|
+ |endSubProgram| |isMult| |rarrow| |UnVectorise| |relativeApprox|
+ |viewDeltaYDefault| |distdfact| |/\\| |moebiusMu| |partition|
+ |extract!| |currentSubProgram| |exprToXXP| |assign| |Vectorise|
+ |rootOf| |viewDeltaXDefault| |separateDegrees| |\\/|
+ |numberOfDivisors| |complete| |bag| |newSubProgram| |apply| |coerce|
+ |setPoly| |allRootsOf| |viewZoomDefault| |trace2PowMod|
+ |sumOfDivisors| |pole?| |clearTheSymbolTable| |first| |construct|
+ |createIrreduciblePoly| |OMputEndAttr| |exponent| |definingPolynomial|
+ |viewPhiDefault| |tracePowMod| |sumOfKthPowerDivisors| |listBranches|
+ |showTheSymbolTable| |rest| |createPrimitivePoly| |OMputEndBind|
+ |exQuo| |positive?| |viewThetaDefault| |irreducible?|
+ |HermiteIntegrate| |plus| |triangular?| |update| |printTypes|
+ |createNormalPoly| |OMputEndBVar| |moebius| |negative?|
+ |pointColorDefault| |decimal| |newTypeLists|
+ |createNormalPrimitivePoly| |OMputEndError| |rightRecip| |zero?|
+ |lineColorDefault| |innerint| |groebnerIdeal| |minPoints| |typeLists|
+ |createPrimitiveNormalPoly| |OMputEndObject| |leftRecip| |augment|
+ |axesColorDefault| |exteriorDifferential| |ideal| |parametric?|
+ |times| |externalList| |nextIrreduciblePoly| |OMputInteger| |parents|
+ |leftPower| |lastSubResultant| |unitsColorDefault| |totalDifferential|
+ |leadingIdeal| |plotPolar| |typeList| |nextPrimitivePoly| |OMputFloat|
+ |pointSizeDefault| |homogeneous?| |backOldPos| |debug3D| |binding|
+ |position| |parametersOf| |nextNormalPoly| |OMputVariable| |rightMult|
+ |meatAxe| |viewPosDefault| |leadingBasisTerm| |generalPosition|
+ |numFunEvals3D| |setProperties| |fortranTypeOf| |nullary?|
+ |nextNormalPrimitivePoly| |OMputString| |makeUnit|
+ |scanOneDimSubspaces| |viewSizeDefault| |ignore?| |quotient|
+ |setAdaptive3D| |empty| |monom| |derivative| |lift|
+ |nextPrimitiveNormalPoly| |OMputSymbol| |reverse!| |expt|
+ |viewDefaults| |computeInt| |zeroDim?| |adaptive3D?|
+ |constantOperator| |loadNativeModule| |leastAffineMultiple| |reduce|
+ |OMgetApp| |point| |nthFactor| |showArrayValues| |viewWriteDefault|
+ |checkForZero| |inRadical?| |setScreenResolution3D| |s19acf|
+ |setCondition!| |constantOpIfCan| |reducedQPowers| |OMgetAtp|
+ |nthExpon| |showScalarValues| |viewWriteAvailable| |logGamma| |in?|
+ |screenResolution3D| |s19adf| |setValue!| |rootOfIrreduciblePoly|
+ |OMgetAttr| |makeMulti| |solveRetract| |var1StepsDefault|
+ |hypergeometric0F1| |element?| |setMaxPoints3D| |s20acf| |status|
+ |comment| |write!| |OMgetBind| |series| |makeTerm| |mainVariable|
+ |rotatez| |center| |zeroDimPrime?| |maxPoints3D| |s20adf| |empty?|
+ |log| |read!| |OMgetBVar| |listOfMonoms| |uniform01| |shiftLeft|
+ |rotatey| |zeroDimPrimary?| |setMinPoints3D| |s21baf| |splitNodeOf!|
+ |setelt| |iomode| |OMgetError| |symmetricSquare| |normal01|
+ |shiftRight| |rotatex| |primaryDecomp| |minPoints3D| |s21bbf|
+ |remove!| |close!| |OMgetObject| |factor1| |exponential1|
+ |karatsubaDivide| |identity| |contract| |tValues| |s21bcf|
+ |subNodeOf?| |reopen!| |OMgetEndApp| |min| |symmetricProduct|
+ |chiSquare1| |monicDivide| |dictionary| |gensym| |tRange| |s21bdf|
+ |nodeOf?| |rightUnit| |OMgetEndAtp| |symmetricPower| |exponential|
+ |divideExponents| |dioSolve| |leadingSupport| |plot|
+ |fortranCompilerName| |updateStatus!| |leftUnit| |OMgetEndAttr|
+ |directSum| |chiSquare| |zeroOf| |unmakeSUP| |newLine| |shrinkable|
+ |pointPlot| |fortranLinkerArgs| |extractSplittingLeaf|
+ |rightMinimalPolynomial| |OMgetEndBind|
+ |solveLinearPolynomialEquationByFractions| |factorFraction| |rootsOf|
+ |makeSUP| |copies| |physicalLength!| |calcRanges| |aspFilename|
+ |squareMatrix| |byte| |leftMinimalPolynomial| |OMgetEndBVar|
+ |hasSolution?| |componentUpperBound| |makeSketch| |vectorise|
+ |sayLength| |physicalLength| |dimensionsOf| |fixPredicate| |transpose|
+ |zero| |associatorDependence| |reverse| |OMgetEndError| |linSolve|
+ |blue| |inrootof| |extend| |setnext!| |flexibleArray| |patternMatch|
+ |restorePrecision| |trim| |droot| |lieAlgebra?| |OMgetEndObject|
+ |LyndonWordsList| |green| |li| |truncate| |setprevious!| |elseBranch|
+ |antiCommutator| |patternMatchTimes| |And| |split| |iroot|
+ |jordanAlgebra?| |OMgetInteger| |LyndonWordsList1| |red| |unknown|
+ |order| |shanksDiscLogAlgorithm| |thenBranch| |commutator| |bernoulli|
+ |Or| |replace| |noncommutativeJordanAlgebra?| |OMgetFloat|
+ |lyndonIfCan| |whitePoint| |size?| |terms| |reflect|
+ |generalizedInverse| |associator| |chebyshevT| |Not| |upperCase!|
+ |jordanAdmissible?| |OMgetVariable| |lyndon| |uniform| |eq?|
+ |squareFreePart| |reify| |imports| |chebyshevU| |complexEigenvalues|
+ |upperCase| |lieAdmissible?| |OMgetString| |lyndon?| |binomial|
+ |doublyTransitive?| |BumInSepFFE| |functorData| |sequence|
+ |cyclotomic| |complexEigenvectors| |lowerCase!| |int|
+ |jacobiIdentity?| |OMgetSymbol| |numberOfComputedEntries| |poisson|
+ |knownInfBasis| |multiplyExponents| |separant| |readBytes!| |euler|
+ |isConnected?| |lowerCase| |powerAssociative?| |OMgetType| |rst|
+ |geometric| |rootSplit| |laurentIfCan| |isobaric?| |readUInt32!|
+ |fixedDivisor| |connectTo| |KrullNumber| |alternative?|
+ |OMencodingBinary| |frst| |ridHack1| |ratDenom| |laurentRep| |weights|
+ |readInt32!| |laguerre| |normalizedAssociate| |numberOfVariables|
+ |flexible?| |OMencodingSGML| |lazyEvaluate| |interpolate| |ratPoly|
+ |rationalPower| |test| |differentialVariables| |readUInt16!|
+ |legendre| |normalize| |algebraicDecompose| |remove|
+ |rightAlternative?| |OMencodingXML| |lazy?| |nullSpace| |rootPower|
+ |dominantTerm| |extractBottom!| |readInt16!| |dmpToHdmp| |outputArgs|
+ |transcendentalDecompose| |leftAlternative?| |OMencodingUnknown|
+ |explicitlyEmpty?| |nullity| |rootProduct| |limitPlus| |extractTop!|
+ |readUInt8!| |hdmpToDmp| |normInvertible?| |internalDecompose| |last|
+ |antiAssociative?| |omError| |explicitEntries?| |rowEchelon|
+ |rootSimp| |split!| |insertBottom!| |readInt8!| |pToHdmp|
+ |normFactors| |decompose| |assoc| |associative?| |errorInfo|
+ |matrixDimensions| |column| |rootKerSimp| |setlast!| |insertTop!|
+ |readByte!| |hdmpToP| |condition| |npcoef| |upDateBranches| |tower|
+ |antiCommutative?| |errorKind| |matrixConcat3D| |row| |leftRank|
+ |setrest!| |bottom!| |setFieldInfo| |dmpToP| |listexp| |preprocess|
+ |rightRank| |commutative?| |OMReadError?| |setelt!| |maxColIndex|
+ |setfirst!| |prefix| |top!| |pol| |pToDmp| |characteristicPolynomial|
+ |internalZeroSetSplit| |rightCharacteristicPolynomial|
+ |OMUnknownSymbol?| |identityMatrix| |minColIndex| |doubleRank|
+ |cycleSplit!| |dequeue| |xn| |sylvesterSequence| |realEigenvalues|
+ |internalAugment| |leftCharacteristicPolynomial| |OMUnknownCD?|
+ |zeroMatrix| |maxRowIndex| |obj| |concat!| |recolor| |eq| |dAndcExp|
+ |sturmSequence| |realEigenvectors| |possiblyInfinite?| |rightNorm|
+ |OMParseError?| |mappingAst| |minRowIndex| |cache| |cycleTail|
+ |drawComplex| |iter| |repSq| |boundOfCauchy| |halfExtendedResultant2|
+ |explicitlyFinite?| |complexNumeric| |leftNorm| |OMwrite| |nullary|
+ |antisymmetric?| |cycleLength| |drawComplexVectorField| |expPot|
+ |sturmVariationsOf| |halfExtendedResultant1| |nextItem| |rightTrace|
+ |po| |fixedPoint| |symmetric?| |cycleEntry| |setRealSteps| |qPot|
+ |lazyVariations| |extendedResultant| |upperBound| |leftTrace| |OMread|
+ |recur| |diagonal?| |invmultisect| |setImagSteps| |lookup| |content|
+ |subResultantsChain| |lowerBound| |nary?| |someBasis| |OMreadFile|
+ |const| |square?| |multisect| |setClipValue| |normal?| |totalDegree|
+ |lazyPseudoQuotient| |iterationVar| |sort!| |OMreadStr| |curry|
+ |rectangularMatrix| |subst| |revert| |option?| |basis| |minimumDegree|
+ |lazyPseudoRemainder| |infiniteProduct| |copyInto!| |substring?|
+ |OMlistCDs| |diag| |characteristic| |weakBiRank| |generalLambert|
+ |range| |exp| |normalElement| |monomials| |bernoulliB|
+ |evenInfiniteProduct| |sorted?| |OMlistSymbols| |curryRight| |round|
+ |biRank| |evenlambert| |colorFunction| |minimalPolynomial| |eulerE|
+ |isPlus| |map| |oddInfiniteProduct| |LiePoly| |suffix?|
+ |OMsupportsCD?| |curryLeft| |fractionPart| |oddlambert| |curveColor|
+ |position!| |numericIfCan| |isTimes| |generalInfiniteProduct| |table|
+ |generator| |quickSort| |OMsupportsSymbol?| |constantRight|
+ |wholePart| |lambert| |nil| |pointColor| |eof?| |complexNumericIfCan|
+ |isExpt| |showAll?| |new| |atanh| |heapSort| |prefix?|
+ |OMunhandledSymbol| |constantLeft| |floor| |lagrange|
+ |associatedEquations| |clip| |inputBinaryFile| |compile| |isPower|
+ |FormatArabic| |showAllElements| |acoth| |shellSort| |OMreceive|
+ |twist| |ceiling| |objects| |univariatePolynomial| |arrayStack|
+ |clipBoolean| |increment| |rroot| |ScanArabic| |delay| |asech|
+ |outputSpacing| |OMsend| |setsubMatrix!| |norm| |base| |integrate|
+ |approximate| |charpol| |FormatRoman| |qroot| |convert| |findCycle|
+ |outputGeneral| |OMserve| |subMatrix| |mightHaveRoots|
+ |multiplyCoefficients| |complex| |parabolicCylindrical| |solve1|
+ |froot| |ScanRoman| |repeating?| |multiple| |outputFixed| |makeop|
+ |swapColumns!| |refine| |quoByVar| |paraboloidal| |innerEigenvectors|
+ |nthr| |ScanFloatIgnoreSpaces| |repeating| |applyQuote|
+ |outputFloating| |opeval| |swapRows!| |middle| |failed| |coefficients|
+ |ellipticCylindrical| |parseString| |firstUncouplingMatrix|
+ |ScanFloatIgnoreSpacesIfCan| |recip| |infix?| |vertConcat| |roman|
+ |stFunc1| |prolateSpheroidal| |unparse| |integral|
+ |numericalIntegration| |integers| |zeroSquareMatrix| |trapezoidal|
+ |mask| |horizConcat| |recoverAfterFail| |stFunc2| |oblateSpheroidal|
+ |binary| |primitiveElement| |rk4| |oddintegers| |ruleset| |incr|
+ |identitySquareMatrix| |rombergo| |squareTop| |showTheRoutinesTable|
+ |stFuncN| |bipolar| |packageCall| |nextPrime| |rk4a| |mapmult| |hi|
+ |lookupFunction| |simpsono| |elRow1!| |deleteRoutine!|
+ |fixedPointExquo| |bipolarCylindrical| |rk4qc| |left| |deriv|
+ |encodingDirectory| |trapezoidalo| |elRow2!| |getExplanations| |ode1|
+ |toroidal| |tablePow| |padicallyExpand| |rk4f| |right| |gderiv|
+ |suchThat| |attributeData| |sup| |elColumn2!| |getMeasure| |ode2|
+ |conical| |solveid| |numberOfFractionalTerms| |aromberg| |compose|
+ |domainTemplate| |imagE| |fractionFreeGauss!| |changeMeasure| |ode|
+ |modTree| |testModulus| |nthFractionalTerm| |asimpson| |addiag|
+ |lSpaceBasis| |imagk| |previous| |mpsode| |multiEuclideanTree| |delta|
+ |HenselLift| |firstNumer| |atrapezoidal| |lazyIntegrate| |finiteBasis|
+ |imagj| |entry?| |fractRagits| UP2UTS |complexZeros| |completeHensel|
+ |firstDenom| |initial| |romberg| |nlde| |principal?| |imagi| |indices|
+ |wholeRagits| |divisorCascade| UTS2UP |next| |multMonom| |precision|
+ |compactFraction| |simpson| |powern| |key| |divisor| |octon| |index?|
+ |radix| LODO2FUN |graeffe| |build| |partialFraction| |useNagFunctions|
+ |ODESolve| |entries| |randnum| RF2UTS |pleskenSplit| |leadingIndex|
+ |gcdPrimitive| |f02aff| |completeSmith| |filename| |rationalPoints|
+ |constDsolve| |key?| |reseed| |bfKeys| |magnitude|
+ |reciprocalPolynomial| |leadingExponent| |symmetricGroup| |f02agf|
+ |diophantineSystem| |nonSingularModel| |showTheIFTable| |symbolIfCan|
+ |seed| |inspect| |cross| |rootRadius| |GospersMethod|
+ |alternatingGroup| |f02ajf| |csubst| |parse| |algSplitSimple|
+ |clearTheIFTable| |argument| |rational| |schwerpunkt| |code| |lambda|
+ |nextSubsetGray| |abelianGroup| |f02akf| |particularSolution|
+ |generate| |hyperelliptic| |iFTable| |constantKernel| |rational?|
+ |normalized?| |setErrorBound| |firstSubsetGray| |cyclicGroup| |f02awf|
+ |mapSolve| |elliptic| |showIntensityFunctions| |constantIfCan|
+ |rationalIfCan| |quasiComponent| |startPolynomial| |clipPointsDefault|
+ |dihedralGroup| |f02axf| |quadratic| |incrementBy|
+ |integralDerivationMatrix| |expint| |kovacic| |setvalue!| |initials|
+ |cycleElt| |drawToScale| |mathieu11| |f02bbf| |cubic|
+ |integralRepresents| |diff| |laplace| |setchildren!| |basicSet|
+ |computeCycleLength| |adaptive| |mathieu12| |f02bjf| |quartic|
+ |integralCoordinates| |trailingCoefficient| |algDsolve| |node?|
+ |printInfo| |infRittWu?| |computeCycleEntry| |figureUnits| |mathieu22|
+ |f02fjf| |aLinear| |yCoordinates| |denomLODE| |normalizeIfCan|
+ |child?| |getCurve| |findConstructor| |putColorInfo| |mathieu23|
+ |f02wef| |aQuadratic| |inverseIntegralMatrixAtInfinity|
+ |indicialEquations| |polCase| |distance| |listLoops| |dualSignature|
+ |appendPoint| |f02xef| |mathieu24| |aCubic| |options|
+ |integralMatrixAtInfinity| |indicialEquation| |distFact| |nodes|
+ |closed?| |tail| |dom| |any| |coerceP| |component| |janko2| |f04adf|
+ |aQuartic| |inverseIntegralMatrix| |denomRicDE| |identification|
+ |rename| |open?| |powerSum| |ranges| |arg1| |entry| |rubiksGroup|
+ |f04arf| |radicalSolve| |before?| |integralMatrix|
+ |leadingCoefficientRicDE| |nil| |infinite| |arbitraryExponent|
  |approximate| |complex| |shallowMutable| |canonical| |noetherian|
  |central| |partiallyOrderedSet| |arbitraryPrecision|
  |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 28497f69..9bc3e7ba 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5448 +1,5460 @@
 
-(3264121 . 3486967810)       
-((-1568 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3363 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3682 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-1256 (-576)) |#2|) 44)) (-3606 (($ $) 80)) (-3622 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-3582 (((-576) (-1 (-112) |#2|) $) 27) (((-576) |#2| $) NIL) (((-576) |#2| $ (-576)) 96)) (-1458 (((-657 |#2|) $) 13)) (-3073 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-2148 (($ (-1 |#2| |#2|) $) 37)) (-4083 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-2271 (($ |#2| $ (-576)) NIL) (($ $ $ (-576)) 67)) (-2951 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-3399 (((-112) (-1 (-112) |#2|) $) 23)) (-2835 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-576)) NIL) (($ $ (-1256 (-576))) 66)) (-3409 (($ $ (-576)) 76) (($ $ (-1256 (-576))) 75)) (-1482 (((-784) (-1 (-112) |#2|) $) 34) (((-784) |#2| $) NIL)) (-2114 (($ $ $ (-576)) 69)) (-1923 (($ $) 68)) (-3511 (($ (-657 |#2|)) 73)) (-1674 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-657 $)) 85)) (-3501 (((-877) $) 92)) (-2147 (((-112) (-1 (-112) |#2|) $) 22)) (-2933 (((-112) $ $) 95)) (-2954 (((-112) $ $) 99))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -2933 ((-112) |#1| |#1|)) (-15 -3501 ((-877) |#1|)) (-15 -2954 ((-112) |#1| |#1|)) (-15 -3363 (|#1| |#1|)) (-15 -3363 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3606 (|#1| |#1|)) (-15 -2114 (|#1| |#1| |#1| (-576))) (-15 -1568 ((-112) |#1|)) (-15 -3073 (|#1| |#1| |#1|)) (-15 -3582 ((-576) |#2| |#1| (-576))) (-15 -3582 ((-576) |#2| |#1|)) (-15 -3582 ((-576) (-1 (-112) |#2|) |#1|)) (-15 -1568 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3073 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3682 (|#2| |#1| (-1256 (-576)) |#2|)) (-15 -2271 (|#1| |#1| |#1| (-576))) (-15 -2271 (|#1| |#2| |#1| (-576))) (-15 -3409 (|#1| |#1| (-1256 (-576)))) (-15 -3409 (|#1| |#1| (-576))) (-15 -4083 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1674 (|#1| (-657 |#1|))) (-15 -1674 (|#1| |#1| |#1|)) (-15 -1674 (|#1| |#2| |#1|)) (-15 -1674 (|#1| |#1| |#2|)) (-15 -2835 (|#1| |#1| (-1256 (-576)))) (-15 -3511 (|#1| (-657 |#2|))) (-15 -2951 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2835 (|#2| |#1| (-576))) (-15 -2835 (|#2| |#1| (-576) |#2|)) (-15 -3682 (|#2| |#1| (-576) |#2|)) (-15 -1482 ((-784) |#2| |#1|)) (-15 -1458 ((-657 |#2|) |#1|)) (-15 -1482 ((-784) (-1 (-112) |#2|) |#1|)) (-15 -3399 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2147 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2148 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4083 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1923 (|#1| |#1|))) (-19 |#2|) (-1239)) (T -18)) 
+(3266860 . 3487133951)       
+((-4077 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-4053 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3709 ((|#2| $ (-577) |#2|) NIL) ((|#2| $ (-1259 (-577)) |#2|) 44)) (-3645 (($ $) 80)) (-3654 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-3618 (((-577) (-1 (-112) |#2|) $) 27) (((-577) |#2| $) NIL) (((-577) |#2| $ (-577)) 96)) (-1461 (((-660 |#2|) $) 13)) (-3283 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-2182 (($ (-1 |#2| |#2|) $) 37)) (-4087 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-2308 (($ |#2| $ (-577)) NIL) (($ $ $ (-577)) 67)) (-1828 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-1514 (((-112) (-1 (-112) |#2|) $) 23)) (-2872 ((|#2| $ (-577) |#2|) NIL) ((|#2| $ (-577)) NIL) (($ $ (-1259 (-577))) 66)) (-3453 (($ $ (-577)) 76) (($ $ (-1259 (-577))) 75)) (-1485 (((-787) (-1 (-112) |#2|) $) 34) (((-787) |#2| $) NIL)) (-4064 (($ $ $ (-577)) 69)) (-1944 (($ $) 68)) (-3553 (($ (-660 |#2|)) 73)) (-1677 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-660 $)) 85)) (-3544 (((-880) $) 92)) (-1524 (((-112) (-1 (-112) |#2|) $) 22)) (-2970 (((-112) $ $) 95)) (-2990 (((-112) $ $) 99))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -2970 ((-112) |#1| |#1|)) (-15 -3544 ((-880) |#1|)) (-15 -2990 ((-112) |#1| |#1|)) (-15 -4053 (|#1| |#1|)) (-15 -4053 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3645 (|#1| |#1|)) (-15 -4064 (|#1| |#1| |#1| (-577))) (-15 -4077 ((-112) |#1|)) (-15 -3283 (|#1| |#1| |#1|)) (-15 -3618 ((-577) |#2| |#1| (-577))) (-15 -3618 ((-577) |#2| |#1|)) (-15 -3618 ((-577) (-1 (-112) |#2|) |#1|)) (-15 -4077 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3283 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3709 (|#2| |#1| (-1259 (-577)) |#2|)) (-15 -2308 (|#1| |#1| |#1| (-577))) (-15 -2308 (|#1| |#2| |#1| (-577))) (-15 -3453 (|#1| |#1| (-1259 (-577)))) (-15 -3453 (|#1| |#1| (-577))) (-15 -4087 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1677 (|#1| (-660 |#1|))) (-15 -1677 (|#1| |#1| |#1|)) (-15 -1677 (|#1| |#2| |#1|)) (-15 -1677 (|#1| |#1| |#2|)) (-15 -2872 (|#1| |#1| (-1259 (-577)))) (-15 -3553 (|#1| (-660 |#2|))) (-15 -1828 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2872 (|#2| |#1| (-577))) (-15 -2872 (|#2| |#1| (-577) |#2|)) (-15 -3709 (|#2| |#1| (-577) |#2|)) (-15 -1485 ((-787) |#2| |#1|)) (-15 -1461 ((-660 |#2|) |#1|)) (-15 -1485 ((-787) (-1 (-112) |#2|) |#1|)) (-15 -1514 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -1524 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2182 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4087 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1944 (|#1| |#1|))) (-19 |#2|) (-1242)) (T -18)) 
 NIL 
-(-10 -8 (-15 -2933 ((-112) |#1| |#1|)) (-15 -3501 ((-877) |#1|)) (-15 -2954 ((-112) |#1| |#1|)) (-15 -3363 (|#1| |#1|)) (-15 -3363 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3606 (|#1| |#1|)) (-15 -2114 (|#1| |#1| |#1| (-576))) (-15 -1568 ((-112) |#1|)) (-15 -3073 (|#1| |#1| |#1|)) (-15 -3582 ((-576) |#2| |#1| (-576))) (-15 -3582 ((-576) |#2| |#1|)) (-15 -3582 ((-576) (-1 (-112) |#2|) |#1|)) (-15 -1568 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3073 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3682 (|#2| |#1| (-1256 (-576)) |#2|)) (-15 -2271 (|#1| |#1| |#1| (-576))) (-15 -2271 (|#1| |#2| |#1| (-576))) (-15 -3409 (|#1| |#1| (-1256 (-576)))) (-15 -3409 (|#1| |#1| (-576))) (-15 -4083 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1674 (|#1| (-657 |#1|))) (-15 -1674 (|#1| |#1| |#1|)) (-15 -1674 (|#1| |#2| |#1|)) (-15 -1674 (|#1| |#1| |#2|)) (-15 -2835 (|#1| |#1| (-1256 (-576)))) (-15 -3511 (|#1| (-657 |#2|))) (-15 -2951 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3622 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2835 (|#2| |#1| (-576))) (-15 -2835 (|#2| |#1| (-576) |#2|)) (-15 -3682 (|#2| |#1| (-576) |#2|)) (-15 -1482 ((-784) |#2| |#1|)) (-15 -1458 ((-657 |#2|) |#1|)) (-15 -1482 ((-784) (-1 (-112) |#2|) |#1|)) (-15 -3399 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2147 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2148 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4083 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1923 (|#1| |#1|))) 
-((-3429 (((-112) $ $) 20 (|has| |#1| (-102)))) (-4313 (((-1294) $ (-576) (-576)) 41 (|has| $ (-6 -4467)))) (-1568 (((-112) (-1 (-112) |#1| |#1|) $) 101) (((-112) $) 95 (|has| |#1| (-862)))) (-3363 (($ (-1 (-112) |#1| |#1|) $) 92 (|has| $ (-6 -4467))) (($ $) 91 (-12 (|has| |#1| (-862)) (|has| $ (-6 -4467))))) (-1850 (($ (-1 (-112) |#1| |#1|) $) 102) (($ $) 96 (|has| |#1| (-862)))) (-3793 (((-112) $ (-784)) 8)) (-3682 ((|#1| $ (-576) |#1|) 53 (|has| $ (-6 -4467))) ((|#1| $ (-1256 (-576)) |#1|) 60 (|has| $ (-6 -4467)))) (-2035 (($ (-1 (-112) |#1|) $) 77 (|has| $ (-6 -4466)))) (-4359 (($) 7 T CONST)) (-3606 (($ $) 93 (|has| $ (-6 -4467)))) (-3768 (($ $) 103)) (-3914 (($ $) 80 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466))))) (-3895 (($ |#1| $) 79 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466)))) (($ (-1 (-112) |#1|) $) 76 (|has| $ (-6 -4466)))) (-3622 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 78 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 75 (|has| $ (-6 -4466))) ((|#1| (-1 |#1| |#1| |#1|) $) 74 (|has| $ (-6 -4466)))) (-2158 ((|#1| $ (-576) |#1|) 54 (|has| $ (-6 -4467)))) (-2083 ((|#1| $ (-576)) 52)) (-3582 (((-576) (-1 (-112) |#1|) $) 100) (((-576) |#1| $) 99 (|has| |#1| (-1122))) (((-576) |#1| $ (-576)) 98 (|has| |#1| (-1122)))) (-1458 (((-657 |#1|) $) 31 (|has| $ (-6 -4466)))) (-4109 (($ (-784) |#1|) 70)) (-1833 (((-112) $ (-784)) 9)) (-3853 (((-576) $) 44 (|has| (-576) (-862)))) (-3707 (($ $ $) 85 (|has| |#1| (-862)))) (-3073 (($ (-1 (-112) |#1| |#1|) $ $) 104) (($ $ $) 97 (|has| |#1| (-862)))) (-2070 (((-657 |#1|) $) 30 (|has| $ (-6 -4466)))) (-1627 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466))))) (-2272 (((-576) $) 45 (|has| (-576) (-862)))) (-1611 (($ $ $) 86 (|has| |#1| (-862)))) (-2148 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4467)))) (-4083 (($ (-1 |#1| |#1|) $) 36) (($ (-1 |#1| |#1| |#1|) $ $) 65)) (-4261 (((-112) $ (-784)) 10)) (-2342 (((-1180) $) 23 (|has| |#1| (-1122)))) (-2271 (($ |#1| $ (-576)) 62) (($ $ $ (-576)) 61)) (-1430 (((-657 (-576)) $) 47)) (-4242 (((-112) (-576) $) 48)) (-1471 (((-1142) $) 22 (|has| |#1| (-1122)))) (-3510 ((|#1| $) 43 (|has| (-576) (-862)))) (-2951 (((-3 |#1| "failed") (-1 (-112) |#1|) $) 73)) (-1987 (($ $ |#1|) 42 (|has| $ (-6 -4467)))) (-3399 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4466)))) (-3236 (($ $ (-657 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122)))) (($ $ (-657 |#1|) (-657 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))))) (-2806 (((-112) $ $) 14)) (-1515 (((-112) |#1| $) 46 (-12 (|has| $ (-6 -4466)) (|has| |#1| (-1122))))) (-2380 (((-657 |#1|) $) 49)) (-3387 (((-112) $) 11)) (-3581 (($) 12)) (-2835 ((|#1| $ (-576) |#1|) 51) ((|#1| $ (-576)) 50) (($ $ (-1256 (-576))) 71)) (-3409 (($ $ (-576)) 64) (($ $ (-1256 (-576))) 63)) (-1482 (((-784) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4466))) (((-784) |#1| $) 29 (-12 (|has| |#1| (-1122)) (|has| $ (-6 -4466))))) (-2114 (($ $ $ (-576)) 94 (|has| $ (-6 -4467)))) (-1923 (($ $) 13)) (-4148 (((-548) $) 81 (|has| |#1| (-626 (-548))))) (-3511 (($ (-657 |#1|)) 72)) (-1674 (($ $ |#1|) 69) (($ |#1| $) 68) (($ $ $) 67) (($ (-657 $)) 66)) (-3501 (((-877) $) 18 (|has| |#1| (-625 (-877))))) (-2046 (((-112) $ $) 21 (|has| |#1| (-102)))) (-2147 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4466)))) (-2985 (((-112) $ $) 87 (|has| |#1| (-862)))) (-2963 (((-112) $ $) 89 (|has| |#1| (-862)))) (-2933 (((-112) $ $) 19 (|has| |#1| (-102)))) (-2973 (((-112) $ $) 88 (|has| |#1| (-862)))) (-2954 (((-112) $ $) 90 (|has| |#1| (-862)))) (-3440 (((-784) $) 6 (|has| $ (-6 -4466))))) 
-(((-19 |#1|) (-141) (-1239)) (T -19)) 
+(-10 -8 (-15 -2970 ((-112) |#1| |#1|)) (-15 -3544 ((-880) |#1|)) (-15 -2990 ((-112) |#1| |#1|)) (-15 -4053 (|#1| |#1|)) (-15 -4053 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3645 (|#1| |#1|)) (-15 -4064 (|#1| |#1| |#1| (-577))) (-15 -4077 ((-112) |#1|)) (-15 -3283 (|#1| |#1| |#1|)) (-15 -3618 ((-577) |#2| |#1| (-577))) (-15 -3618 ((-577) |#2| |#1|)) (-15 -3618 ((-577) (-1 (-112) |#2|) |#1|)) (-15 -4077 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3283 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3709 (|#2| |#1| (-1259 (-577)) |#2|)) (-15 -2308 (|#1| |#1| |#1| (-577))) (-15 -2308 (|#1| |#2| |#1| (-577))) (-15 -3453 (|#1| |#1| (-1259 (-577)))) (-15 -3453 (|#1| |#1| (-577))) (-15 -4087 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -1677 (|#1| (-660 |#1|))) (-15 -1677 (|#1| |#1| |#1|)) (-15 -1677 (|#1| |#2| |#1|)) (-15 -1677 (|#1| |#1| |#2|)) (-15 -2872 (|#1| |#1| (-1259 (-577)))) (-15 -3553 (|#1| (-660 |#2|))) (-15 -1828 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3654 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2872 (|#2| |#1| (-577))) (-15 -2872 (|#2| |#1| (-577) |#2|)) (-15 -3709 (|#2| |#1| (-577) |#2|)) (-15 -1485 ((-787) |#2| |#1|)) (-15 -1461 ((-660 |#2|) |#1|)) (-15 -1485 ((-787) (-1 (-112) |#2|) |#1|)) (-15 -1514 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -1524 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2182 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4087 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1944 (|#1| |#1|))) 
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+(((-19 |#1|) (-141) (-1242)) (T -19)) 
 NIL 
-(-13 (-384 |t#1|) (-10 -7 (-6 -4467))) 
-(((-34) . T) ((-102) -2802 (|has| |#1| (-1122)) (|has| |#1| (-862)) (|has| |#1| (-102))) ((-625 (-877)) -2802 (|has| |#1| (-1122)) (|has| |#1| (-862)) (|has| |#1| (-625 (-877)))) ((-152 |#1|) . T) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-296 #0=(-576) |#1|) . T) ((-296 (-1256 (-576)) $) . T) ((-298 #0# |#1|) . T) ((-319 |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-384 |#1|) . T) ((-501 |#1|) . T) ((-616 #0# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1122))) ((-664 |#1|) . T) ((-862) |has| |#1| (-862)) ((-865) |has| |#1| (-862)) ((-1122) -2802 (|has| |#1| (-1122)) (|has| |#1| (-862))) ((-1239) . T)) 
-((-2721 (((-3 $ "failed") $ $) 12)) (-3022 (($ $) NIL) (($ $ $) 9)) (* (($ (-941) $) NIL) (($ (-784) $) 16) (($ (-576) $) 26))) 
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+(-13 (-385 |t#1|) (-10 -7 (-6 -4471))) 
+(((-34) . T) ((-102) -2839 (|has| |#1| (-1125)) (|has| |#1| (-865)) (|has| |#1| (-102))) ((-626 (-880)) -2839 (|has| |#1| (-1125)) (|has| |#1| (-865)) (|has| |#1| (-626 (-880)))) ((-152 |#1|) . T) ((-627 (-549)) |has| |#1| (-627 (-549))) ((-297 #0=(-577) |#1|) . T) ((-297 (-1259 (-577)) $) . T) ((-299 #0# |#1|) . T) ((-320 |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) ((-385 |#1|) . T) ((-502 |#1|) . T) ((-617 #0# |#1|) . T) ((-527 |#1| |#1|) -12 (|has| |#1| (-320 |#1|)) (|has| |#1| (-1125))) ((-667 |#1|) . T) ((-865) |has| |#1| (-865)) ((-868) |has| |#1| (-865)) ((-1125) -2839 (|has| |#1| (-1125)) (|has| |#1| (-865))) ((-1242) . T)) 
+((-1956 (((-3 $ "failed") $ $) 12)) (-3066 (($ $) NIL) (($ $ $) 9)) (* (($ (-944) $) NIL) (($ (-787) $) 16) (($ (-577) $) 26))) 
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 NIL 
-(-10 -8 (-15 -3022 (|#1| |#1| |#1|)) (-15 -3022 (|#1| |#1|)) (-15 * (|#1| (-576) |#1|)) (-15 -2721 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-784) |#1|)) (-15 * (|#1| (-941) |#1|))) 
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+(-10 -8 (-15 -3066 (|#1| |#1| |#1|)) (-15 -3066 (|#1| |#1|)) (-15 * (|#1| (-577) |#1|)) (-15 -1956 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-787) |#1|)) (-15 * (|#1| (-944) |#1|))) 
+((-3473 (((-112) $ $) 7)) (-3585 (((-112) $) 17)) (-1956 (((-3 $ "failed") $ $) 20)) (-1534 (($) 18 T CONST)) (-2810 (((-1183) $) 10)) (-1474 (((-1145) $) 11)) (-3544 (((-880) $) 12)) (-4448 (((-112) $ $) 6)) (-2806 (($) 19 T CONST)) (-2970 (((-112) $ $) 8)) (-3066 (($ $) 23) (($ $ $) 22)) (-3055 (($ $ $) 15)) (* (($ (-944) $) 14) (($ (-787) $) 16) (($ (-577) $) 24))) 
 (((-21) (-141)) (T -21)) 
-((-3022 (*1 *1 *1) (-4 *1 (-21))) (-3022 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-132) (-659 (-576)) (-10 -8 (-15 -3022 ($ $)) (-15 -3022 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-625 (-877)) . T) ((-659 (-576)) . T) ((-1122) . T) ((-1239) . T)) 
-((-2364 (((-112) $) 10)) (-4359 (($) 15)) (* (($ (-941) $) 14) (($ (-784) $) 19))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-784) |#1|)) (-15 -2364 ((-112) |#1|)) (-15 -4359 (|#1|)) (-15 * (|#1| (-941) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-784) |#1|)) (-15 -2364 ((-112) |#1|)) (-15 -4359 (|#1|)) (-15 * (|#1| (-941) |#1|))) 
-((-3429 (((-112) $ $) 7)) (-2364 (((-112) $) 17)) (-4359 (($) 18 T CONST)) (-2342 (((-1180) $) 10)) (-1471 (((-1142) $) 11)) (-3501 (((-877) $) 12)) (-2046 (((-112) $ $) 6)) (-2769 (($) 19 T CONST)) (-2933 (((-112) $ $) 8)) (-3012 (($ $ $) 15)) (* (($ (-941) $) 14) (($ (-784) $) 16))) 
+((-3066 (*1 *1 *1) (-4 *1 (-21))) (-3066 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-132) (-662 (-577)) (-10 -8 (-15 -3066 ($ $)) (-15 -3066 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-626 (-880)) . T) ((-662 (-577)) . T) ((-1125) . T) ((-1242) . T)) 
+((-3585 (((-112) $) 10)) (-1534 (($) 15)) (* (($ (-944) $) 14) (($ (-787) $) 19))) 
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+NIL 
+(-10 -8 (-15 * (|#1| (-787) |#1|)) (-15 -3585 ((-112) |#1|)) (-15 -1534 (|#1|)) (-15 * (|#1| (-944) |#1|))) 
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 (((-23) (-141)) (T -23)) 
-((-2769 (*1 *1) (-4 *1 (-23))) (-4359 (*1 *1) (-4 *1 (-23))) (-2364 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-784))))) 
-(-13 (-25) (-10 -8 (-15 (-2769) ($) -1509) (-15 -4359 ($) -1509) (-15 -2364 ((-112) $)) (-15 * ($ (-784) $)))) 
-(((-25) . T) ((-102) . T) ((-625 (-877)) . T) ((-1122) . T) ((-1239) . T)) 
-((* (($ (-941) $) 10))) 
-(((-24 |#1|) (-10 -8 (-15 * (|#1| (-941) |#1|))) (-25)) (T -24)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-941) |#1|))) 
-((-3429 (((-112) $ $) 7)) (-2342 (((-1180) $) 10)) (-1471 (((-1142) $) 11)) (-3501 (((-877) $) 12)) (-2046 (((-112) $ $) 6)) (-2933 (((-112) $ $) 8)) (-3012 (($ $ $) 15)) (* (($ (-941) $) 14))) 
+((-2806 (*1 *1) (-4 *1 (-23))) (-1534 (*1 *1) (-4 *1 (-23))) (-3585 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-787))))) 
+(-13 (-25) (-10 -8 (-15 (-2806) ($) -1512) (-15 -1534 ($) -1512) (-15 -3585 ((-112) $)) (-15 * ($ (-787) $)))) 
+(((-25) . T) ((-102) . T) ((-626 (-880)) . T) ((-1125) . T) ((-1242) . T)) 
+((* (($ (-944) $) 10))) 
+(((-24 |#1|) (-10 -8 (-15 * (|#1| (-944) |#1|))) (-25)) (T -24)) 
+NIL 
+(-10 -8 (-15 * (|#1| (-944) |#1|))) 
+((-3473 (((-112) $ $) 7)) (-2810 (((-1183) $) 10)) (-1474 (((-1145) $) 11)) (-3544 (((-880) $) 12)) (-4448 (((-112) $ $) 6)) (-2970 (((-112) $ $) 8)) (-3055 (($ $ $) 15)) (* (($ (-944) $) 14))) 
 (((-25) (-141)) (T -25)) 
-((-3012 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-941))))) 
-(-13 (-1122) (-10 -8 (-15 -3012 ($ $ $)) (-15 * ($ (-941) $)))) 
-(((-102) . T) ((-625 (-877)) . T) ((-1122) . T) ((-1239) . T)) 
-((-3128 (((-657 $) (-972 $)) 32) (((-657 $) (-1194 $)) 16) (((-657 $) (-1194 $) (-1198)) 20)) (-1911 (($ (-972 $)) 30) (($ (-1194 $)) 11) (($ (-1194 $) (-1198)) 60)) (-2708 (((-657 $) (-972 $)) 33) (((-657 $) (-1194 $)) 18) (((-657 $) (-1194 $) (-1198)) 19)) (-3564 (($ (-972 $)) 31) (($ (-1194 $)) 13) (($ (-1194 $) (-1198)) NIL))) 
-(((-26 |#1|) (-10 -8 (-15 -3128 ((-657 |#1|) (-1194 |#1|) (-1198))) (-15 -3128 ((-657 |#1|) (-1194 |#1|))) (-15 -3128 ((-657 |#1|) (-972 |#1|))) (-15 -1911 (|#1| (-1194 |#1|) (-1198))) (-15 -1911 (|#1| (-1194 |#1|))) (-15 -1911 (|#1| (-972 |#1|))) (-15 -2708 ((-657 |#1|) (-1194 |#1|) (-1198))) (-15 -2708 ((-657 |#1|) (-1194 |#1|))) (-15 -2708 ((-657 |#1|) (-972 |#1|))) (-15 -3564 (|#1| (-1194 |#1|) (-1198))) (-15 -3564 (|#1| (-1194 |#1|))) (-15 -3564 (|#1| (-972 |#1|)))) (-27)) (T -26)) 
-NIL 
-(-10 -8 (-15 -3128 ((-657 |#1|) (-1194 |#1|) (-1198))) (-15 -3128 ((-657 |#1|) (-1194 |#1|))) (-15 -3128 ((-657 |#1|) (-972 |#1|))) (-15 -1911 (|#1| (-1194 |#1|) (-1198))) (-15 -1911 (|#1| (-1194 |#1|))) (-15 -1911 (|#1| (-972 |#1|))) (-15 -2708 ((-657 |#1|) (-1194 |#1|) (-1198))) (-15 -2708 ((-657 |#1|) (-1194 |#1|))) (-15 -2708 ((-657 |#1|) (-972 |#1|))) (-15 -3564 (|#1| (-1194 |#1|) (-1198))) (-15 -3564 (|#1| (-1194 |#1|))) (-15 -3564 (|#1| (-972 |#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 
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 NIL 
 (((-98) (-141)) (T -98)) 
 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 
-(-800) 
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-(((-198) (-800)) (T -198)) 
-NIL 
-(-800) 
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-(((-199) (-800)) (T -199)) 
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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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-((-4417 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3622 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4083 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) 
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-((-4083 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *7 (-1239)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3622 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-784)) (-4 *6 (-1239)) (-4 *2 (-1239)) (-5 *1 (-244 *5 *6 *2)))) (-4417 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-784)) (-4 *7 (-1239)) (-4 *5 (-1239)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) 
-(-10 -7 (-15 -4417 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3622 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4083 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) 
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-3750 (-702 (-576))) (|:| |vec| (-1289 (-576)))) (-702 $) (-1289 $)) NIL (-12 (|has| |#2| (-652 (-576))) (|has| |#2| (-1071)))) (((-2 (|:| -3750 (-702 |#2|)) (|:| |vec| (-1289 |#2|))) (-702 $) (-1289 $)) NIL (|has| |#2| (-1071))) (((-702 |#2|) (-702 $)) NIL (|has| |#2| (-1071)))) (-3843 (((-3 $ "failed") $) 58 (|has| |#2| (-1071)))) (-1892 (($) NIL (|has| |#2| (-379)))) (-2158 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4467)))) (-2083 ((|#2| $ (-576)) 56)) (-1458 (((-657 |#2|) $) 14 (|has| $ (-6 -4466)))) (-4094 (((-112) $) NIL (|has| |#2| (-1071)))) (-1833 (((-112) $ (-784)) NIL)) (-3853 (((-576) $) 19 (|has| (-576) (-862)))) (-3707 (($ $ $) NIL (|has| |#2| (-862)))) (-2070 (((-657 |#2|) $) NIL (|has| $ (-6 -4466)))) (-1627 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#2| (-1122))))) (-2272 (((-576) $) NIL (|has| (-576) (-862)))) (-1611 (($ $ $) NIL (|has| |#2| (-862)))) (-2148 (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4467)))) (-4083 (($ (-1 |#2| |#2|) $) NIL)) (-3007 (((-941) 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|#2|)) (|has| |#2| (-1122)))) (($ $ (-657 |#2|) (-657 |#2|)) NIL (-12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1122))))) (-2806 (((-112) $ $) NIL)) (-1515 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4466)) (|has| |#2| (-1122))))) (-2380 (((-657 |#2|) $) NIL)) (-3387 (((-112) $) NIL)) (-3581 (($) NIL)) (-2835 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-576)) 20)) (-1374 ((|#2| $ $) NIL (|has| |#2| (-1071)))) (-1924 (($ (-1289 |#2|)) 17)) (-3863 (((-135)) NIL (|has| |#2| (-374)))) (-2815 (($ $ (-784)) NIL (-12 (|has| |#2| (-237)) (|has| |#2| (-1071)))) (($ $) NIL (-12 (|has| |#2| (-237)) (|has| |#2| (-1071)))) (($ $ (-657 (-1198)) (-657 (-784))) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1198) (-784)) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-657 (-1198))) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1198)) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1071))) (($ $ (-1 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(|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-657 (-1198))) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1198)) NIL (-12 (|has| |#2| (-920 (-1198))) (|has| |#2| (-1071)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1071))) (($ $ (-1 |#2| |#2|) (-784)) NIL (|has| |#2| (-1071)))) (-2985 (((-112) $ $) NIL (|has| |#2| (-862)))) (-2963 (((-112) $ $) NIL (|has| |#2| (-862)))) (-2933 (((-112) $ $) 27 (|has| |#2| (-102)))) (-2973 (((-112) $ $) NIL (|has| |#2| (-862)))) (-2954 (((-112) $ $) 66 (|has| |#2| (-862)))) (-3034 (($ $ |#2|) NIL (|has| |#2| (-374)))) (-3022 (($ $ $) NIL (|has| |#2| (-21))) (($ $) NIL (|has| |#2| (-21)))) (-3012 (($ $ $) 34 (|has| |#2| (-25)))) (** (($ $ (-784)) NIL (|has| |#2| (-1071))) (($ $ (-941)) NIL (|has| |#2| (-1071)))) (* (($ $ $) 46 (|has| |#2| (-1071))) (($ $ |#2|) 44 (|has| |#2| (-739))) (($ |#2| $) 45 (|has| |#2| (-739))) (($ (-576) $) NIL (|has| |#2| (-21))) (($ (-784) $) NIL (|has| |#2| (-23))) (($ (-941) $) NIL (|has| |#2| (-25)))) (-3440 (((-784) $) NIL (|has| $ (-6 -4466))))) 
-(((-245 |#1| |#2|) (-243 |#1| |#2|) (-784) (-1239)) (T -245)) 
-NIL 
-(-243 |#1| |#2|) 
-((-3281 (((-576) (-657 (-1180))) 36) (((-576) (-1180)) 29)) (-1344 (((-1294) (-657 (-1180))) 40) (((-1294) (-1180)) 39)) (-1476 (((-1180)) 16)) (-3067 (((-1180) (-576) (-1180)) 23)) (-3665 (((-657 (-1180)) (-657 (-1180)) (-576) (-1180)) 37) (((-1180) (-1180) (-576) (-1180)) 35)) (-3217 (((-657 (-1180)) (-657 (-1180))) 15) (((-657 (-1180)) (-1180)) 11))) 
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-((-3281 (*1 *2 *3) (-12 (-5 *3 (-657 (-1180))) (-5 *2 (-576)) (-5 *1 (-246)))) (-3281 (*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-576)) (-5 *1 (-246)))) (-1344 (*1 *2 *3) (-12 (-5 *3 (-657 (-1180))) (-5 *2 (-1294)) (-5 *1 (-246)))) (-1344 (*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-246)))) (-3665 (*1 *2 *2 *3 *4) (-12 (-5 *2 (-657 (-1180))) (-5 *3 (-576)) (-5 *4 (-1180)) (-5 *1 (-246)))) (-3665 (*1 *2 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-576)) (-5 *1 (-246)))) (-3067 (*1 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-576)) (-5 *1 (-246)))) (-1476 (*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-246)))) (-3217 (*1 *2 *2) (-12 (-5 *2 (-657 (-1180))) (-5 *1 (-246)))) (-3217 (*1 *2 *3) (-12 (-5 *2 (-657 (-1180))) (-5 *1 (-246)) (-5 *3 (-1180))))) 
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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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-((-4399 ((|#2| |#2| |#2|) 31)) (-1832 (((-115) (-115)) 43)) (-2242 ((|#2| |#2|) 63)) (-3882 ((|#2| |#2|) 66)) (-1379 ((|#2| |#2|) 30)) (-3806 ((|#2| |#2| |#2|) 33)) (-2751 ((|#2| |#2| |#2|) 35)) (-2239 ((|#2| |#2| |#2|) 32)) (-2467 ((|#2| |#2| |#2|) 34)) (-4159 (((-112) (-115)) 41)) (-3270 ((|#2| |#2|) 37)) (-3480 ((|#2| |#2|) 36)) (-1792 ((|#2| |#2|) 25)) (-2238 ((|#2| |#2| |#2|) 28) ((|#2| |#2|) 26)) (-1717 ((|#2| |#2| |#2|) 29))) 
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-NIL 
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-NIL 
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 NIL 
 (-19 |#1|) 
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-NIL 
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 NIL 
 (-57 |#1| |#4| |#5|) 
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-((-4440 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) (|:| -1685 (-1116 (-856 (-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| (-1179 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1685 (-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)))) (-2380 (*1 *2 *1) (-12 (-5 *2 (-657 (-2 (|:| -4291 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4440 (-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| (-1179 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1685 (-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)))) (-2647 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) (|:| -1685 (-1116 (-856 (-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| (-1179 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1685 (-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)))) (-2468 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -4291 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4440 (-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| (-1179 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1685 (-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)))) (-2088 (*1 *1 *2) (-12 (-5 *2 (-657 (-2 (|:| -4291 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227))) (|:| -1685 (-1116 (-856 (-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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-((-1327 ((|#2| |#1| |#2|) 9)) (-4438 ((|#1| |#1| |#2|) 8))) 
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-((-1901 ((|#3| (-1 |#3| |#2|) (-1 |#2| |#1|) |#1|) 11))) 
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-((-1901 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *2 (-1122)) (-5 *1 (-693 *5 *6 *2))))) 
-(-10 -7 (-15 -1901 (|#3| (-1 |#3| |#2|) (-1 |#2| |#1|) |#1|))) 
-((-3429 (((-112) $ $) NIL)) (-2978 (((-1238) $) 21)) (-2926 (((-657 (-1238)) $) 19)) (-3456 (($ (-657 (-1238)) (-1238)) 14)) (-2342 (((-1180) $) NIL)) (-1471 (((-1142) $) NIL)) (-3501 (((-877) $) 29) (($ (-1203)) NIL) (((-1203) $) NIL) (((-1238) $) 22) (($ (-1140)) 10)) (-2046 (((-112) $ $) NIL)) (-2933 (((-112) $ $) NIL))) 
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-((-3596 (*1 *2 *2) (-12 (-5 *2 (-1 *3 (-784) *3)) (-4 *3 (-1122)) (-5 *1 (-695 *3)))) (** (*1 *2 *2 *3) (-12 (-5 *2 (-1 *4 *4)) (-5 *3 (-784)) (-4 *4 (-1122)) (-5 *1 (-695 *4)))) (-3066 (*1 *2 *2) (-12 (-5 *1 (-695 *2)) (-4 *2 (-1122)))) (-2184 (*1 *2 *3 *4) (-12 (-5 *3 (-1 (-657 *5) (-657 *5))) (-5 *4 (-576)) (-5 *2 (-657 *5)) (-5 *1 (-695 *5)) (-4 *5 (-1122)))) (-2184 (*1 *2 *3) (-12 (-5 *3 (-1 *2 *2)) (-5 *1 (-695 *2)) (-4 *2 (-1122)))) (-3501 (*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-695 *3)) (-4 *3 (-1122)))) (-4038 (*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-695 *3)) (-4 *3 (-1122))))) 
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-((-4332 (((-1 |#2| |#1|) (-1 |#2| |#1| |#1|)) 16)) (-2830 (((-1 |#2|) (-1 |#2| |#1|) |#1|) 13)) (-1509 (((-1 |#2| |#1|) (-1 |#2|)) 14)) (-3974 (((-1 |#2| |#1|) |#2|) 11))) 
-(((-696 |#1| |#2|) (-10 -7 (-15 -3974 ((-1 |#2| |#1|) |#2|)) (-15 -2830 ((-1 |#2|) (-1 |#2| |#1|) |#1|)) (-15 -1509 ((-1 |#2| |#1|) (-1 |#2|))) (-15 -4332 ((-1 |#2| |#1|) (-1 |#2| |#1| |#1|)))) (-1122) (-1122)) (T -696)) 
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-((-2518 (((-1 |#3| |#2| |#1|) (-1 |#3| |#1| |#2|)) 17)) (-2738 (((-1 |#3| |#1|) (-1 |#3| |#1| |#2|) |#2|) 11)) (-2220 (((-1 |#3| |#2|) (-1 |#3| |#1| |#2|) |#1|) 13)) (-3010 (((-1 |#3| |#1| |#2|) (-1 |#3| |#1|)) 14)) (-4385 (((-1 |#3| |#1| |#2|) (-1 |#3| |#2|)) 15)) (* (((-1 |#3| |#1|) (-1 |#3| |#2|) (-1 |#2| |#1|)) 21))) 
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-((* (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *7 (-1122)) (-5 *2 (-1 *7 *5)) (-5 *1 (-697 *5 *6 *7)))) (-2518 (*1 *2 *3) (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1122)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-697 *4 *5 *6)))) (-4385 (*1 *2 *3) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-697 *4 *5 *6)) (-4 *4 (-1122)))) (-3010 (*1 *2 *3) (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1122)) (-4 *6 (-1122)) (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-697 *4 *5 *6)) (-4 *5 (-1122)))) (-2220 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1122)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-5 *2 (-1 *6 *5)) (-5 *1 (-697 *4 *5 *6)))) (-2738 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1122)) (-4 *4 (-1122)) (-4 *6 (-1122)) (-5 *2 (-1 *6 *5)) (-5 *1 (-697 *5 *4 *6))))) 
-(-10 -7 (-15 -2738 ((-1 |#3| |#1|) (-1 |#3| |#1| |#2|) |#2|)) (-15 -2220 ((-1 |#3| |#2|) (-1 |#3| |#1| |#2|) |#1|)) (-15 -3010 ((-1 |#3| |#1| |#2|) (-1 |#3| |#1|))) (-15 -4385 ((-1 |#3| |#1| |#2|) (-1 |#3| |#2|))) (-15 -2518 ((-1 |#3| |#2| |#1|) (-1 |#3| |#1| |#2|))) (-15 * ((-1 |#3| |#1|) (-1 |#3| |#2|) (-1 |#2| |#1|)))) 
-((-3622 ((|#5| (-1 |#5| |#1| |#5|) |#4| |#5|) 39)) (-4083 (((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|) 37) ((|#8| (-1 |#5| |#1|) |#4|) 31))) 
-(((-698 |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (-10 -7 (-15 -4083 (|#8| (-1 |#5| |#1|) |#4|)) (-15 -4083 ((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|)) (-15 -3622 (|#5| (-1 |#5| |#1| |#5|) |#4| |#5|))) (-1071) (-384 |#1|) (-384 |#1|) (-700 |#1| |#2| |#3|) (-1071) (-384 |#5|) (-384 |#5|) (-700 |#5| |#6| |#7|)) (T -698)) 
-((-3622 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1071)) (-4 *2 (-1071)) (-4 *6 (-384 *5)) (-4 *7 (-384 *5)) (-4 *8 (-384 *2)) (-4 *9 (-384 *2)) (-5 *1 (-698 *5 *6 *7 *4 *2 *8 *9 *10)) (-4 *4 (-700 *5 *6 *7)) (-4 *10 (-700 *2 *8 *9)))) (-4083 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1071)) (-4 *8 (-1071)) (-4 *6 (-384 *5)) (-4 *7 (-384 *5)) (-4 *2 (-700 *8 *9 *10)) (-5 *1 (-698 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-700 *5 *6 *7)) (-4 *9 (-384 *8)) (-4 *10 (-384 *8)))) (-4083 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1071)) (-4 *8 (-1071)) (-4 *6 (-384 *5)) (-4 *7 (-384 *5)) (-4 *2 (-700 *8 *9 *10)) (-5 *1 (-698 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-700 *5 *6 *7)) (-4 *9 (-384 *8)) (-4 *10 (-384 *8))))) 
-(-10 -7 (-15 -4083 (|#8| (-1 |#5| |#1|) |#4|)) (-15 -4083 ((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|)) (-15 -3622 (|#5| (-1 |#5| |#1| |#5|) |#4| |#5|))) 
-((-3765 (($ (-784) (-784)) 42)) (-2671 (($ $ $) 73)) (-2153 (($ |#3|) 68) (($ $) 69)) (-3864 (((-112) $) 36)) (-1606 (($ $ (-576) (-576)) 84)) (-1371 (($ $ (-576) (-576)) 85)) (-2351 (($ $ (-576) (-576) (-576) (-576)) 90)) (-1506 (($ $) 71)) (-3186 (((-112) $) 15)) (-2337 (($ $ (-576) (-576) $) 91)) (-3682 ((|#2| $ (-576) (-576) |#2|) NIL) (($ $ (-657 (-576)) (-657 (-576)) $) 89)) (-1346 (($ (-784) |#2|) 55)) (-2514 (($ (-657 (-657 |#2|))) 51) (($ (-784) (-784) (-1 |#2| (-576) (-576))) 53)) (-2339 (((-657 (-657 |#2|)) $) 80)) (-1474 (($ $ $) 72)) (-3418 (((-3 $ "failed") $ |#2|) 122)) (-2835 ((|#2| $ (-576) (-576)) NIL) ((|#2| $ (-576) (-576) |#2|) NIL) (($ $ (-657 (-576)) (-657 (-576))) 88)) (-4277 (($ (-657 |#2|)) 56) (($ (-657 $)) 58)) (-2049 (((-112) $) 28)) (-3501 (($ |#4|) 63) (((-877) $) NIL)) (-4299 (((-112) $) 38)) (-3034 (($ $ |#2|) 124)) (-3022 (($ $ $) 95) (($ $) 98)) (-3012 (($ $ $) 93)) (** (($ $ (-784)) 111) (($ $ (-576)) 128)) (* (($ $ $) 104) (($ |#2| $) 100) (($ $ |#2|) 101) (($ (-576) $) 103) ((|#4| $ |#4|) 115) ((|#3| |#3| $) 119))) 
-(((-699 |#1| |#2| |#3| |#4|) (-10 -8 (-15 -3501 ((-877) |#1|)) (-15 ** (|#1| |#1| (-576))) (-15 -3034 (|#1| |#1| |#2|)) (-15 -3418 ((-3 |#1| "failed") |#1| |#2|)) (-15 ** (|#1| |#1| (-784))) (-15 * (|#3| |#3| |#1|)) (-15 * (|#4| |#1| |#4|)) (-15 * (|#1| (-576) |#1|)) (-15 * (|#1| |#1| |#2|)) (-15 * (|#1| |#2| |#1|)) (-15 * (|#1| |#1| |#1|)) (-15 -3022 (|#1| |#1|)) (-15 -3022 (|#1| |#1| |#1|)) (-15 -3012 (|#1| |#1| |#1|)) (-15 -2337 (|#1| |#1| (-576) (-576) |#1|)) (-15 -2351 (|#1| |#1| (-576) (-576) (-576) (-576))) (-15 -1371 (|#1| |#1| (-576) (-576))) (-15 -1606 (|#1| |#1| (-576) (-576))) (-15 -3682 (|#1| |#1| (-657 (-576)) (-657 (-576)) |#1|)) (-15 -2835 (|#1| |#1| (-657 (-576)) (-657 (-576)))) (-15 -2339 ((-657 (-657 |#2|)) |#1|)) (-15 -2671 (|#1| |#1| |#1|)) (-15 -1474 (|#1| |#1| |#1|)) (-15 -1506 (|#1| |#1|)) (-15 -2153 (|#1| |#1|)) (-15 -2153 (|#1| |#3|)) (-15 -3501 (|#1| |#4|)) (-15 -4277 (|#1| (-657 |#1|))) (-15 -4277 (|#1| (-657 |#2|))) (-15 -1346 (|#1| (-784) |#2|)) (-15 -2514 (|#1| (-784) (-784) (-1 |#2| (-576) (-576)))) (-15 -2514 (|#1| (-657 (-657 |#2|)))) (-15 -3765 (|#1| (-784) (-784))) (-15 -4299 ((-112) |#1|)) (-15 -3864 ((-112) |#1|)) (-15 -2049 ((-112) |#1|)) (-15 -3186 ((-112) |#1|)) (-15 -3682 (|#2| |#1| (-576) (-576) |#2|)) (-15 -2835 (|#2| |#1| (-576) (-576) |#2|)) (-15 -2835 (|#2| |#1| (-576) (-576)))) (-700 |#2| |#3| |#4|) (-1071) (-384 |#2|) (-384 |#2|)) (T -699)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
-(-275 |#1|) 
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-(((-833) (-141)) (T -833)) 
-NIL 
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 (((-862) (-141)) (T -862)) 
 NIL 
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-NIL 
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-NIL 
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+(-13 (-875) (-742)) 
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+((-3010 (((-577) $) 21)) (-3567 (((-112) $) 10)) (-3578 (((-112) $) 12)) (-1654 (($ $) 23))) 
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+NIL 
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 (((-865) (-141)) (T -865)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+((-3473 (((-112) $ $) NIL)) (-3017 (((-1241) $) 13)) (-2810 (((-1183) $) NIL)) (-1474 (((-1145) $) NIL)) (-3131 (((-1160) $) 10)) (-3544 (((-880) $) 20) (($ (-1206)) NIL) (((-1206) $) NIL)) (-4448 (((-112) $ $) NIL)) (-2970 (((-112) $ $) NIL))) 
+(((-995) (-13 (-1108) (-10 -8 (-15 -3131 ((-1160) $)) (-15 -3017 ((-1241) $))))) (T -995)) 
+((-3131 (*1 *2 *1) (-12 (-5 *2 (-1160)) (-5 *1 (-995)))) (-3017 (*1 *2 *1) (-12 (-5 *2 (-1241)) (-5 *1 (-995))))) 
+(-13 (-1108) (-10 -8 (-15 -3131 ((-1160) $)) (-15 -3017 ((-1241) $)))) 
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+(((-996) (-13 (-811) (-626 (-660 (-944))) (-10 -8 (-15 -3529 ($ (-660 (-944)))) (-15 -1461 ((-660 (-944)) $)) (-15 -3484 ((-787) $)) (-15 -3518 ((-1182 $) (-787))) (-15 -3508 ((-660 (-891 (-944) (-944))) $)) (-15 -3499 ((-944) $)) (-15 -2360 ($ $))))) (T -996)) 
+((-3529 (*1 *1 *2) (-12 (-5 *2 (-660 (-944))) (-5 *1 (-996)))) (-1461 (*1 *2 *1) (-12 (-5 *2 (-660 (-944))) (-5 *1 (-996)))) (-3484 (*1 *2 *1) (-12 (-5 *2 (-787)) (-5 *1 (-996)))) (-3518 (*1 *2 *3) (-12 (-5 *3 (-787)) (-5 *2 (-1182 (-996))) (-5 *1 (-996)))) (-3508 (*1 *2 *1) (-12 (-5 *2 (-660 (-891 (-944) (-944)))) (-5 *1 (-996)))) (-3499 (*1 *2 *1) (-12 (-5 *2 (-944)) (-5 *1 (-996)))) (-2360 (*1 *1 *1) (-5 *1 (-996)))) 
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+NIL 
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-NIL 
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-((-2342 (((-1180) $) 10)) (-1471 (((-1142) $) 8))) 
-(((-1121 |#1|) (-10 -8 (-15 -2342 ((-1180) |#1|)) (-15 -1471 ((-1142) |#1|))) (-1122)) (T -1121)) 
-NIL 
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-(((-1124 |#1|) (-437 |#1|) (-1122)) (T -1124)) 
-NIL 
-(-437 |#1|) 
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-(((-1125 |#1| |#2| |#3| |#4| |#5|) (-141) (-1122) (-1122) (-1122) (-1122) (-1122)) (T -1125)) 
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-(((-102) . T) ((-625 (-877)) . T) ((-630 (-657 $)) . T) ((-630 |#1|) . T) ((-630 |#2|) . T) ((-630 |#3|) . T) ((-630 |#4|) . T) ((-630 |#5|) . T) ((-296 (-576) $) . T) ((-296 (-657 (-576)) $) . T) ((-1122) . T) ((-1239) . T)) 
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-(((-1126) (-1125 (-1180) (-1198) (-576) (-227) (-877))) (T -1126)) 
-NIL 
-(-1125 (-1180) (-1198) (-576) (-227) (-877)) 
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-NIL 
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-((-2669 (((-1294) $) 22)) (-2829 (($ (-1198) (-446) |#2|) 11)) (-3501 (((-877) $) 16))) 
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+NIL 
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-NIL 
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+NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1198)) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-1198)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-877)) . T) ((-174) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-908 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-908 (-390))))) ((-626 (-908 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-908 (-576))))) ((-234 $) -2802 (-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) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2802 (-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) (-1134)) ((-300) -2802 (|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 (-1198) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1198) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-659 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-659 (-576)) . T) ((-659 |#1|) . T) ((-659 |#2|) |has| |#1| (-374)) ((-659 $) . T) ((-661 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-661 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) ((-661 |#1|) . T) ((-661 |#2|) |has| |#1| (-374)) ((-661 $) . T) ((-653 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-653 |#1|) |has| |#1| (-174)) ((-653 |#2|) |has| |#1| (-374)) ((-653 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-652 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-652 (-576)))) ((-652 |#2|) |has| |#1| (-374)) ((-730 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-730 |#1|) |has| |#1| (-174)) ((-730 |#2|) |has| |#1| (-374)) ((-730 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-739) . T) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-805) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-808) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-833) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-861) -12 (|has| |#1| (-374)) (|has| |#2| (-833))) ((-862) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-833)))) ((-865) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-833)))) ((-912 $ #4=(-1198)) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-920 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-918 (-1198)) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-920 #4#) -2802 (-12 (|has| |#1| (-374)) (|has| |#2| (-920 (-1198)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1198)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-918 (-1198))))) ((-902 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-390)))) ((-902 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-902 (-576)))) ((-900 |#2|) |has| |#1| (-374)) ((-929) -12 (|has| |#1| (-374)) (|has| |#2| (-929))) ((-995 |#1| #0# (-1104)) . T) ((-940) |has| |#1| (-374)) ((-1014 |#2|) |has| |#1| (-374)) ((-1024) |has| |#1| (-38 (-419 (-576)))) ((-1044) -12 (|has| |#1| (-374)) (|has| |#2| (-1044))) ((-1060 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-576)))) ((-1060 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-576)))) ((-1060 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1060 (-1198)))) ((-1060 |#2|) . T) ((-1073 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1073 |#1|) . T) ((-1073 |#2|) |has| |#1| (-374)) ((-1073 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1078 #1#) -2802 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1078 |#1|) . T) ((-1078 |#2|) |has| |#1| (-374)) ((-1078 $) -2802 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1071) . T) ((-1080) . T) ((-1134) . T) ((-1122) . T) ((-1174) -12 (|has| |#1| (-374)) (|has| |#2| (-1174))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1227) |has| |#1| (-38 (-419 (-576)))) ((-1239) . 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-NIL 
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-NIL 
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-(((-1318 |#1|) (-13 (-174) (-379) (-626 (-576)) (-1174)) (-941)) (T -1318)) 
-NIL 
-(-13 (-174) (-379) (-626 (-576)) (-1174)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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T T) -9 NIL 3241743 NIL) (-1309 3236295 3238436 3238824 "XPBWPOLY" 3239577 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1308 3231976 3234271 3234313 "XF" 3234934 NIL XF (NIL T) -9 NIL 3235334 NIL) (-1307 3231597 3231685 3231854 "XF-" 3231859 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1306 3226779 3228068 3228123 "XFALG" 3230295 NIL XFALG (NIL T T) -9 NIL 3231084 NIL) (-1305 3225912 3226016 3226221 "XEXPPKG" 3226671 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1304 3224021 3225762 3225858 "XDPOLY" 3225863 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1303 3222814 3223414 3223457 "XALG" 3223462 NIL XALG (NIL T) -9 NIL 3223573 NIL) (-1302 3216256 3220791 3221285 "WUTSET" 3222406 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1301 3214512 3215308 3215631 "WP" 3216067 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1300 3214114 3214334 3214404 "WHILEAST" 3214464 T WHILEAST (NIL) -8 NIL NIL NIL) (-1299 3213586 3213831 3213925 "WHEREAST" 3214042 T WHEREAST (NIL) -8 NIL NIL NIL) (-1298 3212472 3212670 3212965 "WFFINTBS" 3213383 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1297 3210376 3210803 3211265 "WEIER" 3212044 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1296 3209408 3209858 3209900 "VSPACE" 3210036 NIL VSPACE (NIL T) -9 NIL 3210110 NIL) (-1295 3209246 3209273 3209364 "VSPACE-" 3209369 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1294 3209055 3209097 3209165 "VOID" 3209200 T VOID (NIL) -8 NIL NIL NIL) (-1293 3207191 3207550 3207956 "VIEW" 3208671 T VIEW (NIL) -7 NIL NIL NIL) (-1292 3203615 3204254 3204991 "VIEWDEF" 3206476 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1291 3192919 3195163 3197336 "VIEW3D" 3201464 T VIEW3D (NIL) -8 NIL NIL NIL) (-1290 3185170 3186830 3188409 "VIEW2D" 3191362 T VIEW2D (NIL) -8 NIL NIL NIL) (-1289 3180526 3184940 3185032 "VECTOR" 3185113 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1288 3179103 3179362 3179680 "VECTOR2" 3180256 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1287 3172501 3176807 3176850 "VECTCAT" 3177845 NIL VECTCAT (NIL T) -9 NIL 3178432 NIL) (-1286 3171515 3171769 3172159 "VECTCAT-" 3172164 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1285 3170969 3171166 3171286 "VARIABLE" 3171430 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1284 3170902 3170907 3170937 "UTYPE" 3170942 T UTYPE (NIL) -9 NIL NIL NIL) (-1283 3169732 3169886 3170148 "UTSODETL" 3170728 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1282 3167172 3167632 3168156 "UTSODE" 3169273 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1281 3159120 3164933 3165413 "UTS" 3166750 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1280 3149684 3155054 3155097 "UTSCAT" 3156209 NIL UTSCAT (NIL T) -9 NIL 3156967 NIL) (-1279 3147032 3147754 3148743 "UTSCAT-" 3148748 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1278 3146659 3146702 3146835 "UTS2" 3146983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1277 3140860 3143469 3143512 "URAGG" 3145582 NIL URAGG (NIL T) -9 NIL 3146305 NIL) (-1276 3137799 3138662 3139785 "URAGG-" 3139790 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1275 3133508 3136434 3136899 "UPXSSING" 3137463 NIL UPXSSING (NIL T T NIL NIL) -8 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(NIL T T) -8 NIL NIL NIL) (-1251 2999184 3011544 3011606 "ULSCCAT" 3012244 NIL ULSCCAT (NIL T T) -9 NIL 3012533 NIL) (-1250 2998234 2998479 2998867 "ULSCCAT-" 2998872 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 2987298 2993781 2993824 "ULSCAT" 2994687 NIL ULSCAT (NIL T) -9 NIL 2995418 NIL) (-1248 2986728 2986807 2986986 "ULS2" 2987213 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1247 2985847 2986357 2986464 "UINT8" 2986575 T UINT8 (NIL) -8 NIL NIL 2986660) (-1246 2984965 2985475 2985582 "UINT64" 2985693 T UINT64 (NIL) -8 NIL NIL 2985778) (-1245 2984083 2984593 2984700 "UINT32" 2984811 T UINT32 (NIL) -8 NIL NIL 2984896) (-1244 2983201 2983711 2983818 "UINT16" 2983929 T UINT16 (NIL) -8 NIL NIL 2984014) (-1243 2981490 2982447 2982477 "UFD" 2982689 T UFD (NIL) -9 NIL 2982803 NIL) (-1242 2981284 2981330 2981425 "UFD-" 2981430 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1241 2980366 2980549 2980765 "UDVO" 2981090 T UDVO (NIL) -7 NIL NIL NIL) (-1240 2978182 2978591 2979062 "UDPO" 2979930 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1239 2978115 2978120 2978150 "TYPE" 2978155 T TYPE (NIL) -9 NIL NIL NIL) (-1238 2977875 2978070 2978101 "TYPEAST" 2978106 T TYPEAST (NIL) -8 NIL NIL NIL) (-1237 2976846 2977048 2977288 "TWOFACT" 2977669 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1236 2975869 2976255 2976490 "TUPLE" 2976646 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1235 2973560 2974079 2974618 "TUBETOOL" 2975352 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1234 2972409 2972614 2972855 "TUBE" 2973353 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1233 2967138 2971381 2971664 "TS" 2972161 NIL TS (NIL T) -8 NIL NIL NIL) (-1232 2955778 2959897 2959994 "TSETCAT" 2965263 NIL TSETCAT (NIL T T T T) -9 NIL 2966794 NIL) (-1231 2950510 2952110 2954001 "TSETCAT-" 2954006 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1230 2945149 2945996 2946925 "TRMANIP" 2949646 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1229 2944590 2944653 2944816 "TRIMAT" 2945081 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1228 2942456 2942693 2943050 "TRIGMNIP" 2944339 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1227 2941976 2942089 2942119 "TRIGCAT" 2942332 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1226 2941645 2941724 2941865 "TRIGCAT-" 2941870 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1225 2938493 2940503 2940784 "TREE" 2941399 NIL TREE (NIL T) -8 NIL NIL NIL) (-1224 2937767 2938295 2938325 "TRANFUN" 2938360 T TRANFUN (NIL) -9 NIL 2938426 NIL) (-1223 2937046 2937237 2937517 "TRANFUN-" 2937522 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1222 2936850 2936882 2936943 "TOPSP" 2937007 T TOPSP (NIL) -7 NIL NIL NIL) (-1221 2936198 2936313 2936467 "TOOLSIGN" 2936731 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1220 2934832 2935375 2935614 "TEXTFILE" 2935981 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1219 2932744 2933285 2933714 "TEX" 2934425 T TEX (NIL) -8 NIL NIL NIL) (-1218 2932525 2932556 2932628 "TEX1" 2932707 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1217 2932173 2932236 2932326 "TEMUTL" 2932457 T TEMUTL (NIL) -7 NIL NIL NIL) (-1216 2930327 2930607 2930932 "TBCMPPK" 2931896 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1215 2922036 2928413 2928469 "TBAGG" 2928869 NIL TBAGG (NIL T T) -9 NIL 2929080 NIL) (-1214 2917106 2918594 2920348 "TBAGG-" 2920353 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1213 2916490 2916597 2916742 "TANEXP" 2916995 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1212 2916001 2916265 2916355 "TALGOP" 2916435 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1211 2909397 2915858 2915951 "TABLE" 2915956 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1210 2908809 2908908 2909046 "TABLEAU" 2909294 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1209 2903417 2904637 2905885 "TABLBUMP" 2907595 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1208 2902639 2902786 2902967 "SYSTEM" 2903258 T SYSTEM (NIL) -8 NIL NIL NIL) (-1207 2899098 2899797 2900580 "SYSSOLP" 2901890 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1206 2898896 2899053 2899084 "SYSPTR" 2899089 T SYSPTR (NIL) -8 NIL NIL NIL) (-1205 2897932 2898437 2898556 "SYSNNI" 2898742 NIL SYSNNI (NIL NIL) -8 NIL NIL 2898827) (-1204 2897231 2897690 2897769 "SYSINT" 2897829 NIL SYSINT (NIL NIL) -8 NIL NIL 2897874) (-1203 2893563 2894509 2895219 "SYNTAX" 2896543 T SYNTAX (NIL) -8 NIL NIL NIL) (-1202 2890721 2891323 2891955 "SYMTAB" 2892953 T SYMTAB (NIL) -8 NIL NIL NIL) (-1201 2885970 2886872 2887855 "SYMS" 2889760 T SYMS (NIL) -8 NIL NIL NIL) (-1200 2883205 2885428 2885658 "SYMPOLY" 2885775 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1199 2882722 2882797 2882920 "SYMFUNC" 2883117 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1198 2878742 2880034 2880847 "SYMBOL" 2881931 T SYMBOL (NIL) -8 NIL NIL NIL) (-1197 2872281 2873970 2875690 "SWITCH" 2877044 T SWITCH (NIL) -8 NIL NIL NIL) (-1196 2865625 2871237 2871531 "SUTS" 2872045 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1195 2857801 2865007 2865271 "SUPXS" 2865419 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2849284 2857419 2857545 "SUP" 2857710 NIL SUP (NIL T) -8 NIL NIL NIL) (-1193 2848443 2848570 2848787 "SUPFRACF" 2849152 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1192 2848064 2848123 2848236 "SUP2" 2848378 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1191 2846512 2846786 2847142 "SUMRF" 2847763 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1190 2845847 2845913 2846105 "SUMFS" 2846433 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1189 2828634 2845159 2845401 "SULS" 2845663 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1188 2828236 2828456 2828526 "SUCHTAST" 2828586 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1187 2827531 2827761 2827901 "SUCH" 2828144 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1186 2821398 2822437 2823396 "SUBSPACE" 2826619 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1185 2820828 2820918 2821082 "SUBRESP" 2821286 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1184 2814196 2815493 2816804 "STTF" 2819564 NIL STTF (NIL T) -7 NIL NIL NIL) (-1183 2808369 2809489 2810636 "STTFNC" 2813096 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1182 2799682 2801551 2803345 "STTAYLOR" 2806610 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1181 2792818 2799546 2799629 "STRTBL" 2799634 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1180 2787779 2792527 2792626 "STRING" 2792741 T STRING (NIL) -8 NIL NIL NIL) (-1179 2780535 2785398 2786009 "STREAM" 2787203 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1178 2780045 2780122 2780266 "STREAM3" 2780452 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1177 2779027 2779210 2779445 "STREAM2" 2779858 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1176 2778715 2778767 2778860 "STREAM1" 2778969 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1175 2777731 2777912 2778143 "STINPROD" 2778531 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1174 2777269 2777479 2777509 "STEP" 2777589 T STEP (NIL) -9 NIL 2777667 NIL) (-1173 2776456 2776758 2776906 "STEPAST" 2777143 T STEPAST (NIL) -8 NIL NIL NIL) (-1172 2769894 2776355 2776432 "STBL" 2776437 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1171 2764964 2769057 2769100 "STAGG" 2769253 NIL STAGG (NIL T) -9 NIL 2769342 NIL) (-1170 2762666 2763268 2764140 "STAGG-" 2764145 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1169 2760816 2762436 2762528 "STACK" 2762609 NIL STACK (NIL T) -8 NIL NIL NIL) (-1168 2753511 2758957 2759413 "SREGSET" 2760446 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1167 2745936 2747305 2748818 "SRDCMPK" 2752117 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1166 2738773 2743295 2743325 "SRAGG" 2744628 T SRAGG (NIL) -9 NIL 2745236 NIL) (-1165 2737790 2738045 2738424 "SRAGG-" 2738429 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1164 2731974 2736737 2737158 "SQMATRIX" 2737416 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1163 2725662 2728692 2729419 "SPLTREE" 2731319 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1162 2721625 2722318 2722964 "SPLNODE" 2725088 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1161 2720672 2720905 2720935 "SPFCAT" 2721379 T SPFCAT (NIL) -9 NIL NIL NIL) (-1160 2719409 2719619 2719883 "SPECOUT" 2720430 T SPECOUT (NIL) -7 NIL NIL NIL) (-1159 2710505 2712377 2712407 "SPADXPT" 2717083 T SPADXPT (NIL) -9 NIL 2719247 NIL) (-1158 2710266 2710306 2710375 "SPADPRSR" 2710458 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1157 2708315 2710221 2710252 "SPADAST" 2710257 T SPADAST (NIL) -8 NIL NIL NIL) (-1156 2700246 2702019 2702062 "SPACEC" 2706435 NIL SPACEC (NIL T) -9 NIL 2708251 NIL) (-1155 2698376 2700178 2700227 "SPACE3" 2700232 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1154 2697128 2697299 2697590 "SORTPAK" 2698181 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1153 2695220 2695523 2695935 "SOLVETRA" 2696792 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1152 2694270 2694492 2694753 "SOLVESER" 2694993 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1151 2689574 2690462 2691457 "SOLVERAD" 2693322 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1150 2685389 2685998 2686727 "SOLVEFOR" 2688941 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1149 2679659 2684738 2684835 "SNTSCAT" 2684840 NIL SNTSCAT (NIL T T T T) -9 NIL 2684910 NIL) (-1148 2673765 2677982 2678373 "SMTS" 2679349 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1147 2668174 2673653 2673730 "SMP" 2673735 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1146 2666333 2666634 2667032 "SMITH" 2667871 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1145 2658437 2662912 2663015 "SMATCAT" 2664366 NIL SMATCAT (NIL NIL T T T) -9 NIL 2664916 NIL) (-1144 2655377 2656200 2657378 "SMATCAT-" 2657383 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1143 2653018 2654585 2654628 "SKAGG" 2654889 NIL SKAGG (NIL T) -9 NIL 2655024 NIL) (-1142 2649208 2652491 2652675 "SINT" 2652827 T SINT (NIL) -8 NIL NIL 2652989) (-1141 2648980 2649018 2649084 "SIMPAN" 2649164 T SIMPAN (NIL) -7 NIL NIL NIL) (-1140 2648259 2648515 2648655 "SIG" 2648862 T SIG (NIL) -8 NIL NIL NIL) (-1139 2647097 2647318 2647593 "SIGNRF" 2648018 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1138 2645930 2646081 2646365 "SIGNEF" 2646926 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1137 2645236 2645513 2645637 "SIGAST" 2645828 T SIGAST (NIL) -8 NIL NIL NIL) (-1136 2642926 2643380 2643886 "SHP" 2644777 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1135 2636755 2642827 2642903 "SHDP" 2642908 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1134 2636314 2636506 2636536 "SGROUP" 2636629 T SGROUP (NIL) -9 NIL 2636691 NIL) (-1133 2636172 2636198 2636271 "SGROUP-" 2636276 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1132 2632963 2633661 2634384 "SGCF" 2635471 T SGCF (NIL) -7 NIL NIL NIL) (-1131 2627331 2632410 2632507 "SFRTCAT" 2632512 NIL SFRTCAT (NIL T T T T) -9 NIL 2632551 NIL) (-1130 2620752 2621770 2622906 "SFRGCD" 2626314 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1129 2613878 2614951 2616137 "SFQCMPK" 2619685 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1128 2613498 2613587 2613698 "SFORT" 2613819 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1127 2612616 2613338 2613459 "SEXOF" 2613464 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1126 2611723 2612497 2612565 "SEX" 2612570 T SEX (NIL) -8 NIL NIL NIL) (-1125 2607504 2608219 2608314 "SEXCAT" 2610936 NIL SEXCAT (NIL T T T T T) -9 NIL 2611496 NIL) (-1124 2604657 2607438 2607486 "SET" 2607491 NIL SET (NIL T) -8 NIL NIL NIL) (-1123 2602881 2603370 2603675 "SETMN" 2604398 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1122 2602447 2602599 2602629 "SETCAT" 2602746 T SETCAT (NIL) -9 NIL 2602831 NIL) (-1121 2602227 2602279 2602378 "SETCAT-" 2602383 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1120 2598588 2600688 2600731 "SETAGG" 2601601 NIL SETAGG (NIL T) -9 NIL 2601941 NIL) (-1119 2598046 2598162 2598399 "SETAGG-" 2598404 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1118 2597489 2597742 2597843 "SEQAST" 2597967 T SEQAST (NIL) -8 NIL NIL NIL) (-1117 2596688 2596982 2597043 "SEGXCAT" 2597329 NIL SEGXCAT (NIL T T) -9 NIL 2597449 NIL) (-1116 2595694 2596354 2596536 "SEG" 2596541 NIL SEG (NIL T) -8 NIL NIL NIL) (-1115 2594673 2594887 2594930 "SEGCAT" 2595452 NIL SEGCAT (NIL T) -9 NIL 2595673 NIL) (-1114 2593605 2594036 2594244 "SEGBIND" 2594500 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1113 2593226 2593285 2593398 "SEGBIND2" 2593540 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1112 2592799 2593027 2593104 "SEGAST" 2593171 T SEGAST (NIL) -8 NIL NIL NIL) (-1111 2592018 2592144 2592348 "SEG2" 2592643 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1110 2591389 2591953 2592000 "SDVAR" 2592005 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1109 2583640 2591159 2591289 "SDPOL" 2591294 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1108 2582233 2582499 2582818 "SCPKG" 2583355 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1107 2581397 2581569 2581761 "SCOPE" 2582063 T SCOPE (NIL) -8 NIL NIL NIL) (-1106 2580617 2580751 2580930 "SCACHE" 2581252 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1105 2580249 2580435 2580465 "SASTCAT" 2580470 T SASTCAT (NIL) -9 NIL 2580483 NIL) (-1104 2579736 2580084 2580160 "SAOS" 2580195 T SAOS (NIL) -8 NIL NIL NIL) (-1103 2579301 2579336 2579509 "SAERFFC" 2579695 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1102 2572964 2579198 2579278 "SAE" 2579283 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1101 2572557 2572592 2572751 "SAEFACT" 2572923 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1100 2570878 2571192 2571593 "RURPK" 2572223 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1099 2569515 2569821 2570126 "RULESET" 2570712 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1098 2566738 2567268 2567726 "RULE" 2569196 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1097 2566350 2566532 2566615 "RULECOLD" 2566690 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1096 2566140 2566168 2566239 "RTVALUE" 2566301 T RTVALUE (NIL) -8 NIL NIL NIL) (-1095 2565611 2565857 2565951 "RSTRCAST" 2566068 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1094 2560459 2561254 2562174 "RSETGCD" 2564810 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1093 2549689 2554768 2554865 "RSETCAT" 2558984 NIL RSETCAT (NIL T T T T) -9 NIL 2560081 NIL) (-1092 2547616 2548155 2548979 "RSETCAT-" 2548984 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1091 2540002 2541378 2542898 "RSDCMPK" 2546215 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1090 2537967 2538434 2538508 "RRCC" 2539594 NIL RRCC (NIL T T) -9 NIL 2539938 NIL) (-1089 2537318 2537492 2537771 "RRCC-" 2537776 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1088 2536761 2537014 2537115 "RPTAST" 2537239 T RPTAST (NIL) -8 NIL NIL NIL) (-1087 2510237 2519873 2519940 "RPOLCAT" 2530606 NIL RPOLCAT (NIL T T T) -9 NIL 2533766 NIL) (-1086 2501735 2504075 2507197 "RPOLCAT-" 2507202 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1085 2492672 2499946 2500428 "ROUTINE" 2501275 T ROUTINE (NIL) -8 NIL NIL NIL) (-1084 2489333 2492298 2492438 "ROMAN" 2492554 T ROMAN (NIL) -8 NIL NIL NIL) (-1083 2487577 2488193 2488453 "ROIRC" 2489138 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1082 2483781 2486066 2486096 "RNS" 2486400 T RNS (NIL) -9 NIL 2486674 NIL) (-1081 2482290 2482673 2483207 "RNS-" 2483282 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1080 2481679 2482087 2482117 "RNG" 2482122 T RNG (NIL) -9 NIL 2482143 NIL) (-1079 2480682 2481044 2481246 "RNGBIND" 2481530 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1078 2480067 2480455 2480498 "RMODULE" 2480503 NIL RMODULE (NIL T) -9 NIL 2480530 NIL) (-1077 2478903 2478997 2479333 "RMCAT2" 2479968 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1076 2475753 2478249 2478546 "RMATRIX" 2478665 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1075 2468580 2470840 2470955 "RMATCAT" 2474314 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2475296 NIL) (-1074 2467955 2468102 2468409 "RMATCAT-" 2468414 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1073 2467570 2467742 2467785 "RLINSET" 2467847 NIL RLINSET (NIL T) -9 NIL 2467891 NIL) (-1072 2467137 2467212 2467340 "RINTERP" 2467489 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1071 2466181 2466735 2466765 "RING" 2466821 T RING (NIL) -9 NIL 2466913 NIL) (-1070 2465973 2466017 2466114 "RING-" 2466119 NIL RING- (NIL T) -8 NIL NIL NIL) (-1069 2464814 2465051 2465309 "RIDIST" 2465737 T RIDIST (NIL) -7 NIL NIL NIL) (-1068 2456103 2464282 2464488 "RGCHAIN" 2464662 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1067 2455439 2455845 2455886 "RGBCSPC" 2455944 NIL RGBCSPC (NIL T) -9 NIL 2455996 NIL) (-1066 2454583 2454964 2455005 "RGBCMDL" 2455237 NIL RGBCMDL (NIL T) -9 NIL 2455351 NIL) (-1065 2451577 2452191 2452861 "RF" 2453947 NIL RF (NIL T) -7 NIL NIL NIL) (-1064 2451223 2451286 2451389 "RFFACTOR" 2451508 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1063 2450948 2450983 2451080 "RFFACT" 2451182 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1062 2449065 2449429 2449811 "RFDIST" 2450588 T RFDIST (NIL) -7 NIL NIL NIL) (-1061 2448518 2448610 2448773 "RETSOL" 2448967 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1060 2448154 2448234 2448277 "RETRACT" 2448410 NIL RETRACT (NIL T) -9 NIL 2448497 NIL) (-1059 2448003 2448028 2448115 "RETRACT-" 2448120 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1058 2447605 2447825 2447895 "RETAST" 2447955 T RETAST (NIL) -8 NIL NIL NIL) (-1057 2440349 2447258 2447385 "RESULT" 2447500 T RESULT (NIL) -8 NIL NIL NIL) (-1056 2438940 2439618 2439817 "RESRING" 2440252 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1055 2438576 2438625 2438723 "RESLATC" 2438877 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1054 2438281 2438316 2438423 "REPSQ" 2438535 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1053 2435703 2436283 2436885 "REP" 2437701 T REP (NIL) -7 NIL NIL NIL) (-1052 2435400 2435435 2435546 "REPDB" 2435662 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1051 2429300 2430689 2431912 "REP2" 2434212 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1050 2425677 2426358 2427166 "REP1" 2428527 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1049 2418373 2423818 2424274 "REGSET" 2425307 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1048 2417138 2417521 2417771 "REF" 2418158 NIL REF (NIL T) -8 NIL NIL NIL) (-1047 2416515 2416618 2416785 "REDORDER" 2417022 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1046 2412483 2415728 2415955 "RECLOS" 2416343 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1045 2411535 2411716 2411931 "REALSOLV" 2412290 T REALSOLV (NIL) -7 NIL NIL NIL) (-1044 2411381 2411422 2411452 "REAL" 2411457 T REAL (NIL) -9 NIL 2411492 NIL) (-1043 2407864 2408666 2409550 "REAL0Q" 2410546 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1042 2403465 2404453 2405514 "REAL0" 2406845 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1041 2402936 2403182 2403276 "RDUCEAST" 2403393 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1040 2402341 2402413 2402620 "RDIV" 2402858 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1039 2401409 2401583 2401796 "RDIST" 2402163 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1038 2400006 2400293 2400665 "RDETRS" 2401117 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1037 2397818 2398272 2398810 "RDETR" 2399548 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1036 2396443 2396721 2397118 "RDEEFS" 2397534 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1035 2394952 2395258 2395683 "RDEEF" 2396131 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1034 2388985 2391906 2391936 "RCFIELD" 2393231 T RCFIELD (NIL) -9 NIL 2393962 NIL) (-1033 2387049 2387553 2388249 "RCFIELD-" 2388324 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1032 2383293 2385122 2385165 "RCAGG" 2386249 NIL RCAGG (NIL T) -9 NIL 2386714 NIL) (-1031 2382921 2383015 2383178 "RCAGG-" 2383183 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1030 2382256 2382368 2382533 "RATRET" 2382805 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1029 2381809 2381876 2381997 "RATFACT" 2382184 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1028 2381117 2381237 2381389 "RANDSRC" 2381679 T RANDSRC (NIL) -7 NIL NIL NIL) (-1027 2380851 2380895 2380968 "RADUTIL" 2381066 T RADUTIL (NIL) -7 NIL NIL NIL) (-1026 2373679 2379682 2379993 "RADIX" 2380574 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1025 2364139 2373521 2373651 "RADFF" 2373656 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1024 2363786 2363861 2363891 "RADCAT" 2364051 T RADCAT (NIL) -9 NIL NIL NIL) (-1023 2363568 2363616 2363716 "RADCAT-" 2363721 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1022 2361669 2363338 2363430 "QUEUE" 2363511 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1021 2357930 2361602 2361650 "QUAT" 2361655 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1020 2357561 2357604 2357735 "QUATCT2" 2357881 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2350359 2353984 2354026 "QUATCAT" 2354817 NIL QUATCAT (NIL T) -9 NIL 2355583 NIL) (-1018 2346498 2347535 2348925 "QUATCAT-" 2349021 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1017 2343938 2345546 2345589 "QUAGG" 2345970 NIL QUAGG (NIL T) -9 NIL 2346145 NIL) (-1016 2343540 2343760 2343830 "QQUTAST" 2343890 T QQUTAST (NIL) -8 NIL NIL NIL) (-1015 2342553 2343053 2343218 "QFORM" 2343421 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1014 2332885 2338400 2338442 "QFCAT" 2339110 NIL QFCAT (NIL T) -9 NIL 2340111 NIL) (-1013 2328452 2329653 2331247 "QFCAT-" 2331343 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2328083 2328126 2328257 "QFCAT2" 2328403 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1011 2327538 2327648 2327780 "QEQUAT" 2327973 T QEQUAT (NIL) -8 NIL NIL NIL) (-1010 2320664 2321737 2322923 "QCMPACK" 2326471 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1009 2318202 2318650 2319080 "QALGSET" 2320319 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1008 2317437 2317613 2317849 "QALGSET2" 2318020 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1007 2316122 2316346 2316665 "PWFFINTB" 2317210 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1006 2314297 2314465 2314821 "PUSHVAR" 2315936 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1005 2310186 2311240 2311283 "PTRANFN" 2313194 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1004 2308577 2308868 2309192 "PTPACK" 2309897 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1003 2308206 2308263 2308374 "PTFUNC2" 2308514 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1002 2302601 2306995 2307038 "PTCAT" 2307338 NIL PTCAT (NIL T) -9 NIL 2307491 NIL) (-1001 2302256 2302291 2302417 "PSQFR" 2302560 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1000 2300846 2301144 2301480 "PSEUDLIN" 2301954 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-999 2287609 2289980 2292304 "PSETPK" 2298606 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-998 2280627 2283367 2283463 "PSETCAT" 2286484 NIL PSETCAT (NIL T T T T) -9 NIL 2287298 NIL) (-997 2278463 2279097 2279918 "PSETCAT-" 2279923 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-996 2277812 2277977 2278005 "PSCURVE" 2278273 T PSCURVE (NIL) -9 NIL 2278440 NIL) (-995 2273796 2275312 2275377 "PSCAT" 2276221 NIL PSCAT (NIL T T T) -9 NIL 2276461 NIL) (-994 2272859 2273075 2273475 "PSCAT-" 2273480 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-993 2271218 2271928 2272191 "PRTITION" 2272616 T PRTITION (NIL) -8 NIL NIL NIL) (-992 2270693 2270939 2271031 "PRTDAST" 2271146 T PRTDAST (NIL) -8 NIL NIL NIL) (-991 2259783 2261997 2264185 "PRS" 2268555 NIL PRS (NIL T T) -7 NIL NIL NIL) (-990 2257569 2259105 2259145 "PRQAGG" 2259328 NIL PRQAGG (NIL T) -9 NIL 2259430 NIL) (-989 2256905 2257210 2257238 "PROPLOG" 2257377 T PROPLOG (NIL) -9 NIL 2257492 NIL) (-988 2256509 2256566 2256689 "PROPFUN2" 2256828 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-987 2255824 2255945 2256117 "PROPFUN1" 2256370 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-986 2254005 2254571 2254868 "PROPFRML" 2255560 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-985 2253474 2253581 2253709 "PROPERTY" 2253897 T PROPERTY (NIL) -8 NIL NIL NIL) (-984 2247532 2251640 2252460 "PRODUCT" 2252700 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-983 2244810 2246990 2247224 "PR" 2247343 NIL PR (NIL T T) -8 NIL NIL NIL) (-982 2244606 2244638 2244697 "PRINT" 2244771 T PRINT (NIL) -7 NIL NIL NIL) (-981 2243946 2244063 2244215 "PRIMES" 2244486 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-980 2242011 2242412 2242878 "PRIMELT" 2243525 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-979 2241740 2241789 2241817 "PRIMCAT" 2241941 T PRIMCAT (NIL) -9 NIL NIL NIL) (-978 2237858 2241678 2241723 "PRIMARR" 2241728 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-977 2236865 2237043 2237271 "PRIMARR2" 2237676 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-976 2236508 2236564 2236675 "PREASSOC" 2236803 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-975 2235983 2236116 2236144 "PPCURVE" 2236349 T PPCURVE (NIL) -9 NIL 2236485 NIL) (-974 2235578 2235778 2235861 "PORTNUM" 2235920 T PORTNUM (NIL) -8 NIL NIL NIL) (-973 2232937 2233336 2233928 "POLYROOT" 2235159 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-972 2226843 2232541 2232701 "POLY" 2232810 NIL POLY (NIL T) -8 NIL NIL NIL) (-971 2226226 2226284 2226518 "POLYLIFT" 2226779 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-970 2222501 2222950 2223579 "POLYCATQ" 2225771 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-969 2208843 2214248 2214313 "POLYCAT" 2217827 NIL POLYCAT (NIL T T T) -9 NIL 2219705 NIL) (-968 2202292 2204154 2206538 "POLYCAT-" 2206543 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2201879 2201947 2202067 "POLY2UP" 2202218 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-966 2201511 2201568 2201677 "POLY2" 2201816 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-965 2200196 2200435 2200711 "POLUTIL" 2201285 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-964 2198551 2198828 2199159 "POLTOPOL" 2199918 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-963 2194017 2198485 2198532 "POINT" 2198537 NIL POINT (NIL T) -8 NIL NIL NIL) (-962 2192204 2192561 2192936 "PNTHEORY" 2193662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-961 2190662 2190959 2191358 "PMTOOLS" 2191902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-960 2190255 2190333 2190450 "PMSYM" 2190578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-959 2189763 2189832 2190007 "PMQFCAT" 2190180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-958 2189118 2189228 2189384 "PMPRED" 2189640 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-957 2188511 2188597 2188759 "PMPREDFS" 2189019 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-956 2187175 2187383 2187761 "PMPLCAT" 2188273 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-955 2186707 2186786 2186938 "PMLSAGG" 2187090 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-954 2186180 2186256 2186438 "PMKERNEL" 2186625 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-953 2185797 2185872 2185985 "PMINS" 2186099 NIL PMINS (NIL T) -7 NIL NIL NIL) (-952 2185239 2185308 2185517 "PMFS" 2185722 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-951 2184467 2184585 2184790 "PMDOWN" 2185116 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-950 2183634 2183792 2183973 "PMASS" 2184306 T PMASS (NIL) -7 NIL NIL NIL) (-949 2182907 2183017 2183180 "PMASSFS" 2183521 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-948 2182562 2182630 2182724 "PLOTTOOL" 2182833 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-947 2177169 2178373 2179521 "PLOT" 2181434 T PLOT (NIL) -8 NIL NIL NIL) (-946 2172973 2174017 2174938 "PLOT3D" 2176268 T PLOT3D (NIL) -8 NIL NIL NIL) (-945 2171885 2172062 2172297 "PLOT1" 2172777 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-944 2147276 2151951 2156802 "PLEQN" 2167151 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-943 2146594 2146716 2146896 "PINTERP" 2147141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-942 2146287 2146334 2146437 "PINTERPA" 2146541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-941 2145503 2146051 2146138 "PI" 2146178 T PI (NIL) -8 NIL NIL 2146245) (-940 2143786 2144761 2144789 "PID" 2144971 T PID (NIL) -9 NIL 2145105 NIL) (-939 2143537 2143574 2143649 "PICOERCE" 2143743 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-938 2142857 2142996 2143172 "PGROEB" 2143393 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-937 2138444 2139258 2140163 "PGE" 2141972 T PGE (NIL) -7 NIL NIL NIL) (-936 2136567 2136814 2137180 "PGCD" 2138161 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-935 2135905 2136008 2136169 "PFRPAC" 2136451 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-934 2132545 2134453 2134806 "PFR" 2135584 NIL PFR (NIL T) -8 NIL NIL NIL) (-933 2130934 2131178 2131503 "PFOTOOLS" 2132292 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-932 2129467 2129706 2130057 "PFOQ" 2130691 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-931 2127968 2128180 2128536 "PFO" 2129251 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-930 2124521 2127857 2127926 "PF" 2127931 NIL PF (NIL NIL) -8 NIL NIL NIL) (-929 2121841 2123112 2123140 "PFECAT" 2123725 T PFECAT (NIL) -9 NIL 2124109 NIL) (-928 2121286 2121440 2121654 "PFECAT-" 2121659 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-927 2119889 2120141 2120442 "PFBRU" 2121035 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-926 2117755 2118107 2118539 "PFBR" 2119540 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-925 2113801 2115267 2115914 "PERM" 2117141 NIL PERM (NIL T) -8 NIL NIL NIL) (-924 2109035 2110008 2110878 "PERMGRP" 2112964 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-923 2107099 2108059 2108100 "PERMCAT" 2108500 NIL PERMCAT (NIL T) -9 NIL 2108798 NIL) (-922 2106752 2106793 2106917 "PERMAN" 2107052 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-921 2104243 2106417 2106539 "PENDTREE" 2106663 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-920 2103172 2103387 2103428 "PDSPC" 2103961 NIL PDSPC (NIL T) -9 NIL 2104206 NIL) (-919 2102275 2102493 2102855 "PDSPC-" 2102860 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-918 2101157 2101925 2101966 "PDRING" 2101971 NIL PDRING (NIL T) -9 NIL 2101999 NIL) (-917 2100044 2100662 2100716 "PDMOD" 2100721 NIL PDMOD (NIL T T) -9 NIL 2100825 NIL) (-916 2097259 2098037 2098705 "PDEPROB" 2099396 T PDEPROB (NIL) -8 NIL NIL NIL) (-915 2094804 2095308 2095863 "PDEPACK" 2096724 T PDEPACK (NIL) -7 NIL NIL NIL) (-914 2093716 2093906 2094157 "PDECOMP" 2094603 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-913 2091281 2092124 2092152 "PDECAT" 2092939 T PDECAT (NIL) -9 NIL 2093652 NIL) (-912 2090910 2090965 2091019 "PDDOM" 2091184 NIL PDDOM (NIL T T) -9 NIL 2091264 NIL) (-911 2090729 2090759 2090866 "PDDOM-" 2090871 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-910 2090480 2090513 2090603 "PCOMP" 2090690 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-909 2088658 2089281 2089578 "PBWLB" 2090209 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-908 2081131 2082731 2084069 "PATTERN" 2087341 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-907 2080763 2080820 2080929 "PATTERN2" 2081068 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-906 2078520 2078908 2079365 "PATTERN1" 2080352 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-905 2075888 2076469 2076950 "PATRES" 2078085 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-904 2075452 2075519 2075651 "PATRES2" 2075815 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-903 2073335 2073740 2074147 "PATMATCH" 2075119 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-902 2072831 2073040 2073081 "PATMAB" 2073188 NIL PATMAB (NIL T) -9 NIL 2073271 NIL) (-901 2071349 2071685 2071943 "PATLRES" 2072636 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-900 2070895 2071018 2071059 "PATAB" 2071064 NIL PATAB (NIL T) -9 NIL 2071236 NIL) (-899 2069077 2069472 2069895 "PARTPERM" 2070492 T PARTPERM (NIL) -7 NIL NIL NIL) (-898 2068698 2068761 2068863 "PARSURF" 2069008 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-897 2068330 2068387 2068496 "PARSU2" 2068635 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-896 2068094 2068134 2068201 "PARSER" 2068283 T PARSER (NIL) -7 NIL NIL NIL) (-895 2067715 2067778 2067880 "PARSCURV" 2068025 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-894 2067347 2067404 2067513 "PARSC2" 2067652 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-893 2066986 2067044 2067141 "PARPCURV" 2067283 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-892 2066618 2066675 2066784 "PARPC2" 2066923 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-891 2065679 2065991 2066173 "PARAMAST" 2066456 T PARAMAST (NIL) -8 NIL NIL NIL) (-890 2065199 2065285 2065404 "PAN2EXPR" 2065580 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-889 2063976 2064320 2064548 "PALETTE" 2064991 T PALETTE (NIL) -8 NIL NIL NIL) (-888 2062369 2062981 2063341 "PAIR" 2063662 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-887 2055961 2061626 2061821 "PADICRC" 2062223 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-886 2048877 2055305 2055490 "PADICRAT" 2055808 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-885 2047192 2048814 2048859 "PADIC" 2048864 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-884 2044288 2045852 2045892 "PADICCT" 2046473 NIL PADICCT (NIL NIL) -9 NIL 2046755 NIL) (-883 2043245 2043445 2043713 "PADEPAC" 2044075 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-882 2042457 2042590 2042796 "PADE" 2043107 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-881 2040844 2041665 2041945 "OWP" 2042261 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-880 2040337 2040550 2040647 "OVERSET" 2040767 T OVERSET (NIL) -8 NIL NIL NIL) (-879 2039383 2039942 2040114 "OVAR" 2040205 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-878 2038647 2038768 2038929 "OUT" 2039242 T OUT (NIL) -7 NIL NIL NIL) (-877 2027519 2029756 2031956 "OUTFORM" 2036467 T OUTFORM (NIL) -8 NIL NIL NIL) (-876 2026855 2027116 2027243 "OUTBFILE" 2027412 T OUTBFILE (NIL) -8 NIL NIL NIL) (-875 2026162 2026327 2026355 "OUTBCON" 2026673 T OUTBCON (NIL) -9 NIL 2026839 NIL) (-874 2025763 2025875 2026032 "OUTBCON-" 2026037 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-873 2025143 2025492 2025581 "OSI" 2025694 T OSI (NIL) -8 NIL NIL NIL) (-872 2024646 2024984 2025012 "OSGROUP" 2025017 T OSGROUP (NIL) -9 NIL 2025039 NIL) (-871 2023391 2023618 2023903 "ORTHPOL" 2024393 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-870 2020942 2023226 2023347 "OREUP" 2023352 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-869 2018345 2020633 2020760 "ORESUP" 2020884 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-868 2015873 2016373 2016934 "OREPCTO" 2017834 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-867 2009545 2011746 2011787 "OREPCAT" 2014135 NIL OREPCAT (NIL T) -9 NIL 2015239 NIL) (-866 2006692 2007474 2008532 "OREPCAT-" 2008537 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-865 2005939 2006162 2006190 "ORDTYPE" 2006499 T ORDTYPE (NIL) -9 NIL 2006662 NIL) (-864 2005282 2005456 2005711 "ORDTYPE-" 2005716 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-863 2004708 2005021 2005179 "ORDSTRCT" 2005184 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-862 2004278 2004576 2004604 "ORDSET" 2004609 T ORDSET (NIL) -9 NIL 2004631 NIL) (-861 2002816 2003607 2003635 "ORDRING" 2003837 T ORDRING (NIL) -9 NIL 2003962 NIL) (-860 2002461 2002555 2002699 "ORDRING-" 2002704 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-859 2001814 2002277 2002305 "ORDMON" 2002310 T ORDMON (NIL) -9 NIL 2002331 NIL) (-858 2000976 2001123 2001318 "ORDFUNS" 2001663 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-857 2000287 2000706 2000734 "ORDFIN" 2000799 T ORDFIN (NIL) -9 NIL 2000873 NIL) (-856 1996846 1998873 1999282 "ORDCOMP" 1999911 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-855 1996112 1996239 1996425 "ORDCOMP2" 1996706 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-854 1992693 1993603 1994417 "OPTPROB" 1995318 T OPTPROB (NIL) -8 NIL NIL NIL) (-853 1989495 1990134 1990838 "OPTPACK" 1992009 T OPTPACK (NIL) -7 NIL NIL NIL) (-852 1987168 1987934 1987962 "OPTCAT" 1988781 T OPTCAT (NIL) -9 NIL 1989431 NIL) (-851 1986552 1986845 1986950 "OPSIG" 1987083 T OPSIG (NIL) -8 NIL NIL NIL) (-850 1986320 1986359 1986425 "OPQUERY" 1986506 T OPQUERY (NIL) -7 NIL NIL NIL) (-849 1983451 1984631 1985135 "OP" 1985849 NIL OP (NIL T) -8 NIL NIL NIL) (-848 1982811 1983037 1983078 "OPERCAT" 1983290 NIL OPERCAT (NIL T) -9 NIL 1983387 NIL) (-847 1982566 1982622 1982739 "OPERCAT-" 1982744 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-846 1979379 1981363 1981732 "ONECOMP" 1982230 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-845 1978684 1978799 1978973 "ONECOMP2" 1979251 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-844 1978103 1978209 1978339 "OMSERVER" 1978574 T OMSERVER (NIL) -7 NIL NIL NIL) (-843 1974965 1977543 1977583 "OMSAGG" 1977644 NIL OMSAGG (NIL T) -9 NIL 1977708 NIL) (-842 1973588 1973851 1974133 "OMPKG" 1974703 T OMPKG (NIL) -7 NIL NIL NIL) (-841 1973018 1973121 1973149 "OM" 1973448 T OM (NIL) -9 NIL NIL NIL) (-840 1971565 1972567 1972736 "OMLO" 1972899 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-839 1970525 1970672 1970892 "OMEXPR" 1971391 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-838 1969816 1970071 1970207 "OMERR" 1970409 T OMERR (NIL) -8 NIL NIL NIL) (-837 1968967 1969237 1969397 "OMERRK" 1969676 T OMERRK (NIL) -8 NIL NIL NIL) (-836 1968418 1968644 1968752 "OMENC" 1968879 T OMENC (NIL) -8 NIL NIL NIL) (-835 1962313 1963498 1964669 "OMDEV" 1967267 T OMDEV (NIL) -8 NIL NIL NIL) (-834 1961382 1961553 1961747 "OMCONN" 1962139 T OMCONN (NIL) -8 NIL NIL NIL) (-833 1959876 1960852 1960880 "OINTDOM" 1960885 T OINTDOM (NIL) -9 NIL 1960906 NIL) (-832 1957214 1958564 1958901 "OFMONOID" 1959571 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-831 1956586 1957151 1957196 "ODVAR" 1957201 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-830 1954009 1956331 1956486 "ODR" 1956491 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-829 1946314 1953785 1953911 "ODPOL" 1953916 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-828 1940113 1946186 1946291 "ODP" 1946296 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-827 1938879 1939094 1939369 "ODETOOLS" 1939887 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-826 1935846 1936504 1937220 "ODESYS" 1938212 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-825 1930728 1931636 1932661 "ODERTRIC" 1934921 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-824 1930154 1930236 1930430 "ODERED" 1930640 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-823 1927042 1927590 1928267 "ODERAT" 1929577 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-822 1924001 1924466 1925063 "ODEPRRIC" 1926571 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-821 1921944 1922540 1923026 "ODEPROB" 1923535 T ODEPROB (NIL) -8 NIL NIL NIL) (-820 1918464 1918949 1919596 "ODEPRIM" 1921423 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-819 1917713 1917815 1918075 "ODEPAL" 1918356 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-818 1913875 1914666 1915530 "ODEPACK" 1916869 T ODEPACK (NIL) -7 NIL NIL NIL) (-817 1912936 1913043 1913265 "ODEINT" 1913764 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-816 1907037 1908462 1909909 "ODEIFTBL" 1911509 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-815 1902435 1903221 1904173 "ODEEF" 1906196 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-814 1901784 1901873 1902096 "ODECONST" 1902340 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-813 1899895 1900556 1900584 "ODECAT" 1901189 T ODECAT (NIL) -9 NIL 1901720 NIL) (-812 1896750 1899600 1899722 "OCT" 1899805 NIL OCT (NIL T) -8 NIL NIL NIL) (-811 1896388 1896431 1896558 "OCTCT2" 1896701 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-810 1890995 1893431 1893471 "OC" 1894568 NIL OC (NIL T) -9 NIL 1895426 NIL) (-809 1888222 1888970 1889960 "OC-" 1890054 NIL OC- (NIL T T) -8 NIL NIL NIL) (-808 1887547 1888015 1888043 "OCAMON" 1888048 T OCAMON (NIL) -9 NIL 1888069 NIL) (-807 1887051 1887392 1887420 "OASGP" 1887425 T OASGP (NIL) -9 NIL 1887445 NIL) (-806 1886285 1886774 1886802 "OAMONS" 1886842 T OAMONS (NIL) -9 NIL 1886885 NIL) (-805 1885672 1886105 1886133 "OAMON" 1886138 T OAMON (NIL) -9 NIL 1886158 NIL) (-804 1884903 1885421 1885449 "OAGROUP" 1885454 T OAGROUP (NIL) -9 NIL 1885474 NIL) (-803 1884593 1884643 1884731 "NUMTUBE" 1884847 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-802 1878166 1879684 1881220 "NUMQUAD" 1883077 T NUMQUAD (NIL) -7 NIL NIL NIL) (-801 1873922 1874910 1875935 "NUMODE" 1877161 T NUMODE (NIL) -7 NIL NIL NIL) (-800 1871263 1872143 1872171 "NUMINT" 1873094 T NUMINT (NIL) -9 NIL 1873858 NIL) (-799 1870211 1870408 1870626 "NUMFMT" 1871065 T NUMFMT (NIL) -7 NIL NIL NIL) (-798 1856570 1859515 1862047 "NUMERIC" 1867718 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-797 1850940 1856019 1856114 "NTSCAT" 1856119 NIL NTSCAT (NIL T T T T) -9 NIL 1856158 NIL) (-796 1850134 1850299 1850492 "NTPOLFN" 1850779 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-795 1837935 1846959 1847771 "NSUP" 1849355 NIL NSUP (NIL T) -8 NIL NIL NIL) (-794 1837567 1837624 1837733 "NSUP2" 1837872 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-793 1827517 1837341 1837474 "NSMP" 1837479 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-792 1825949 1826250 1826607 "NREP" 1827205 NIL NREP (NIL T) -7 NIL NIL NIL) (-791 1824540 1824792 1825150 "NPCOEF" 1825692 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-790 1823606 1823721 1823937 "NORMRETR" 1824421 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-789 1821647 1821937 1822346 "NORMPK" 1823314 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-788 1821332 1821360 1821484 "NORMMA" 1821613 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-787 1821132 1821289 1821318 "NONE" 1821323 T NONE (NIL) -8 NIL NIL NIL) (-786 1820921 1820950 1821019 "NONE1" 1821096 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-785 1820418 1820480 1820659 "NODE1" 1820853 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-784 1818699 1819550 1819805 "NNI" 1820152 T NNI (NIL) -8 NIL NIL 1820387) (-783 1817119 1817432 1817796 "NLINSOL" 1818367 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-782 1813360 1814355 1815254 "NIPROB" 1816240 T NIPROB (NIL) -8 NIL NIL NIL) (-781 1812117 1812351 1812653 "NFINTBAS" 1813122 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-780 1811291 1811767 1811808 "NETCLT" 1811980 NIL NETCLT (NIL T) -9 NIL 1812062 NIL) (-779 1809999 1810230 1810511 "NCODIV" 1811059 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-778 1809761 1809798 1809873 "NCNTFRAC" 1809956 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-777 1807941 1808305 1808725 "NCEP" 1809386 NIL NCEP (NIL T) -7 NIL NIL NIL) (-776 1806778 1807551 1807579 "NASRING" 1807689 T NASRING (NIL) -9 NIL 1807769 NIL) (-775 1806573 1806617 1806711 "NASRING-" 1806716 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-774 1805666 1806191 1806219 "NARNG" 1806336 T NARNG (NIL) -9 NIL 1806427 NIL) (-773 1805358 1805425 1805559 "NARNG-" 1805564 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-772 1804237 1804444 1804679 "NAGSP" 1805143 T NAGSP (NIL) -7 NIL NIL NIL) (-771 1795509 1797193 1798866 "NAGS" 1802584 T NAGS (NIL) -7 NIL NIL NIL) (-770 1794057 1794365 1794696 "NAGF07" 1795198 T NAGF07 (NIL) -7 NIL NIL NIL) (-769 1788595 1789886 1791193 "NAGF04" 1792770 T NAGF04 (NIL) -7 NIL NIL NIL) (-768 1781563 1783177 1784810 "NAGF02" 1786982 T NAGF02 (NIL) -7 NIL NIL NIL) (-767 1776787 1777887 1779004 "NAGF01" 1780466 T NAGF01 (NIL) -7 NIL NIL NIL) (-766 1770415 1771981 1773566 "NAGE04" 1775222 T NAGE04 (NIL) -7 NIL NIL NIL) (-765 1761584 1763705 1765835 "NAGE02" 1768305 T NAGE02 (NIL) -7 NIL NIL NIL) (-764 1757537 1758484 1759448 "NAGE01" 1760640 T NAGE01 (NIL) -7 NIL NIL NIL) (-763 1755332 1755866 1756424 "NAGD03" 1756999 T NAGD03 (NIL) -7 NIL NIL NIL) (-762 1747082 1749010 1750964 "NAGD02" 1753398 T NAGD02 (NIL) -7 NIL NIL NIL) (-761 1740893 1742318 1743758 "NAGD01" 1745662 T NAGD01 (NIL) -7 NIL NIL NIL) (-760 1737102 1737924 1738761 "NAGC06" 1740076 T NAGC06 (NIL) -7 NIL NIL NIL) (-759 1735567 1735899 1736255 "NAGC05" 1736766 T NAGC05 (NIL) -7 NIL NIL NIL) (-758 1734943 1735062 1735206 "NAGC02" 1735443 T NAGC02 (NIL) -7 NIL NIL NIL) (-757 1733888 1734471 1734511 "NAALG" 1734590 NIL NAALG (NIL T) -9 NIL 1734651 NIL) (-756 1733723 1733752 1733842 "NAALG-" 1733847 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-755 1727673 1728781 1729968 "MULTSQFR" 1732619 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-754 1726992 1727067 1727251 "MULTFACT" 1727585 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-753 1719663 1723577 1723630 "MTSCAT" 1724700 NIL MTSCAT (NIL T T) -9 NIL 1725215 NIL) (-752 1719375 1719429 1719521 "MTHING" 1719603 NIL MTHING (NIL T) -7 NIL NIL NIL) (-751 1719167 1719200 1719260 "MSYSCMD" 1719335 T MSYSCMD (NIL) -7 NIL NIL NIL) (-750 1715249 1717922 1718242 "MSET" 1718880 NIL MSET (NIL T) -8 NIL NIL NIL) (-749 1712318 1714810 1714851 "MSETAGG" 1714856 NIL MSETAGG (NIL T) -9 NIL 1714890 NIL) (-748 1708160 1709697 1710442 "MRING" 1711618 NIL MRING (NIL T T) -8 NIL NIL NIL) (-747 1707726 1707793 1707924 "MRF2" 1708087 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-746 1707344 1707379 1707523 "MRATFAC" 1707685 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-745 1704956 1705251 1705682 "MPRFF" 1707049 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-744 1698977 1704810 1704907 "MPOLY" 1704912 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-743 1698467 1698502 1698710 "MPCPF" 1698936 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-742 1697981 1698024 1698208 "MPC3" 1698418 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-741 1697176 1697257 1697478 "MPC2" 1697896 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695477 1695814 1696204 "MONOTOOL" 1696836 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-739 1694688 1695005 1695033 "MONOID" 1695252 T MONOID (NIL) -9 NIL 1695399 NIL) (-738 1694234 1694353 1694534 "MONOID-" 1694539 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-737 1683824 1690054 1690113 "MONOGEN" 1690787 NIL MONOGEN (NIL T T) -9 NIL 1691243 NIL) (-736 1681042 1681777 1682777 "MONOGEN-" 1682896 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-735 1679861 1680307 1680335 "MONADWU" 1680727 T MONADWU (NIL) -9 NIL 1680965 NIL) (-734 1679233 1679392 1679640 "MONADWU-" 1679645 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-733 1678578 1678822 1678850 "MONAD" 1679057 T MONAD (NIL) -9 NIL 1679169 NIL) (-732 1678263 1678341 1678473 "MONAD-" 1678478 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-731 1676552 1677176 1677455 "MOEBIUS" 1678016 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-730 1675816 1676220 1676260 "MODULE" 1676265 NIL MODULE (NIL T) -9 NIL 1676304 NIL) (-729 1675384 1675480 1675670 "MODULE-" 1675675 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-728 1673064 1673748 1674075 "MODRING" 1675208 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-727 1670008 1671169 1671690 "MODOP" 1672593 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-726 1668596 1669075 1669352 "MODMONOM" 1669871 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-725 1658364 1666887 1667301 "MODMON" 1668233 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-724 1655520 1657208 1657484 "MODFIELD" 1658239 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-723 1654497 1654801 1654991 "MMLFORM" 1655350 T MMLFORM (NIL) -8 NIL NIL NIL) (-722 1654023 1654066 1654245 "MMAP" 1654448 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-721 1652088 1652855 1652896 "MLO" 1653319 NIL MLO (NIL T) -9 NIL 1653561 NIL) (-720 1649454 1649970 1650572 "MLIFT" 1651569 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-719 1648845 1648929 1649083 "MKUCFUNC" 1649365 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-718 1648444 1648514 1648637 "MKRECORD" 1648768 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-717 1647491 1647653 1647881 "MKFUNC" 1648255 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-716 1646879 1646983 1647139 "MKFLCFN" 1647374 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-715 1646156 1646258 1646443 "MKBCFUNC" 1646772 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-714 1642745 1645710 1645846 "MINT" 1646040 T MINT (NIL) -8 NIL NIL NIL) (-713 1641557 1641800 1642077 "MHROWRED" 1642500 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-712 1636937 1640092 1640497 "MFLOAT" 1641172 T MFLOAT (NIL) -8 NIL NIL NIL) (-711 1636294 1636370 1636541 "MFINFACT" 1636849 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-710 1632609 1633457 1634341 "MESH" 1635430 T MESH (NIL) -7 NIL NIL NIL) (-709 1630999 1631311 1631664 "MDDFACT" 1632296 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-708 1627769 1630130 1630171 "MDAGG" 1630426 NIL MDAGG (NIL T) -9 NIL 1630569 NIL) (-707 1616463 1627062 1627269 "MCMPLX" 1627582 T MCMPLX (NIL) -8 NIL NIL NIL) (-706 1615600 1615746 1615947 "MCDEN" 1616312 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-705 1613490 1613760 1614140 "MCALCFN" 1615330 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-704 1612415 1612655 1612888 "MAYBE" 1613296 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-703 1610027 1610550 1611112 "MATSTOR" 1611886 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-702 1605939 1609399 1609647 "MATRIX" 1609812 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-701 1601705 1602412 1603148 "MATLIN" 1605296 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-700 1591531 1594762 1594839 "MATCAT" 1599871 NIL MATCAT (NIL T T T) -9 NIL 1601343 NIL) (-699 1587724 1588794 1590207 "MATCAT-" 1590212 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-698 1586318 1586471 1586804 "MATCAT2" 1587559 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-697 1584430 1584754 1585138 "MAPPKG3" 1585993 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-696 1583411 1583584 1583806 "MAPPKG2" 1584254 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-695 1581910 1582194 1582521 "MAPPKG1" 1583117 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-694 1580989 1581316 1581493 "MAPPAST" 1581753 T MAPPAST (NIL) -8 NIL NIL NIL) (-693 1580600 1580658 1580781 "MAPHACK3" 1580925 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-692 1580192 1580253 1580367 "MAPHACK2" 1580532 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-691 1579630 1579733 1579875 "MAPHACK1" 1580083 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-690 1577709 1578330 1578634 "MAGMA" 1579358 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-689 1577188 1577433 1577524 "MACROAST" 1577638 T MACROAST (NIL) -8 NIL NIL NIL) (-688 1573609 1575427 1575888 "M3D" 1576760 NIL M3D (NIL T) -8 NIL NIL NIL) (-687 1567659 1571920 1571961 "LZSTAGG" 1572743 NIL LZSTAGG (NIL T) -9 NIL 1573038 NIL) (-686 1563617 1564790 1566247 "LZSTAGG-" 1566252 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-685 1560704 1561508 1561995 "LWORD" 1563162 NIL LWORD (NIL T) -8 NIL NIL NIL) (-684 1560280 1560508 1560583 "LSTAST" 1560649 T LSTAST (NIL) -8 NIL NIL NIL) (-683 1553170 1560051 1560185 "LSQM" 1560190 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-682 1552394 1552533 1552761 "LSPP" 1553025 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-681 1550206 1550507 1550963 "LSMP" 1552083 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-680 1546985 1547659 1548389 "LSMP1" 1549508 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-679 1540787 1546075 1546116 "LSAGG" 1546178 NIL LSAGG (NIL T) -9 NIL 1546256 NIL) (-678 1537482 1538406 1539619 "LSAGG-" 1539624 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-677 1535081 1536626 1536875 "LPOLY" 1537277 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-676 1534663 1534748 1534871 "LPEFRAC" 1534990 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-675 1532984 1533757 1534010 "LO" 1534495 NIL LO (NIL T T T) -8 NIL NIL NIL) (-674 1532596 1532734 1532762 "LOGIC" 1532873 T LOGIC (NIL) -9 NIL 1532954 NIL) (-673 1532458 1532481 1532552 "LOGIC-" 1532557 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-672 1531651 1531791 1531984 "LODOOPS" 1532314 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-671 1529074 1531567 1531633 "LODO" 1531638 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-670 1527612 1527847 1528200 "LODOF" 1528821 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-669 1523816 1526247 1526288 "LODOCAT" 1526726 NIL LODOCAT (NIL T) -9 NIL 1526937 NIL) (-668 1523549 1523607 1523734 "LODOCAT-" 1523739 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-667 1520869 1523390 1523508 "LODO2" 1523513 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-666 1518304 1520806 1520851 "LODO1" 1520856 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-665 1517185 1517350 1517655 "LODEEF" 1518127 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-664 1512463 1515351 1515392 "LNAGG" 1516254 NIL LNAGG (NIL T) -9 NIL 1516689 NIL) (-663 1511610 1511824 1512166 "LNAGG-" 1512171 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-662 1507746 1508535 1509174 "LMOPS" 1511025 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-661 1507135 1507523 1507564 "LMODULE" 1507569 NIL LMODULE (NIL T) -9 NIL 1507595 NIL) (-660 1504336 1506780 1506903 "LMDICT" 1507045 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-659 1503954 1504126 1504167 "LLINSET" 1504228 NIL LLINSET (NIL T) -9 NIL 1504272 NIL) (-658 1503653 1503862 1503922 "LITERAL" 1503927 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-657 1496819 1502587 1502891 "LIST" 1503382 NIL LIST (NIL T) -8 NIL NIL NIL) (-656 1496344 1496418 1496557 "LIST3" 1496739 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-655 1495351 1495529 1495757 "LIST2" 1496162 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-654 1493485 1493797 1494196 "LIST2MAP" 1494998 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-653 1493116 1493304 1493345 "LINSET" 1493350 NIL LINSET (NIL T) -9 NIL 1493384 NIL) (-652 1491529 1492143 1492184 "LINEXP" 1492674 NIL LINEXP (NIL T) -9 NIL 1492947 NIL) (-651 1490421 1490991 1491167 "LINELT" 1491405 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-650 1488998 1489258 1489569 "LINDEP" 1490173 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485765 1486484 1487261 "LIMITRF" 1488253 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1484068 1484364 1484773 "LIMITPS" 1485460 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478496 1483579 1483807 "LIE" 1483889 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477430 1477899 1477939 "LIECAT" 1478079 NIL LIECAT (NIL T) -9 NIL 1478230 NIL) (-645 1477271 1477298 1477386 "LIECAT-" 1477391 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469864 1476811 1476967 "LIB" 1477135 T LIB (NIL) -8 NIL NIL NIL) (-643 1465499 1466382 1467317 "LGROBP" 1468981 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463497 1463771 1464121 "LF" 1465220 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462337 1463029 1463057 "LFCAT" 1463264 T LFCAT (NIL) -9 NIL 1463403 NIL) (-640 1459239 1459869 1460557 "LEXTRIPK" 1461701 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455983 1456809 1457312 "LEXP" 1458819 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455459 1455704 1455796 "LETAST" 1455911 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453857 1454170 1454571 "LEADCDET" 1455141 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1453047 1453121 1453350 "LAZM3PK" 1453778 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447964 1451124 1451662 "LAUPOL" 1452559 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447543 1447587 1447748 "LAPLACE" 1447914 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445482 1446644 1446895 "LA" 1447376 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444462 1445046 1445087 "LALG" 1445149 NIL LALG (NIL T) -9 NIL 1445208 NIL) (-631 1444176 1444235 1444371 "LALG-" 1444376 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1444011 1444035 1444076 "KVTFROM" 1444138 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442934 1443378 1443563 "KTVLOGIC" 1443846 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442769 1442793 1442834 "KRCFROM" 1442896 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441673 1441860 1442159 "KOVACIC" 1442569 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441508 1441532 1441573 "KONVERT" 1441635 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441343 1441367 1441408 "KOERCE" 1441470 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1439174 1439936 1440313 "KERNEL" 1440999 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438670 1438751 1438883 "KERNEL2" 1439088 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432381 1437147 1437201 "KDAGG" 1437578 NIL KDAGG (NIL T T) -9 NIL 1437784 NIL) (-621 1431910 1432034 1432239 "KDAGG-" 1432244 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1425058 1431571 1431726 "KAFILE" 1431788 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419486 1424569 1424797 "JORDAN" 1424879 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418865 1419135 1419256 "JOINAST" 1419385 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418711 1418770 1418825 "JAVACODE" 1418830 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414938 1416888 1416942 "IXAGG" 1417871 NIL IXAGG (NIL T T) -9 NIL 1418330 NIL) (-615 1413857 1414163 1414582 "IXAGG-" 1414587 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409390 1413779 1413838 "IVECTOR" 1413843 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1408156 1408393 1408659 "ITUPLE" 1409157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406658 1406835 1407130 "ITRIGMNP" 1407978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405403 1405607 1405890 "ITFUN3" 1406434 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1405035 1405092 1405201 "ITFUN2" 1405340 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1404194 1404515 1404689 "ITFORM" 1404881 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1402155 1403214 1403492 "ITAYLOR" 1403949 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1391100 1396292 1397455 "ISUPS" 1401025 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1390204 1390344 1390580 "ISUMP" 1390947 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385582 1390149 1390190 "ISTRING" 1390195 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1385058 1385303 1385395 "ISAST" 1385510 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384267 1384349 1384565 "IRURPK" 1384972 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1383203 1383404 1383644 "IRSN" 1384047 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381274 1381629 1382058 "IRRF2F" 1382841 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1381021 1381059 1381135 "IRREDFFX" 1381230 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379636 1379895 1380194 "IROOT" 1380754 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376240 1377320 1378012 "IR" 1378976 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375445 1375733 1375884 "IRFORM" 1376109 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1373058 1373553 1374119 "IR2" 1374923 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1372158 1372271 1372485 "IR2F" 1372941 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371949 1371983 1372043 "IPRNTPK" 1372118 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368530 1371838 1371907 "IPF" 1371912 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366857 1368455 1368512 "IPADIC" 1368517 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1366169 1366417 1366547 "IP4ADDR" 1366747 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365543 1365798 1365930 "IOMODE" 1366057 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364616 1365140 1365267 "IOBFILE" 1365436 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1364104 1364520 1364548 "IOBCON" 1364553 T IOBCON (NIL) -9 NIL 1364574 NIL) (-587 1363615 1363673 1363856 "INVLAPLA" 1364040 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353263 1355617 1358003 "INTTR" 1361279 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349598 1350340 1351205 "INTTOOLS" 1352448 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1349184 1349275 1349392 "INTSLPE" 1349501 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1347137 1349107 1349166 "INTRVL" 1349171 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344739 1345251 1345826 "INTRF" 1346622 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1344150 1344247 1344389 "INTRET" 1344637 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1342147 1342536 1343006 "INTRAT" 1343758 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339410 1339993 1340612 "INTPM" 1341632 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1336155 1336754 1337492 "INTPAF" 1338796 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331334 1332296 1333347 "INTPACK" 1335124 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1328146 1331131 1331240 "INT" 1331245 T INT (NIL) -8 NIL NIL NIL) (-575 1327398 1327550 1327758 "INTHERTR" 1327988 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326837 1326917 1327105 "INTHERAL" 1327312 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324683 1325126 1325583 "INTHEORY" 1326400 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1316089 1317710 1319482 "INTG0" 1323035 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296662 1301452 1306262 "INTFTBL" 1311299 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295911 1296049 1296222 "INTFACT" 1296521 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293338 1293784 1294341 "INTEF" 1295465 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291691 1292430 1292458 "INTDOM" 1292759 T INTDOM (NIL) -9 NIL 1292966 NIL) (-567 1291060 1291234 1291476 "INTDOM-" 1291481 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287420 1289349 1289403 "INTCAT" 1290202 NIL INTCAT (NIL T) -9 NIL 1290523 NIL) (-565 1286892 1286995 1287123 "INTBIT" 1287312 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285591 1285745 1286052 "INTALG" 1286737 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1285074 1285164 1285321 "INTAF" 1285495 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278423 1284884 1285024 "INTABL" 1285029 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277756 1278222 1278287 "INT8" 1278321 T INT8 (NIL) -8 NIL NIL 1278366) (-560 1277088 1277554 1277619 "INT64" 1277653 T INT64 (NIL) -8 NIL NIL 1277698) (-559 1276420 1276886 1276951 "INT32" 1276985 T INT32 (NIL) -8 NIL NIL 1277030) (-558 1275752 1276218 1276283 "INT16" 1276317 T INT16 (NIL) -8 NIL NIL 1276362) (-557 1270447 1273300 1273328 "INS" 1274262 T INS (NIL) -9 NIL 1274927 NIL) (-556 1267687 1268458 1269432 "INS-" 1269505 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266462 1266689 1266987 "INPSIGN" 1267440 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265580 1265697 1265894 "INPRODPF" 1266342 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264474 1264591 1264828 "INPRODFF" 1265460 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263474 1263626 1263886 "INNMFACT" 1264310 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262671 1262768 1262956 "INMODGCD" 1263373 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1261179 1261424 1261748 "INFSP" 1262416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260363 1260480 1260663 "INFPROD0" 1261059 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257218 1258428 1258943 "INFORM" 1259856 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256828 1256888 1256986 "INFORM1" 1257153 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256351 1256440 1256554 "INFINITY" 1256734 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255527 1256071 1256172 "INETCLTS" 1256270 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1254143 1254393 1254714 "INEP" 1255275 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253348 1254040 1254105 "INDE" 1254110 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252912 1252980 1253097 "INCRMAPS" 1253275 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251730 1252181 1252387 "INBFILE" 1252726 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1247029 1247966 1248910 "INBFF" 1250818 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245937 1246206 1246234 "INBCON" 1246747 T INBCON (NIL) -9 NIL 1247013 NIL) (-538 1245189 1245412 1245688 "INBCON-" 1245693 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244668 1244913 1245004 "INAST" 1245118 T INAST (NIL) -8 NIL NIL NIL) (-536 1244095 1244347 1244453 "IMPTAST" 1244582 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240496 1243939 1244043 "IMATRIX" 1244048 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1239204 1239327 1239643 "IMATQF" 1240352 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237424 1237651 1237988 "IMATLIN" 1238960 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1232005 1237348 1237406 "ILIST" 1237411 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229913 1231865 1231978 "IIARRAY2" 1231983 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225311 1229824 1229888 "IFF" 1229893 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224658 1224928 1225044 "IFAST" 1225215 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219656 1223950 1224138 "IFARRAY" 1224515 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218836 1219560 1219633 "IFAMON" 1219638 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218420 1218485 1218539 "IEVALAB" 1218746 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1218095 1218163 1218323 "IEVALAB-" 1218328 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217542 1218010 1218072 "IDPO" 1218077 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216750 1217431 1217506 "IDPOAMS" 1217511 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1216015 1216639 1216714 "IDPOAM" 1216719 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214561 1215022 1215074 "IDPC" 1215586 NIL IDPC (NIL T T) -9 NIL 1215867 NIL) (-520 1213989 1214453 1214526 "IDPAM" 1214531 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213881 1213954 "IDPAG" 1213959 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2118 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL 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T) ((-629 $) -2839 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-626 (-880)) . T) ((-174) -2839 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-627 (-228)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-627 (-549)) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-549)))) ((-627 (-911 (-391))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-391))))) ((-627 (-911 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-627 (-911 (-577))))) ((-235 $) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-233 |#2|) |has| |#1| (-375)) ((-239) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-238) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-273 |#2|) |has| |#1| (-375)) ((-249) |has| |#1| (-375)) ((-295) |has| |#1| (-38 (-420 (-577)))) ((-297 #0# |#1|) . T) ((-297 |#2| $) -12 (|has| |#1| (-375)) (|has| |#2| (-297 |#2| |#2|))) ((-297 $ $) |has| (-577) (-1137)) ((-301) -2839 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-320 |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-375) |has| |#1| (-375)) ((-350 |#2|) |has| |#1| (-375)) ((-389 |#2|) |has| |#1| (-375)) ((-413 |#2|) |has| |#1| (-375)) ((-465) |has| |#1| (-375)) ((-506) |has| |#1| (-38 (-420 (-577)))) ((-527 (-1201) |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-527 (-1201) |#2|))) ((-527 |#2| |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-569) -2839 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-662 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 |#2|) |has| |#1| (-375)) ((-662 $) . T) ((-664 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-664 #3=(-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-664 |#1|) . T) ((-664 |#2|) |has| |#1| (-375)) ((-664 $) . T) ((-656 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-656 |#1|) |has| |#1| (-174)) ((-656 |#2|) |has| |#1| (-375)) ((-656 $) -2839 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-654 #3#) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-654 |#2|) |has| |#1| (-375)) ((-733 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-733 |#1|) |has| |#1| (-174)) ((-733 |#2|) |has| |#1| (-375)) ((-733 $) -2839 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-742) . T) ((-807) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-808) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-810) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-811) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-836) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-864) -12 (|has| |#1| (-375)) (|has| |#2| (-836))) ((-865) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-865))) (-12 (|has| |#1| (-375)) (|has| |#2| (-836)))) ((-868) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-865))) (-12 (|has| |#1| (-375)) (|has| |#2| (-836)))) ((-915 $ #4=(-1201)) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-923 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-921 (-1201)) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-923 #4#) -2839 (-12 (|has| |#1| (-375)) (|has| |#2| (-923 (-1201)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-921 (-1201)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-921 (-1201))))) ((-905 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-391)))) ((-905 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-905 (-577)))) ((-903 |#2|) |has| |#1| (-375)) ((-932) -12 (|has| |#1| (-375)) (|has| |#2| (-932))) ((-998 |#1| #0# (-1107)) . T) ((-943) |has| |#1| (-375)) ((-1017 |#2|) |has| |#1| (-375)) ((-1027) |has| |#1| (-38 (-420 (-577)))) ((-1047) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-1063 (-420 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 #2#) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-1201)))) ((-1063 |#2|) . T) ((-1076 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1076 |#1|) . T) ((-1076 |#2|) |has| |#1| (-375)) ((-1076 $) -2839 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1081 #1#) -2839 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-375)) ((-1081 $) -2839 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) -12 (|has| |#1| (-375)) (|has| |#2| (-1177))) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . 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+((-2058 (((-660 (-1107)) $) 34)) (-2248 (($ $) 31)) (-2030 (($ |#2| |#3|) NIL) (($ $ (-1107) |#3|) 28) (($ $ (-660 (-1107)) (-660 |#3|)) 27)) (-2209 (($ $) 14)) (-2221 ((|#2| $) 12)) (-2887 ((|#3| $) 10))) 
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+NIL 
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(($ (-944) $) NIL) (($ (-787) $) NIL) (($ (-577) $) NIL) (($ $ $) NIL) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (-420 (-577)) $) NIL (|has| |#1| (-38 (-420 (-577))))) (($ $ (-420 (-577))) NIL (|has| |#1| (-38 (-420 (-577))))))) 
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+((-3921 (*1 *2 *1) (|partial| -12 (-4 *3 (-13 (-1063 (-577)) (-654 (-577)) (-465))) (-5 *2 (-859 *4)) (-5 *1 (-1278 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1227) (-443 *3))) (-14 *5 (-1201)) (-14 *6 *4))) (-3910 (*1 *2 *1) (|partial| -12 (-4 *3 (-13 (-1063 (-577)) (-654 (-577)) (-465))) (-5 *2 (-2 (|:| |%term| (-2 (|:| |%coef| (-1277 *4 *5 *6)) (|:| |%expon| (-330 *4 *5 *6)) (|:| |%expTerms| (-660 (-2 (|:| |k| (-420 (-577))) (|:| |c| *4)))))) (|:| |%type| (-1183)))) (-5 *1 (-1278 *3 *4 *5 *6)) (-4 *4 (-13 (-27) (-1227) (-443 *3))) (-14 *5 (-1201)) (-14 *6 *4)))) 
+(-13 (-337 (-1277 |#2| |#3| |#4|) (-330 |#2| |#3| |#4|)) (-569) (-10 -8 (-15 -3921 ((-3 (-859 |#2|) "failed") $)) (-15 -3910 ((-3 (-2 (|:| |%term| (-2 (|:| |%coef| (-1277 |#2| |#3| |#4|)) (|:| |%expon| (-330 |#2| |#3| |#4|)) (|:| |%expTerms| (-660 (-2 (|:| |k| (-420 (-577))) (|:| |c| |#2|)))))) (|:| |%type| (-1183))) "failed") $)))) 
+((-3115 ((|#2| $) 34)) (-2950 ((|#2| $) 18)) (-4428 (($ $) 53)) (-3933 (($ $ (-577)) 85)) (-3828 (((-112) $ (-787)) 46)) (-4374 ((|#2| $ |#2|) 82)) (-3945 ((|#2| $ |#2|) 78)) (-3709 ((|#2| $ "value" |#2|) NIL) ((|#2| $ "first" |#2|) 71) (($ $ "rest" $) 75) ((|#2| $ "last" |#2|) 73)) (-4384 (($ $ (-660 $)) 81)) (-2939 ((|#2| $) 17)) (-3563 (($ $) NIL) (($ $ (-787)) 59)) (-4426 (((-660 $) $) 31)) (-4394 (((-112) $ $) 69)) (-1479 (((-112) $ (-787)) 45)) (-1443 (((-112) $ (-787)) 43)) (-3371 (((-112) $) 33)) (-3927 ((|#2| $) 25) (($ $ (-787)) 64)) (-2872 ((|#2| $ "value") NIL) ((|#2| $ "first") 10) (($ $ "rest") 16) ((|#2| $ "last") 13)) (-1885 (((-112) $) 23)) (-4004 (($ $) 56)) (-3981 (($ $) 86)) (-4016 (((-787) $) 58)) (-4026 (($ $) 57)) (-1677 (($ $ $) 77) (($ |#2| $) NIL)) (-3322 (((-660 $) $) 32)) (-2970 (((-112) $ $) 67)) (-3484 (((-787) $) 52))) 
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"WFFINTBS" 3216122 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1300 3213115 3213542 3214004 "WEIER" 3214783 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1299 3212147 3212597 3212639 "VSPACE" 3212775 NIL VSPACE (NIL T) -9 NIL 3212849 NIL) (-1298 3211985 3212012 3212103 "VSPACE-" 3212108 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1297 3211794 3211836 3211904 "VOID" 3211939 T VOID (NIL) -8 NIL NIL NIL) (-1296 3209930 3210289 3210695 "VIEW" 3211410 T VIEW (NIL) -7 NIL NIL NIL) (-1295 3206354 3206993 3207730 "VIEWDEF" 3209215 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1294 3195658 3197902 3200075 "VIEW3D" 3204203 T VIEW3D (NIL) -8 NIL NIL NIL) (-1293 3187909 3189569 3191148 "VIEW2D" 3194101 T VIEW2D (NIL) -8 NIL NIL NIL) (-1292 3183265 3187679 3187771 "VECTOR" 3187852 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1291 3181842 3182101 3182419 "VECTOR2" 3182995 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1290 3175240 3179546 3179589 "VECTCAT" 3180584 NIL VECTCAT (NIL T) -9 NIL 3181171 NIL) (-1289 3174254 3174508 3174898 "VECTCAT-" 3174903 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3173708 3173905 3174025 "VARIABLE" 3174169 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1287 3173641 3173646 3173676 "UTYPE" 3173681 T UTYPE (NIL) -9 NIL NIL NIL) (-1286 3172471 3172625 3172887 "UTSODETL" 3173467 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1285 3169911 3170371 3170895 "UTSODE" 3172012 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1284 3161859 3167672 3168152 "UTS" 3169489 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1283 3152423 3157793 3157836 "UTSCAT" 3158948 NIL UTSCAT (NIL T) -9 NIL 3159706 NIL) (-1282 3149771 3150493 3151482 "UTSCAT-" 3151487 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1281 3149398 3149441 3149574 "UTS2" 3149722 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1280 3143599 3146208 3146251 "URAGG" 3148321 NIL URAGG (NIL T) -9 NIL 3149044 NIL) (-1279 3140538 3141401 3142524 "URAGG-" 3142529 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1278 3136247 3139173 3139638 "UPXSSING" 3140202 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1277 3128423 3135629 3135893 "UPXS" 3136041 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1276 3121496 3128327 3128399 "UPXSCONS" 3128404 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1275 3110903 3117699 3117761 "UPXSCCA" 3118335 NIL UPXSCCA (NIL T T) -9 NIL 3118568 NIL) (-1274 3110541 3110626 3110800 "UPXSCCA-" 3110805 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1273 3099800 3106369 3106412 "UPXSCAT" 3107060 NIL UPXSCAT (NIL T) -9 NIL 3107669 NIL) (-1272 3099230 3099309 3099488 "UPXS2" 3099715 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1271 3097884 3098137 3098488 "UPSQFREE" 3098973 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1270 3091092 3094152 3094207 "UPSCAT" 3095287 NIL UPSCAT (NIL T T) -9 NIL 3096052 NIL) (-1269 3090296 3090503 3090830 "UPSCAT-" 3090835 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1268 3075378 3083423 3083466 "UPOLYC" 3085567 NIL UPOLYC (NIL T) -9 NIL 3086788 NIL) (-1267 3066706 3069132 3072279 "UPOLYC-" 3072284 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1266 3066333 3066376 3066509 "UPOLYC2" 3066657 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3057868 3066016 3066145 "UP" 3066252 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1264 3057207 3057314 3057478 "UPMP" 3057757 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1263 3056760 3056841 3056980 "UPDIVP" 3057120 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1262 3055328 3055577 3055893 "UPDECOMP" 3056509 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1261 3054559 3054671 3054857 "UPCDEN" 3055212 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1260 3054078 3054147 3054296 "UP2" 3054484 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1259 3052545 3053282 3053559 "UNISEG" 3053836 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1258 3051760 3051887 3052092 "UNISEG2" 3052388 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1257 3050820 3051000 3051226 "UNIFACT" 3051576 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1256 3033572 3050132 3050374 "ULS" 3050636 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3021202 3033476 3033548 "ULSCONS" 3033553 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1254 3001923 3014283 3014345 "ULSCCAT" 3014983 NIL ULSCCAT (NIL T T) -9 NIL 3015272 NIL) (-1253 3000973 3001218 3001606 "ULSCCAT-" 3001611 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1252 2990037 2996520 2996563 "ULSCAT" 2997426 NIL ULSCAT (NIL T) -9 NIL 2998157 NIL) (-1251 2989467 2989546 2989725 "ULS2" 2989952 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1250 2988586 2989096 2989203 "UINT8" 2989314 T UINT8 (NIL) -8 NIL NIL 2989399) (-1249 2987704 2988214 2988321 "UINT64" 2988432 T UINT64 (NIL) -8 NIL NIL 2988517) (-1248 2986822 2987332 2987439 "UINT32" 2987550 T UINT32 (NIL) -8 NIL NIL 2987635) (-1247 2985940 2986450 2986557 "UINT16" 2986668 T UINT16 (NIL) -8 NIL NIL 2986753) (-1246 2984229 2985186 2985216 "UFD" 2985428 T UFD (NIL) -9 NIL 2985542 NIL) (-1245 2984023 2984069 2984164 "UFD-" 2984169 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1244 2983105 2983288 2983504 "UDVO" 2983829 T UDVO (NIL) -7 NIL NIL NIL) (-1243 2980921 2981330 2981801 "UDPO" 2982669 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1242 2980854 2980859 2980889 "TYPE" 2980894 T TYPE (NIL) -9 NIL NIL NIL) (-1241 2980614 2980809 2980840 "TYPEAST" 2980845 T TYPEAST (NIL) -8 NIL NIL NIL) (-1240 2979585 2979787 2980027 "TWOFACT" 2980408 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1239 2978608 2978994 2979229 "TUPLE" 2979385 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1238 2976299 2976818 2977357 "TUBETOOL" 2978091 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1237 2975148 2975353 2975594 "TUBE" 2976092 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1236 2969877 2974120 2974403 "TS" 2974900 NIL TS (NIL T) -8 NIL NIL NIL) (-1235 2958515 2962634 2962731 "TSETCAT" 2968000 NIL TSETCAT (NIL T T T T) -9 NIL 2969532 NIL) (-1234 2953247 2954847 2956738 "TSETCAT-" 2956743 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1233 2947886 2948733 2949662 "TRMANIP" 2952383 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1232 2947327 2947390 2947553 "TRIMAT" 2947818 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1231 2945193 2945430 2945787 "TRIGMNIP" 2947076 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1230 2944713 2944826 2944856 "TRIGCAT" 2945069 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1229 2944382 2944461 2944602 "TRIGCAT-" 2944607 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1228 2941230 2943240 2943521 "TREE" 2944136 NIL TREE (NIL T) -8 NIL NIL NIL) (-1227 2940504 2941032 2941062 "TRANFUN" 2941097 T TRANFUN (NIL) -9 NIL 2941163 NIL) (-1226 2939783 2939974 2940254 "TRANFUN-" 2940259 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1225 2939587 2939619 2939680 "TOPSP" 2939744 T TOPSP (NIL) -7 NIL NIL NIL) (-1224 2938935 2939050 2939204 "TOOLSIGN" 2939468 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1223 2937569 2938112 2938351 "TEXTFILE" 2938718 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1222 2935481 2936022 2936451 "TEX" 2937162 T TEX (NIL) -8 NIL NIL NIL) (-1221 2935262 2935293 2935365 "TEX1" 2935444 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1220 2934910 2934973 2935063 "TEMUTL" 2935194 T TEMUTL (NIL) -7 NIL NIL NIL) (-1219 2933064 2933344 2933669 "TBCMPPK" 2934633 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1218 2924773 2931150 2931206 "TBAGG" 2931606 NIL TBAGG (NIL T T) -9 NIL 2931817 NIL) (-1217 2919843 2921331 2923085 "TBAGG-" 2923090 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1216 2919227 2919334 2919479 "TANEXP" 2919732 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1215 2918738 2919002 2919092 "TALGOP" 2919172 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1214 2912134 2918595 2918688 "TABLE" 2918693 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1213 2911546 2911645 2911783 "TABLEAU" 2912031 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1212 2906154 2907374 2908622 "TABLBUMP" 2910332 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1211 2905376 2905523 2905704 "SYSTEM" 2905995 T SYSTEM (NIL) -8 NIL NIL NIL) (-1210 2901835 2902534 2903317 "SYSSOLP" 2904627 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1209 2901633 2901790 2901821 "SYSPTR" 2901826 T SYSPTR (NIL) -8 NIL NIL NIL) (-1208 2900669 2901174 2901293 "SYSNNI" 2901479 NIL SYSNNI (NIL NIL) -8 NIL NIL 2901564) (-1207 2899968 2900427 2900506 "SYSINT" 2900566 NIL SYSINT (NIL NIL) -8 NIL NIL 2900611) (-1206 2896300 2897246 2897956 "SYNTAX" 2899280 T SYNTAX (NIL) -8 NIL NIL NIL) (-1205 2893458 2894060 2894692 "SYMTAB" 2895690 T SYMTAB (NIL) -8 NIL NIL NIL) (-1204 2888707 2889609 2890592 "SYMS" 2892497 T SYMS (NIL) -8 NIL NIL NIL) (-1203 2885942 2888165 2888395 "SYMPOLY" 2888512 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1202 2885459 2885534 2885657 "SYMFUNC" 2885854 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1201 2881479 2882771 2883584 "SYMBOL" 2884668 T SYMBOL (NIL) -8 NIL NIL NIL) (-1200 2875018 2876707 2878427 "SWITCH" 2879781 T SWITCH (NIL) -8 NIL NIL NIL) (-1199 2868362 2873974 2874268 "SUTS" 2874782 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 2860538 2867744 2868008 "SUPXS" 2868156 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 2852021 2860156 2860282 "SUP" 2860447 NIL SUP (NIL T) -8 NIL NIL NIL) (-1196 2851180 2851307 2851524 "SUPFRACF" 2851889 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1195 2850801 2850860 2850973 "SUP2" 2851115 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1194 2849249 2849523 2849879 "SUMRF" 2850500 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1193 2848584 2848650 2848842 "SUMFS" 2849170 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1192 2831371 2847896 2848138 "SULS" 2848400 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2830973 2831193 2831263 "SUCHTAST" 2831323 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1190 2830268 2830498 2830638 "SUCH" 2830881 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1189 2824135 2825174 2826133 "SUBSPACE" 2829356 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1188 2823565 2823655 2823819 "SUBRESP" 2824023 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1187 2816933 2818230 2819541 "STTF" 2822301 NIL STTF (NIL T) -7 NIL NIL NIL) (-1186 2811106 2812226 2813373 "STTFNC" 2815833 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1185 2802419 2804288 2806082 "STTAYLOR" 2809347 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1184 2795555 2802283 2802366 "STRTBL" 2802371 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1183 2790516 2795264 2795363 "STRING" 2795478 T STRING (NIL) -8 NIL NIL NIL) (-1182 2783272 2788135 2788746 "STREAM" 2789940 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1181 2782782 2782859 2783003 "STREAM3" 2783189 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1180 2781764 2781947 2782182 "STREAM2" 2782595 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1179 2781452 2781504 2781597 "STREAM1" 2781706 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1178 2780468 2780649 2780880 "STINPROD" 2781268 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1177 2780006 2780216 2780246 "STEP" 2780326 T STEP (NIL) -9 NIL 2780404 NIL) (-1176 2779193 2779495 2779643 "STEPAST" 2779880 T STEPAST (NIL) -8 NIL NIL NIL) (-1175 2772631 2779092 2779169 "STBL" 2779174 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1174 2767701 2771794 2771837 "STAGG" 2771990 NIL STAGG (NIL T) -9 NIL 2772079 NIL) (-1173 2765403 2766005 2766877 "STAGG-" 2766882 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1172 2763553 2765173 2765265 "STACK" 2765346 NIL STACK (NIL T) -8 NIL NIL NIL) (-1171 2756248 2761694 2762150 "SREGSET" 2763183 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1170 2748673 2750042 2751555 "SRDCMPK" 2754854 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1169 2741510 2746032 2746062 "SRAGG" 2747365 T SRAGG (NIL) -9 NIL 2747973 NIL) (-1168 2740527 2740782 2741161 "SRAGG-" 2741166 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1167 2734711 2739474 2739895 "SQMATRIX" 2740153 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1166 2728399 2731429 2732156 "SPLTREE" 2734056 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1165 2724362 2725055 2725701 "SPLNODE" 2727825 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1164 2723409 2723642 2723672 "SPFCAT" 2724116 T SPFCAT (NIL) -9 NIL NIL NIL) (-1163 2722146 2722356 2722620 "SPECOUT" 2723167 T SPECOUT (NIL) -7 NIL NIL NIL) (-1162 2713242 2715114 2715144 "SPADXPT" 2719820 T SPADXPT (NIL) -9 NIL 2721984 NIL) (-1161 2713003 2713043 2713112 "SPADPRSR" 2713195 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1160 2711052 2712958 2712989 "SPADAST" 2712994 T SPADAST (NIL) -8 NIL NIL NIL) (-1159 2702983 2704756 2704799 "SPACEC" 2709172 NIL SPACEC (NIL T) -9 NIL 2710988 NIL) (-1158 2701113 2702915 2702964 "SPACE3" 2702969 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1157 2699865 2700036 2700327 "SORTPAK" 2700918 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1156 2697957 2698260 2698672 "SOLVETRA" 2699529 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1155 2697007 2697229 2697490 "SOLVESER" 2697730 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1154 2692311 2693199 2694194 "SOLVERAD" 2696059 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1153 2688126 2688735 2689464 "SOLVEFOR" 2691678 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1152 2682395 2687474 2687571 "SNTSCAT" 2687576 NIL SNTSCAT (NIL T T T T) -9 NIL 2687646 NIL) (-1151 2676501 2680718 2681109 "SMTS" 2682085 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1150 2670910 2676389 2676466 "SMP" 2676471 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1149 2669069 2669370 2669768 "SMITH" 2670607 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1148 2661173 2665648 2665751 "SMATCAT" 2667102 NIL SMATCAT (NIL NIL T T T) -9 NIL 2667652 NIL) (-1147 2658113 2658936 2660114 "SMATCAT-" 2660119 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1146 2655754 2657321 2657364 "SKAGG" 2657625 NIL SKAGG (NIL T) -9 NIL 2657760 NIL) (-1145 2651944 2655227 2655411 "SINT" 2655563 T SINT (NIL) -8 NIL NIL 2655725) (-1144 2651716 2651754 2651820 "SIMPAN" 2651900 T SIMPAN (NIL) -7 NIL NIL NIL) (-1143 2650995 2651251 2651391 "SIG" 2651598 T SIG (NIL) -8 NIL NIL NIL) (-1142 2649833 2650054 2650329 "SIGNRF" 2650754 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1141 2648666 2648817 2649101 "SIGNEF" 2649662 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1140 2647972 2648249 2648373 "SIGAST" 2648564 T SIGAST (NIL) -8 NIL NIL NIL) (-1139 2645662 2646116 2646622 "SHP" 2647513 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1138 2639491 2645563 2645639 "SHDP" 2645644 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1137 2639050 2639242 2639272 "SGROUP" 2639365 T SGROUP (NIL) -9 NIL 2639427 NIL) (-1136 2638908 2638934 2639007 "SGROUP-" 2639012 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1135 2635699 2636397 2637120 "SGCF" 2638207 T SGCF (NIL) -7 NIL NIL NIL) (-1134 2630066 2635145 2635242 "SFRTCAT" 2635247 NIL SFRTCAT (NIL T T T T) -9 NIL 2635286 NIL) (-1133 2623487 2624505 2625641 "SFRGCD" 2629049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1132 2616613 2617686 2618872 "SFQCMPK" 2622420 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2616233 2616322 2616433 "SFORT" 2616554 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1130 2615351 2616073 2616194 "SEXOF" 2616199 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1129 2614458 2615232 2615300 "SEX" 2615305 T SEX (NIL) -8 NIL NIL NIL) (-1128 2610239 2610954 2611049 "SEXCAT" 2613671 NIL SEXCAT (NIL T T T T T) -9 NIL 2614231 NIL) (-1127 2607392 2610173 2610221 "SET" 2610226 NIL SET (NIL T) -8 NIL NIL NIL) (-1126 2605616 2606105 2606410 "SETMN" 2607133 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1125 2605182 2605334 2605364 "SETCAT" 2605481 T SETCAT (NIL) -9 NIL 2605566 NIL) (-1124 2604962 2605014 2605113 "SETCAT-" 2605118 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1123 2601323 2603423 2603466 "SETAGG" 2604336 NIL SETAGG (NIL T) -9 NIL 2604676 NIL) (-1122 2600781 2600897 2601134 "SETAGG-" 2601139 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1121 2600224 2600477 2600578 "SEQAST" 2600702 T SEQAST (NIL) -8 NIL NIL NIL) (-1120 2599423 2599717 2599778 "SEGXCAT" 2600064 NIL SEGXCAT (NIL T T) -9 NIL 2600184 NIL) (-1119 2598429 2599089 2599271 "SEG" 2599276 NIL SEG (NIL T) -8 NIL NIL NIL) (-1118 2597408 2597622 2597665 "SEGCAT" 2598187 NIL SEGCAT (NIL T) -9 NIL 2598408 NIL) (-1117 2596340 2596771 2596979 "SEGBIND" 2597235 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1116 2595961 2596020 2596133 "SEGBIND2" 2596275 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1115 2595534 2595762 2595839 "SEGAST" 2595906 T SEGAST (NIL) -8 NIL NIL NIL) (-1114 2594753 2594879 2595083 "SEG2" 2595378 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1113 2594124 2594688 2594735 "SDVAR" 2594740 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1112 2586375 2593894 2594024 "SDPOL" 2594029 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1111 2584968 2585234 2585553 "SCPKG" 2586090 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1110 2584132 2584304 2584496 "SCOPE" 2584798 T SCOPE (NIL) -8 NIL NIL NIL) (-1109 2583352 2583486 2583665 "SCACHE" 2583987 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1108 2582984 2583170 2583200 "SASTCAT" 2583205 T SASTCAT (NIL) -9 NIL 2583218 NIL) (-1107 2582471 2582819 2582895 "SAOS" 2582930 T SAOS (NIL) -8 NIL NIL NIL) (-1106 2582036 2582071 2582244 "SAERFFC" 2582430 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1105 2575699 2581933 2582013 "SAE" 2582018 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1104 2575292 2575327 2575486 "SAEFACT" 2575658 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1103 2573613 2573927 2574328 "RURPK" 2574958 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1102 2572250 2572556 2572861 "RULESET" 2573447 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1101 2569473 2570003 2570461 "RULE" 2571931 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1100 2569085 2569267 2569350 "RULECOLD" 2569425 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1099 2568875 2568903 2568974 "RTVALUE" 2569036 T RTVALUE (NIL) -8 NIL NIL NIL) (-1098 2568346 2568592 2568686 "RSTRCAST" 2568803 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1097 2563194 2563989 2564909 "RSETGCD" 2567545 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1096 2552423 2557502 2557599 "RSETCAT" 2561718 NIL RSETCAT (NIL T T T T) -9 NIL 2562815 NIL) (-1095 2550350 2550889 2551713 "RSETCAT-" 2551718 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1094 2542736 2544112 2545632 "RSDCMPK" 2548949 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2540701 2541168 2541242 "RRCC" 2542328 NIL RRCC (NIL T T) -9 NIL 2542672 NIL) (-1092 2540052 2540226 2540505 "RRCC-" 2540510 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1091 2539495 2539748 2539849 "RPTAST" 2539973 T RPTAST (NIL) -8 NIL NIL NIL) (-1090 2512971 2522607 2522674 "RPOLCAT" 2533340 NIL RPOLCAT (NIL T T T) -9 NIL 2536500 NIL) (-1089 2504469 2506809 2509931 "RPOLCAT-" 2509936 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1088 2495406 2502680 2503162 "ROUTINE" 2504009 T ROUTINE (NIL) -8 NIL NIL NIL) (-1087 2492067 2495032 2495172 "ROMAN" 2495288 T ROMAN (NIL) -8 NIL NIL NIL) (-1086 2490311 2490927 2491187 "ROIRC" 2491872 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1085 2486515 2488800 2488830 "RNS" 2489134 T RNS (NIL) -9 NIL 2489408 NIL) (-1084 2485024 2485407 2485941 "RNS-" 2486016 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1083 2484413 2484821 2484851 "RNG" 2484856 T RNG (NIL) -9 NIL 2484877 NIL) (-1082 2483416 2483778 2483980 "RNGBIND" 2484264 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1081 2482801 2483189 2483232 "RMODULE" 2483237 NIL RMODULE (NIL T) -9 NIL 2483264 NIL) (-1080 2481637 2481731 2482067 "RMCAT2" 2482702 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1079 2478487 2480983 2481280 "RMATRIX" 2481399 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1078 2471314 2473574 2473689 "RMATCAT" 2477048 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2478030 NIL) (-1077 2470689 2470836 2471143 "RMATCAT-" 2471148 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1076 2470304 2470476 2470519 "RLINSET" 2470581 NIL RLINSET (NIL T) -9 NIL 2470625 NIL) (-1075 2469871 2469946 2470074 "RINTERP" 2470223 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1074 2468915 2469469 2469499 "RING" 2469555 T RING (NIL) -9 NIL 2469647 NIL) (-1073 2468707 2468751 2468848 "RING-" 2468853 NIL RING- (NIL T) -8 NIL NIL NIL) (-1072 2467548 2467785 2468043 "RIDIST" 2468471 T RIDIST (NIL) -7 NIL NIL NIL) (-1071 2458837 2467016 2467222 "RGCHAIN" 2467396 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1070 2458173 2458579 2458620 "RGBCSPC" 2458678 NIL RGBCSPC (NIL T) -9 NIL 2458730 NIL) (-1069 2457317 2457698 2457739 "RGBCMDL" 2457971 NIL RGBCMDL (NIL T) -9 NIL 2458085 NIL) (-1068 2454311 2454925 2455595 "RF" 2456681 NIL RF (NIL T) -7 NIL NIL NIL) (-1067 2453957 2454020 2454123 "RFFACTOR" 2454242 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1066 2453682 2453717 2453814 "RFFACT" 2453916 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1065 2451799 2452163 2452545 "RFDIST" 2453322 T RFDIST (NIL) -7 NIL NIL NIL) (-1064 2451252 2451344 2451507 "RETSOL" 2451701 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1063 2450888 2450968 2451011 "RETRACT" 2451144 NIL RETRACT (NIL T) -9 NIL 2451231 NIL) (-1062 2450737 2450762 2450849 "RETRACT-" 2450854 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1061 2450339 2450559 2450629 "RETAST" 2450689 T RETAST (NIL) -8 NIL NIL NIL) (-1060 2443083 2449992 2450119 "RESULT" 2450234 T RESULT (NIL) -8 NIL NIL NIL) (-1059 2441674 2442352 2442551 "RESRING" 2442986 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1058 2441310 2441359 2441457 "RESLATC" 2441611 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1057 2441015 2441050 2441157 "REPSQ" 2441269 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1056 2438437 2439017 2439619 "REP" 2440435 T REP (NIL) -7 NIL NIL NIL) (-1055 2438134 2438169 2438280 "REPDB" 2438396 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1054 2432034 2433423 2434646 "REP2" 2436946 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1053 2428411 2429092 2429900 "REP1" 2431261 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1052 2421107 2426552 2427008 "REGSET" 2428041 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1051 2419872 2420255 2420505 "REF" 2420892 NIL REF (NIL T) -8 NIL NIL NIL) (-1050 2419249 2419352 2419519 "REDORDER" 2419756 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1049 2415217 2418462 2418689 "RECLOS" 2419077 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1048 2414269 2414450 2414665 "REALSOLV" 2415024 T REALSOLV (NIL) -7 NIL NIL NIL) (-1047 2414115 2414156 2414186 "REAL" 2414191 T REAL (NIL) -9 NIL 2414226 NIL) (-1046 2410598 2411400 2412284 "REAL0Q" 2413280 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1045 2406199 2407187 2408248 "REAL0" 2409579 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1044 2405670 2405916 2406010 "RDUCEAST" 2406127 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1043 2405075 2405147 2405354 "RDIV" 2405592 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1042 2404143 2404317 2404530 "RDIST" 2404897 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1041 2402740 2403027 2403399 "RDETRS" 2403851 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1040 2400552 2401006 2401544 "RDETR" 2402282 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1039 2399177 2399455 2399852 "RDEEFS" 2400268 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1038 2397686 2397992 2398417 "RDEEF" 2398865 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1037 2391719 2394640 2394670 "RCFIELD" 2395965 T RCFIELD (NIL) -9 NIL 2396696 NIL) (-1036 2389783 2390287 2390983 "RCFIELD-" 2391058 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1035 2386027 2387856 2387899 "RCAGG" 2388983 NIL RCAGG (NIL T) -9 NIL 2389448 NIL) (-1034 2385655 2385749 2385912 "RCAGG-" 2385917 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1033 2384990 2385102 2385267 "RATRET" 2385539 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1032 2384543 2384610 2384731 "RATFACT" 2384918 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1031 2383851 2383971 2384123 "RANDSRC" 2384413 T RANDSRC (NIL) -7 NIL NIL NIL) (-1030 2383585 2383629 2383702 "RADUTIL" 2383800 T RADUTIL (NIL) -7 NIL NIL NIL) (-1029 2376413 2382416 2382727 "RADIX" 2383308 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1028 2366873 2376255 2376385 "RADFF" 2376390 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1027 2366520 2366595 2366625 "RADCAT" 2366785 T RADCAT (NIL) -9 NIL NIL NIL) (-1026 2366302 2366350 2366450 "RADCAT-" 2366455 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1025 2364403 2366072 2366164 "QUEUE" 2366245 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1024 2360664 2364336 2364384 "QUAT" 2364389 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1023 2360295 2360338 2360469 "QUATCT2" 2360615 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2353093 2356718 2356760 "QUATCAT" 2357551 NIL QUATCAT (NIL T) -9 NIL 2358317 NIL) (-1021 2349232 2350269 2351659 "QUATCAT-" 2351755 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2346672 2348280 2348323 "QUAGG" 2348704 NIL QUAGG (NIL T) -9 NIL 2348879 NIL) (-1019 2346274 2346494 2346564 "QQUTAST" 2346624 T QQUTAST (NIL) -8 NIL NIL NIL) (-1018 2345287 2345787 2345952 "QFORM" 2346155 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1017 2335619 2341134 2341176 "QFCAT" 2341844 NIL QFCAT (NIL T) -9 NIL 2342845 NIL) (-1016 2331186 2332387 2333981 "QFCAT-" 2334077 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1015 2330817 2330860 2330991 "QFCAT2" 2331137 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2330272 2330382 2330514 "QEQUAT" 2330707 T QEQUAT (NIL) -8 NIL NIL NIL) (-1013 2323398 2324471 2325657 "QCMPACK" 2329205 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1012 2320936 2321384 2321814 "QALGSET" 2323053 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1011 2320171 2320347 2320583 "QALGSET2" 2320754 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1010 2318856 2319080 2319399 "PWFFINTB" 2319944 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1009 2317031 2317199 2317555 "PUSHVAR" 2318670 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1008 2312920 2313974 2314017 "PTRANFN" 2315928 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1007 2311311 2311602 2311926 "PTPACK" 2312631 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1006 2310940 2310997 2311108 "PTFUNC2" 2311248 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1005 2305335 2309729 2309772 "PTCAT" 2310072 NIL PTCAT (NIL T) -9 NIL 2310225 NIL) (-1004 2304990 2305025 2305151 "PSQFR" 2305294 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1003 2303580 2303878 2304214 "PSEUDLIN" 2304688 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1002 2290304 2292675 2295001 "PSETPK" 2301340 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1001 2283300 2286040 2286138 "PSETCAT" 2289179 NIL PSETCAT (NIL T T T T) -9 NIL 2289993 NIL) (-1000 2281133 2281767 2282591 "PSETCAT-" 2282596 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-999 2280482 2280647 2280675 "PSCURVE" 2280943 T PSCURVE (NIL) -9 NIL 2281110 NIL) (-998 2276466 2277982 2278047 "PSCAT" 2278891 NIL PSCAT (NIL T T T) -9 NIL 2279131 NIL) (-997 2275529 2275745 2276145 "PSCAT-" 2276150 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-996 2273888 2274598 2274861 "PRTITION" 2275286 T PRTITION (NIL) -8 NIL NIL NIL) (-995 2273363 2273609 2273701 "PRTDAST" 2273816 T PRTDAST (NIL) -8 NIL NIL NIL) (-994 2262453 2264667 2266855 "PRS" 2271225 NIL PRS (NIL T T) -7 NIL NIL NIL) (-993 2260239 2261775 2261815 "PRQAGG" 2261998 NIL PRQAGG (NIL T) -9 NIL 2262100 NIL) (-992 2259575 2259880 2259908 "PROPLOG" 2260047 T PROPLOG (NIL) -9 NIL 2260162 NIL) (-991 2259179 2259236 2259359 "PROPFUN2" 2259498 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-990 2258494 2258615 2258787 "PROPFUN1" 2259040 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-989 2256675 2257241 2257538 "PROPFRML" 2258230 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-988 2256144 2256251 2256379 "PROPERTY" 2256567 T PROPERTY (NIL) -8 NIL NIL NIL) (-987 2250202 2254310 2255130 "PRODUCT" 2255370 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-986 2247480 2249660 2249894 "PR" 2250013 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2247276 2247308 2247367 "PRINT" 2247441 T PRINT (NIL) -7 NIL NIL NIL) (-984 2246616 2246733 2246885 "PRIMES" 2247156 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-983 2244681 2245082 2245548 "PRIMELT" 2246195 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-982 2244410 2244459 2244487 "PRIMCAT" 2244611 T PRIMCAT (NIL) -9 NIL NIL NIL) (-981 2240528 2244348 2244393 "PRIMARR" 2244398 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-980 2239535 2239713 2239941 "PRIMARR2" 2240346 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-979 2239178 2239234 2239345 "PREASSOC" 2239473 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-978 2238653 2238786 2238814 "PPCURVE" 2239019 T PPCURVE (NIL) -9 NIL 2239155 NIL) (-977 2238248 2238448 2238531 "PORTNUM" 2238590 T PORTNUM (NIL) -8 NIL NIL NIL) (-976 2235607 2236006 2236598 "POLYROOT" 2237829 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-975 2229513 2235211 2235371 "POLY" 2235480 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2228896 2228954 2229188 "POLYLIFT" 2229449 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-973 2225171 2225620 2226249 "POLYCATQ" 2228441 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-972 2211513 2216918 2216983 "POLYCAT" 2220497 NIL POLYCAT (NIL T T T) -9 NIL 2222375 NIL) (-971 2204962 2206824 2209208 "POLYCAT-" 2209213 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-970 2204549 2204617 2204737 "POLY2UP" 2204888 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-969 2204181 2204238 2204347 "POLY2" 2204486 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-968 2202866 2203105 2203381 "POLUTIL" 2203955 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-967 2201221 2201498 2201829 "POLTOPOL" 2202588 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-966 2196687 2201155 2201202 "POINT" 2201207 NIL POINT (NIL T) -8 NIL NIL NIL) (-965 2194874 2195231 2195606 "PNTHEORY" 2196332 T PNTHEORY (NIL) -7 NIL NIL NIL) (-964 2193332 2193629 2194028 "PMTOOLS" 2194572 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-963 2192925 2193003 2193120 "PMSYM" 2193248 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-962 2192433 2192502 2192677 "PMQFCAT" 2192850 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-961 2191788 2191898 2192054 "PMPRED" 2192310 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-960 2191181 2191267 2191429 "PMPREDFS" 2191689 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-959 2189845 2190053 2190431 "PMPLCAT" 2190943 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-958 2189377 2189456 2189608 "PMLSAGG" 2189760 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-957 2188850 2188926 2189108 "PMKERNEL" 2189295 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-956 2188467 2188542 2188655 "PMINS" 2188769 NIL PMINS (NIL T) -7 NIL NIL NIL) (-955 2187909 2187978 2188187 "PMFS" 2188392 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-954 2187137 2187255 2187460 "PMDOWN" 2187786 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-953 2186304 2186462 2186643 "PMASS" 2186976 T PMASS (NIL) -7 NIL NIL NIL) (-952 2185577 2185687 2185850 "PMASSFS" 2186191 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-951 2185232 2185300 2185394 "PLOTTOOL" 2185503 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-950 2179839 2181043 2182191 "PLOT" 2184104 T PLOT (NIL) -8 NIL NIL NIL) (-949 2175643 2176687 2177608 "PLOT3D" 2178938 T PLOT3D (NIL) -8 NIL NIL NIL) (-948 2174555 2174732 2174967 "PLOT1" 2175447 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-947 2149946 2154621 2159472 "PLEQN" 2169821 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-946 2149264 2149386 2149566 "PINTERP" 2149811 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-945 2148957 2149004 2149107 "PINTERPA" 2149211 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-944 2148173 2148721 2148808 "PI" 2148848 T PI (NIL) -8 NIL NIL 2148915) (-943 2146456 2147431 2147459 "PID" 2147641 T PID (NIL) -9 NIL 2147775 NIL) (-942 2146207 2146244 2146319 "PICOERCE" 2146413 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-941 2145527 2145666 2145842 "PGROEB" 2146063 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-940 2141114 2141928 2142833 "PGE" 2144642 T PGE (NIL) -7 NIL NIL NIL) (-939 2139237 2139484 2139850 "PGCD" 2140831 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-938 2138575 2138678 2138839 "PFRPAC" 2139121 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-937 2135215 2137123 2137476 "PFR" 2138254 NIL PFR (NIL T) -8 NIL NIL NIL) (-936 2133604 2133848 2134173 "PFOTOOLS" 2134962 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-935 2132137 2132376 2132727 "PFOQ" 2133361 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-934 2130638 2130850 2131206 "PFO" 2131921 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-933 2127191 2130527 2130596 "PF" 2130601 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2124511 2125782 2125810 "PFECAT" 2126395 T PFECAT (NIL) -9 NIL 2126779 NIL) (-931 2123956 2124110 2124324 "PFECAT-" 2124329 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-930 2122559 2122811 2123112 "PFBRU" 2123705 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-929 2120425 2120777 2121209 "PFBR" 2122210 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-928 2116471 2117937 2118584 "PERM" 2119811 NIL PERM (NIL T) -8 NIL NIL NIL) (-927 2111705 2112678 2113548 "PERMGRP" 2115634 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-926 2109769 2110729 2110770 "PERMCAT" 2111170 NIL PERMCAT (NIL T) -9 NIL 2111468 NIL) (-925 2109422 2109463 2109587 "PERMAN" 2109722 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-924 2106913 2109087 2109209 "PENDTREE" 2109333 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-923 2105842 2106057 2106098 "PDSPC" 2106631 NIL PDSPC (NIL T) -9 NIL 2106876 NIL) (-922 2104945 2105163 2105525 "PDSPC-" 2105530 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-921 2103827 2104595 2104636 "PDRING" 2104641 NIL PDRING (NIL T) -9 NIL 2104669 NIL) (-920 2102714 2103332 2103386 "PDMOD" 2103391 NIL PDMOD (NIL T T) -9 NIL 2103495 NIL) (-919 2099929 2100707 2101375 "PDEPROB" 2102066 T PDEPROB (NIL) -8 NIL NIL NIL) (-918 2097474 2097978 2098533 "PDEPACK" 2099394 T PDEPACK (NIL) -7 NIL NIL NIL) (-917 2096386 2096576 2096827 "PDECOMP" 2097273 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-916 2093951 2094794 2094822 "PDECAT" 2095609 T PDECAT (NIL) -9 NIL 2096322 NIL) (-915 2093580 2093635 2093689 "PDDOM" 2093854 NIL PDDOM (NIL T T) -9 NIL 2093934 NIL) (-914 2093399 2093429 2093536 "PDDOM-" 2093541 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-913 2093150 2093183 2093273 "PCOMP" 2093360 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-912 2091328 2091951 2092248 "PBWLB" 2092879 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-911 2083801 2085401 2086739 "PATTERN" 2090011 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-910 2083433 2083490 2083599 "PATTERN2" 2083738 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-909 2081190 2081578 2082035 "PATTERN1" 2083022 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-908 2078558 2079139 2079620 "PATRES" 2080755 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-907 2078122 2078189 2078321 "PATRES2" 2078485 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-906 2076005 2076410 2076817 "PATMATCH" 2077789 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-905 2075501 2075710 2075751 "PATMAB" 2075858 NIL PATMAB (NIL T) -9 NIL 2075941 NIL) (-904 2074019 2074355 2074613 "PATLRES" 2075306 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-903 2073565 2073688 2073729 "PATAB" 2073734 NIL PATAB (NIL T) -9 NIL 2073906 NIL) (-902 2071747 2072142 2072565 "PARTPERM" 2073162 T PARTPERM (NIL) -7 NIL NIL NIL) (-901 2071368 2071431 2071533 "PARSURF" 2071678 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-900 2071000 2071057 2071166 "PARSU2" 2071305 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-899 2070764 2070804 2070871 "PARSER" 2070953 T PARSER (NIL) -7 NIL NIL NIL) (-898 2070385 2070448 2070550 "PARSCURV" 2070695 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-897 2070017 2070074 2070183 "PARSC2" 2070322 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-896 2069656 2069714 2069811 "PARPCURV" 2069953 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-895 2069288 2069345 2069454 "PARPC2" 2069593 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-894 2068349 2068661 2068843 "PARAMAST" 2069126 T PARAMAST (NIL) -8 NIL NIL NIL) (-893 2067869 2067955 2068074 "PAN2EXPR" 2068250 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-892 2066646 2066990 2067218 "PALETTE" 2067661 T PALETTE (NIL) -8 NIL NIL NIL) (-891 2065039 2065651 2066011 "PAIR" 2066332 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-890 2058631 2064296 2064491 "PADICRC" 2064893 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-889 2051547 2057975 2058160 "PADICRAT" 2058478 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-888 2049862 2051484 2051529 "PADIC" 2051534 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-887 2046958 2048522 2048562 "PADICCT" 2049143 NIL PADICCT (NIL NIL) -9 NIL 2049425 NIL) (-886 2045915 2046115 2046383 "PADEPAC" 2046745 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-885 2045127 2045260 2045466 "PADE" 2045777 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-884 2043514 2044335 2044615 "OWP" 2044931 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-883 2043007 2043220 2043317 "OVERSET" 2043437 T OVERSET (NIL) -8 NIL NIL NIL) (-882 2042053 2042612 2042784 "OVAR" 2042875 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-881 2041317 2041438 2041599 "OUT" 2041912 T OUT (NIL) -7 NIL NIL NIL) (-880 2030189 2032426 2034626 "OUTFORM" 2039137 T OUTFORM (NIL) -8 NIL NIL NIL) (-879 2029525 2029786 2029913 "OUTBFILE" 2030082 T OUTBFILE (NIL) -8 NIL NIL NIL) (-878 2028832 2028997 2029025 "OUTBCON" 2029343 T OUTBCON (NIL) -9 NIL 2029509 NIL) (-877 2028433 2028545 2028702 "OUTBCON-" 2028707 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-876 2027813 2028162 2028251 "OSI" 2028364 T OSI (NIL) -8 NIL NIL NIL) (-875 2027316 2027654 2027682 "OSGROUP" 2027687 T OSGROUP (NIL) -9 NIL 2027709 NIL) (-874 2026061 2026288 2026573 "ORTHPOL" 2027063 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-873 2023612 2025896 2026017 "OREUP" 2026022 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-872 2021015 2023303 2023430 "ORESUP" 2023554 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-871 2018543 2019043 2019604 "OREPCTO" 2020504 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-870 2012215 2014416 2014457 "OREPCAT" 2016805 NIL OREPCAT (NIL T) -9 NIL 2017909 NIL) (-869 2009362 2010144 2011202 "OREPCAT-" 2011207 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-868 2008609 2008832 2008860 "ORDTYPE" 2009169 T ORDTYPE (NIL) -9 NIL 2009332 NIL) (-867 2007952 2008126 2008381 "ORDTYPE-" 2008386 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-866 2007378 2007691 2007849 "ORDSTRCT" 2007854 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-865 2006948 2007246 2007274 "ORDSET" 2007279 T ORDSET (NIL) -9 NIL 2007301 NIL) (-864 2005486 2006277 2006305 "ORDRING" 2006507 T ORDRING (NIL) -9 NIL 2006632 NIL) (-863 2005131 2005225 2005369 "ORDRING-" 2005374 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-862 2004484 2004947 2004975 "ORDMON" 2004980 T ORDMON (NIL) -9 NIL 2005001 NIL) (-861 2003646 2003793 2003988 "ORDFUNS" 2004333 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-860 2002957 2003376 2003404 "ORDFIN" 2003469 T ORDFIN (NIL) -9 NIL 2003543 NIL) (-859 1999516 2001543 2001952 "ORDCOMP" 2002581 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-858 1998782 1998909 1999095 "ORDCOMP2" 1999376 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-857 1995363 1996273 1997087 "OPTPROB" 1997988 T OPTPROB (NIL) -8 NIL NIL NIL) (-856 1992165 1992804 1993508 "OPTPACK" 1994679 T OPTPACK (NIL) -7 NIL NIL NIL) (-855 1989838 1990604 1990632 "OPTCAT" 1991451 T OPTCAT (NIL) -9 NIL 1992101 NIL) (-854 1989222 1989515 1989620 "OPSIG" 1989753 T OPSIG (NIL) -8 NIL NIL NIL) (-853 1988990 1989029 1989095 "OPQUERY" 1989176 T OPQUERY (NIL) -7 NIL NIL NIL) (-852 1986121 1987301 1987805 "OP" 1988519 NIL OP (NIL T) -8 NIL NIL NIL) (-851 1985481 1985707 1985748 "OPERCAT" 1985960 NIL OPERCAT (NIL T) -9 NIL 1986057 NIL) (-850 1985236 1985292 1985409 "OPERCAT-" 1985414 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-849 1982049 1984033 1984402 "ONECOMP" 1984900 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-848 1981354 1981469 1981643 "ONECOMP2" 1981921 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1980773 1980879 1981009 "OMSERVER" 1981244 T OMSERVER (NIL) -7 NIL NIL NIL) (-846 1977635 1980213 1980253 "OMSAGG" 1980314 NIL OMSAGG (NIL T) -9 NIL 1980378 NIL) (-845 1976258 1976521 1976803 "OMPKG" 1977373 T OMPKG (NIL) -7 NIL NIL NIL) (-844 1975688 1975791 1975819 "OM" 1976118 T OM (NIL) -9 NIL NIL NIL) (-843 1974235 1975237 1975406 "OMLO" 1975569 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 1973195 1973342 1973562 "OMEXPR" 1974061 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-841 1972486 1972741 1972877 "OMERR" 1973079 T OMERR (NIL) -8 NIL NIL NIL) (-840 1971637 1971907 1972067 "OMERRK" 1972346 T OMERRK (NIL) -8 NIL NIL NIL) (-839 1971088 1971314 1971422 "OMENC" 1971549 T OMENC (NIL) -8 NIL NIL NIL) (-838 1964983 1966168 1967339 "OMDEV" 1969937 T OMDEV (NIL) -8 NIL NIL NIL) (-837 1964052 1964223 1964417 "OMCONN" 1964809 T OMCONN (NIL) -8 NIL NIL NIL) (-836 1962546 1963522 1963550 "OINTDOM" 1963555 T OINTDOM (NIL) -9 NIL 1963576 NIL) (-835 1959884 1961234 1961571 "OFMONOID" 1962241 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-834 1959256 1959821 1959866 "ODVAR" 1959871 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-833 1956679 1959001 1959156 "ODR" 1959161 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-832 1948984 1956455 1956581 "ODPOL" 1956586 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-831 1942783 1948856 1948961 "ODP" 1948966 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-830 1941549 1941764 1942039 "ODETOOLS" 1942557 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-829 1938516 1939174 1939890 "ODESYS" 1940882 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-828 1933398 1934306 1935331 "ODERTRIC" 1937591 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-827 1932824 1932906 1933100 "ODERED" 1933310 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-826 1929712 1930260 1930937 "ODERAT" 1932247 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-825 1926671 1927136 1927733 "ODEPRRIC" 1929241 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-824 1924614 1925210 1925696 "ODEPROB" 1926205 T ODEPROB (NIL) -8 NIL NIL NIL) (-823 1921134 1921619 1922266 "ODEPRIM" 1924093 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-822 1920383 1920485 1920745 "ODEPAL" 1921026 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-821 1916545 1917336 1918200 "ODEPACK" 1919539 T ODEPACK (NIL) -7 NIL NIL NIL) (-820 1915606 1915713 1915935 "ODEINT" 1916434 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-819 1909707 1911132 1912579 "ODEIFTBL" 1914179 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-818 1905105 1905891 1906843 "ODEEF" 1908866 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-817 1904454 1904543 1904766 "ODECONST" 1905010 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-816 1902565 1903226 1903254 "ODECAT" 1903859 T ODECAT (NIL) -9 NIL 1904390 NIL) (-815 1899420 1902270 1902392 "OCT" 1902475 NIL OCT (NIL T) -8 NIL NIL NIL) (-814 1899058 1899101 1899228 "OCTCT2" 1899371 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-813 1893665 1896101 1896141 "OC" 1897238 NIL OC (NIL T) -9 NIL 1898096 NIL) (-812 1890892 1891640 1892630 "OC-" 1892724 NIL OC- (NIL T T) -8 NIL NIL NIL) (-811 1890217 1890685 1890713 "OCAMON" 1890718 T OCAMON (NIL) -9 NIL 1890739 NIL) (-810 1889721 1890062 1890090 "OASGP" 1890095 T OASGP (NIL) -9 NIL 1890115 NIL) (-809 1888955 1889444 1889472 "OAMONS" 1889512 T OAMONS (NIL) -9 NIL 1889555 NIL) (-808 1888342 1888775 1888803 "OAMON" 1888808 T OAMON (NIL) -9 NIL 1888828 NIL) (-807 1887573 1888091 1888119 "OAGROUP" 1888124 T OAGROUP (NIL) -9 NIL 1888144 NIL) (-806 1887263 1887313 1887401 "NUMTUBE" 1887517 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-805 1880836 1882354 1883890 "NUMQUAD" 1885747 T NUMQUAD (NIL) -7 NIL NIL NIL) (-804 1876592 1877580 1878605 "NUMODE" 1879831 T NUMODE (NIL) -7 NIL NIL NIL) (-803 1873933 1874813 1874841 "NUMINT" 1875764 T NUMINT (NIL) -9 NIL 1876528 NIL) (-802 1872881 1873078 1873296 "NUMFMT" 1873735 T NUMFMT (NIL) -7 NIL NIL NIL) (-801 1859240 1862185 1864717 "NUMERIC" 1870388 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-800 1853609 1858688 1858783 "NTSCAT" 1858788 NIL NTSCAT (NIL T T T T) -9 NIL 1858827 NIL) (-799 1852803 1852968 1853161 "NTPOLFN" 1853448 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-798 1840604 1849628 1850440 "NSUP" 1852024 NIL NSUP (NIL T) -8 NIL NIL NIL) (-797 1840236 1840293 1840402 "NSUP2" 1840541 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-796 1830186 1840010 1840143 "NSMP" 1840148 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-795 1828618 1828919 1829276 "NREP" 1829874 NIL NREP (NIL T) -7 NIL NIL NIL) (-794 1827209 1827461 1827819 "NPCOEF" 1828361 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-793 1826275 1826390 1826606 "NORMRETR" 1827090 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-792 1824316 1824606 1825015 "NORMPK" 1825983 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-791 1824001 1824029 1824153 "NORMMA" 1824282 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-790 1823801 1823958 1823987 "NONE" 1823992 T NONE (NIL) -8 NIL NIL NIL) (-789 1823590 1823619 1823688 "NONE1" 1823765 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-788 1823087 1823149 1823328 "NODE1" 1823522 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-787 1821368 1822219 1822474 "NNI" 1822821 T NNI (NIL) -8 NIL NIL 1823056) (-786 1819788 1820101 1820465 "NLINSOL" 1821036 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-785 1816029 1817024 1817923 "NIPROB" 1818909 T NIPROB (NIL) -8 NIL NIL NIL) (-784 1814786 1815020 1815322 "NFINTBAS" 1815791 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-783 1813960 1814436 1814477 "NETCLT" 1814649 NIL NETCLT (NIL T) -9 NIL 1814731 NIL) (-782 1812668 1812899 1813180 "NCODIV" 1813728 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-781 1812430 1812467 1812542 "NCNTFRAC" 1812625 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-780 1810610 1810974 1811394 "NCEP" 1812055 NIL NCEP (NIL T) -7 NIL NIL NIL) (-779 1809447 1810220 1810248 "NASRING" 1810358 T NASRING (NIL) -9 NIL 1810438 NIL) (-778 1809242 1809286 1809380 "NASRING-" 1809385 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-777 1808335 1808860 1808888 "NARNG" 1809005 T NARNG (NIL) -9 NIL 1809096 NIL) (-776 1808027 1808094 1808228 "NARNG-" 1808233 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-775 1806906 1807113 1807348 "NAGSP" 1807812 T NAGSP (NIL) -7 NIL NIL NIL) (-774 1798178 1799862 1801535 "NAGS" 1805253 T NAGS (NIL) -7 NIL NIL NIL) (-773 1796726 1797034 1797365 "NAGF07" 1797867 T NAGF07 (NIL) -7 NIL NIL NIL) (-772 1791264 1792555 1793862 "NAGF04" 1795439 T NAGF04 (NIL) -7 NIL NIL NIL) (-771 1784232 1785846 1787479 "NAGF02" 1789651 T NAGF02 (NIL) -7 NIL NIL NIL) (-770 1779456 1780556 1781673 "NAGF01" 1783135 T NAGF01 (NIL) -7 NIL NIL NIL) (-769 1773084 1774650 1776235 "NAGE04" 1777891 T NAGE04 (NIL) -7 NIL NIL NIL) (-768 1764253 1766374 1768504 "NAGE02" 1770974 T NAGE02 (NIL) -7 NIL NIL NIL) (-767 1760206 1761153 1762117 "NAGE01" 1763309 T NAGE01 (NIL) -7 NIL NIL NIL) (-766 1758001 1758535 1759093 "NAGD03" 1759668 T NAGD03 (NIL) -7 NIL NIL NIL) (-765 1749751 1751679 1753633 "NAGD02" 1756067 T NAGD02 (NIL) -7 NIL NIL NIL) (-764 1743562 1744987 1746427 "NAGD01" 1748331 T NAGD01 (NIL) -7 NIL NIL NIL) (-763 1739771 1740593 1741430 "NAGC06" 1742745 T NAGC06 (NIL) -7 NIL NIL NIL) (-762 1738236 1738568 1738924 "NAGC05" 1739435 T NAGC05 (NIL) -7 NIL NIL NIL) (-761 1737612 1737731 1737875 "NAGC02" 1738112 T NAGC02 (NIL) -7 NIL NIL NIL) (-760 1736557 1737140 1737180 "NAALG" 1737259 NIL NAALG (NIL T) -9 NIL 1737320 NIL) (-759 1736392 1736421 1736511 "NAALG-" 1736516 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-758 1730342 1731450 1732637 "MULTSQFR" 1735288 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-757 1729661 1729736 1729920 "MULTFACT" 1730254 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-756 1722332 1726246 1726299 "MTSCAT" 1727369 NIL MTSCAT (NIL T T) -9 NIL 1727884 NIL) (-755 1722044 1722098 1722190 "MTHING" 1722272 NIL MTHING (NIL T) -7 NIL NIL NIL) (-754 1721836 1721869 1721929 "MSYSCMD" 1722004 T MSYSCMD (NIL) -7 NIL NIL NIL) (-753 1717918 1720591 1720911 "MSET" 1721549 NIL MSET (NIL T) -8 NIL NIL NIL) (-752 1714987 1717479 1717520 "MSETAGG" 1717525 NIL MSETAGG (NIL T) -9 NIL 1717559 NIL) (-751 1710829 1712366 1713111 "MRING" 1714287 NIL MRING (NIL T T) -8 NIL NIL NIL) (-750 1710395 1710462 1710593 "MRF2" 1710756 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-749 1710013 1710048 1710192 "MRATFAC" 1710354 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-748 1707625 1707920 1708351 "MPRFF" 1709718 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-747 1701646 1707479 1707576 "MPOLY" 1707581 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-746 1701136 1701171 1701379 "MPCPF" 1701605 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-745 1700650 1700693 1700877 "MPC3" 1701087 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-744 1699845 1699926 1700147 "MPC2" 1700565 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-743 1698146 1698483 1698873 "MONOTOOL" 1699505 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-742 1697357 1697674 1697702 "MONOID" 1697921 T MONOID (NIL) -9 NIL 1698068 NIL) (-741 1696903 1697022 1697203 "MONOID-" 1697208 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-740 1686493 1692723 1692782 "MONOGEN" 1693456 NIL MONOGEN (NIL T T) -9 NIL 1693912 NIL) (-739 1683711 1684446 1685446 "MONOGEN-" 1685565 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-738 1682530 1682976 1683004 "MONADWU" 1683396 T MONADWU (NIL) -9 NIL 1683634 NIL) (-737 1681902 1682061 1682309 "MONADWU-" 1682314 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-736 1681247 1681491 1681519 "MONAD" 1681726 T MONAD (NIL) -9 NIL 1681838 NIL) (-735 1680932 1681010 1681142 "MONAD-" 1681147 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-734 1679221 1679845 1680124 "MOEBIUS" 1680685 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-733 1678485 1678889 1678929 "MODULE" 1678934 NIL MODULE (NIL T) -9 NIL 1678973 NIL) (-732 1678053 1678149 1678339 "MODULE-" 1678344 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-731 1675733 1676417 1676744 "MODRING" 1677877 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1672677 1673838 1674359 "MODOP" 1675262 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-729 1671265 1671744 1672021 "MODMONOM" 1672540 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-728 1661033 1669556 1669970 "MODMON" 1670902 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-727 1658189 1659877 1660153 "MODFIELD" 1660908 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1657166 1657470 1657660 "MMLFORM" 1658019 T MMLFORM (NIL) -8 NIL NIL NIL) (-725 1656692 1656735 1656914 "MMAP" 1657117 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-724 1654757 1655524 1655565 "MLO" 1655988 NIL MLO (NIL T) -9 NIL 1656230 NIL) (-723 1652123 1652639 1653241 "MLIFT" 1654238 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-722 1651514 1651598 1651752 "MKUCFUNC" 1652034 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-721 1651113 1651183 1651306 "MKRECORD" 1651437 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-720 1650160 1650322 1650550 "MKFUNC" 1650924 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-719 1649548 1649652 1649808 "MKFLCFN" 1650043 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-718 1648825 1648927 1649112 "MKBCFUNC" 1649441 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-717 1645414 1648379 1648515 "MINT" 1648709 T MINT (NIL) -8 NIL NIL NIL) (-716 1644226 1644469 1644746 "MHROWRED" 1645169 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-715 1639606 1642761 1643166 "MFLOAT" 1643841 T MFLOAT (NIL) -8 NIL NIL NIL) (-714 1638963 1639039 1639210 "MFINFACT" 1639518 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-713 1635278 1636126 1637010 "MESH" 1638099 T MESH (NIL) -7 NIL NIL NIL) (-712 1633668 1633980 1634333 "MDDFACT" 1634965 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-711 1630438 1632799 1632840 "MDAGG" 1633095 NIL MDAGG (NIL T) -9 NIL 1633238 NIL) (-710 1619132 1629731 1629938 "MCMPLX" 1630251 T MCMPLX (NIL) -8 NIL NIL NIL) (-709 1618269 1618415 1618616 "MCDEN" 1618981 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-708 1616159 1616429 1616809 "MCALCFN" 1617999 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-707 1615084 1615324 1615557 "MAYBE" 1615965 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-706 1612696 1613219 1613781 "MATSTOR" 1614555 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-705 1608608 1612068 1612316 "MATRIX" 1612481 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-704 1604374 1605081 1605817 "MATLIN" 1607965 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-703 1594200 1597431 1597508 "MATCAT" 1602540 NIL MATCAT (NIL T T T) -9 NIL 1604012 NIL) (-702 1590393 1591463 1592876 "MATCAT-" 1592881 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-701 1588987 1589140 1589473 "MATCAT2" 1590228 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-700 1587099 1587423 1587807 "MAPPKG3" 1588662 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-699 1586080 1586253 1586475 "MAPPKG2" 1586923 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-698 1584579 1584863 1585190 "MAPPKG1" 1585786 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-697 1583658 1583985 1584162 "MAPPAST" 1584422 T MAPPAST (NIL) -8 NIL NIL NIL) (-696 1583269 1583327 1583450 "MAPHACK3" 1583594 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-695 1582861 1582922 1583036 "MAPHACK2" 1583201 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-694 1582299 1582402 1582544 "MAPHACK1" 1582752 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-693 1580378 1580999 1581303 "MAGMA" 1582027 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-692 1579857 1580102 1580193 "MACROAST" 1580307 T MACROAST (NIL) -8 NIL NIL NIL) (-691 1576278 1578096 1578557 "M3D" 1579429 NIL M3D (NIL T) -8 NIL NIL NIL) (-690 1570328 1574589 1574630 "LZSTAGG" 1575412 NIL LZSTAGG (NIL T) -9 NIL 1575707 NIL) (-689 1566286 1567459 1568916 "LZSTAGG-" 1568921 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-688 1563373 1564177 1564664 "LWORD" 1565831 NIL LWORD (NIL T) -8 NIL NIL NIL) (-687 1562949 1563177 1563252 "LSTAST" 1563318 T LSTAST (NIL) -8 NIL NIL NIL) (-686 1555839 1562720 1562854 "LSQM" 1562859 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-685 1555063 1555202 1555430 "LSPP" 1555694 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-684 1552875 1553176 1553632 "LSMP" 1554752 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-683 1549654 1550328 1551058 "LSMP1" 1552177 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-682 1543456 1548744 1548785 "LSAGG" 1548847 NIL LSAGG (NIL T) -9 NIL 1548925 NIL) (-681 1540151 1541075 1542288 "LSAGG-" 1542293 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-680 1537750 1539295 1539544 "LPOLY" 1539946 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-679 1537332 1537417 1537540 "LPEFRAC" 1537659 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-678 1535653 1536426 1536679 "LO" 1537164 NIL LO (NIL T T T) -8 NIL NIL NIL) (-677 1535265 1535403 1535431 "LOGIC" 1535542 T LOGIC (NIL) -9 NIL 1535623 NIL) (-676 1535127 1535150 1535221 "LOGIC-" 1535226 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-675 1534320 1534460 1534653 "LODOOPS" 1534983 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-674 1531743 1534236 1534302 "LODO" 1534307 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1530281 1530516 1530869 "LODOF" 1531490 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-672 1526485 1528916 1528957 "LODOCAT" 1529395 NIL LODOCAT (NIL T) -9 NIL 1529606 NIL) (-671 1526218 1526276 1526403 "LODOCAT-" 1526408 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-670 1523538 1526059 1526177 "LODO2" 1526182 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-669 1520973 1523475 1523520 "LODO1" 1523525 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-668 1519854 1520019 1520324 "LODEEF" 1520796 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-667 1515132 1518020 1518061 "LNAGG" 1518923 NIL LNAGG (NIL T) -9 NIL 1519358 NIL) (-666 1514279 1514493 1514835 "LNAGG-" 1514840 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-665 1510415 1511204 1511843 "LMOPS" 1513694 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-664 1509804 1510192 1510233 "LMODULE" 1510238 NIL LMODULE (NIL T) -9 NIL 1510264 NIL) (-663 1507005 1509449 1509572 "LMDICT" 1509714 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-662 1506623 1506795 1506836 "LLINSET" 1506897 NIL LLINSET (NIL T) -9 NIL 1506941 NIL) (-661 1506322 1506531 1506591 "LITERAL" 1506596 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-660 1499488 1505256 1505560 "LIST" 1506051 NIL LIST (NIL T) -8 NIL NIL NIL) (-659 1499013 1499087 1499226 "LIST3" 1499408 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-658 1498020 1498198 1498426 "LIST2" 1498831 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-657 1496154 1496466 1496865 "LIST2MAP" 1497667 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-656 1495785 1495973 1496014 "LINSET" 1496019 NIL LINSET (NIL T) -9 NIL 1496053 NIL) (-655 1494725 1495293 1495460 "LINFORM" 1495670 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-654 1493138 1493752 1493793 "LINEXP" 1494283 NIL LINEXP (NIL T) -9 NIL 1494556 NIL) (-653 1491876 1492618 1492799 "LINELT" 1493009 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-652 1490453 1490713 1491024 "LINDEP" 1491628 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-651 1489697 1490185 1490295 "LINBASIS" 1490383 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-650 1486464 1487183 1487960 "LIMITRF" 1488952 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-649 1484767 1485063 1485472 "LIMITPS" 1486159 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-648 1479195 1484278 1484506 "LIE" 1484588 NIL LIE (NIL T T) -8 NIL NIL NIL) (-647 1478129 1478598 1478638 "LIECAT" 1478778 NIL LIECAT (NIL T) -9 NIL 1478929 NIL) (-646 1477970 1477997 1478085 "LIECAT-" 1478090 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-645 1470563 1477510 1477666 "LIB" 1477834 T LIB (NIL) -8 NIL NIL NIL) (-644 1466198 1467081 1468016 "LGROBP" 1469680 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-643 1464196 1464470 1464820 "LF" 1465919 NIL LF (NIL T T) -7 NIL NIL NIL) (-642 1463036 1463728 1463756 "LFCAT" 1463963 T LFCAT (NIL) -9 NIL 1464102 NIL) (-641 1459938 1460568 1461256 "LEXTRIPK" 1462400 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-640 1456682 1457508 1458011 "LEXP" 1459518 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-639 1456158 1456403 1456495 "LETAST" 1456610 T LETAST (NIL) -8 NIL NIL NIL) (-638 1454556 1454869 1455270 "LEADCDET" 1455840 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-637 1453746 1453820 1454049 "LAZM3PK" 1454477 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-636 1448663 1451823 1452361 "LAUPOL" 1453258 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-635 1448242 1448286 1448447 "LAPLACE" 1448613 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-634 1446181 1447343 1447594 "LA" 1448075 NIL LA (NIL T T T) -8 NIL NIL NIL) (-633 1445161 1445745 1445786 "LALG" 1445848 NIL LALG (NIL T) -9 NIL 1445907 NIL) (-632 1444875 1444934 1445070 "LALG-" 1445075 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-631 1444710 1444734 1444775 "KVTFROM" 1444837 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-630 1443633 1444077 1444262 "KTVLOGIC" 1444545 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-629 1443468 1443492 1443533 "KRCFROM" 1443595 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-628 1442372 1442559 1442858 "KOVACIC" 1443268 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-627 1442207 1442231 1442272 "KONVERT" 1442334 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-626 1442042 1442066 1442107 "KOERCE" 1442169 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-625 1439873 1440635 1441012 "KERNEL" 1441698 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-624 1439369 1439450 1439582 "KERNEL2" 1439787 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-623 1433080 1437846 1437900 "KDAGG" 1438277 NIL KDAGG (NIL T T) -9 NIL 1438483 NIL) (-622 1432609 1432733 1432938 "KDAGG-" 1432943 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-621 1425757 1432270 1432425 "KAFILE" 1432487 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-620 1420185 1425268 1425496 "JORDAN" 1425578 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1419564 1419834 1419955 "JOINAST" 1420084 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1419410 1419469 1419524 "JAVACODE" 1419529 T JAVACODE (NIL) -8 NIL NIL NIL) (-617 1415637 1417587 1417641 "IXAGG" 1418570 NIL IXAGG (NIL T T) -9 NIL 1419029 NIL) (-616 1414556 1414862 1415281 "IXAGG-" 1415286 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-615 1410089 1414478 1414537 "IVECTOR" 1414542 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-614 1408855 1409092 1409358 "ITUPLE" 1409856 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-613 1407357 1407534 1407829 "ITRIGMNP" 1408677 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-612 1406102 1406306 1406589 "ITFUN3" 1407133 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-611 1405734 1405791 1405900 "ITFUN2" 1406039 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-610 1404893 1405214 1405388 "ITFORM" 1405580 T ITFORM (NIL) -8 NIL NIL NIL) (-609 1402854 1403913 1404191 "ITAYLOR" 1404648 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-608 1391799 1396991 1398154 "ISUPS" 1401724 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-607 1390903 1391043 1391279 "ISUMP" 1391646 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-606 1386281 1390848 1390889 "ISTRING" 1390894 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-605 1385757 1386002 1386094 "ISAST" 1386209 T ISAST (NIL) -8 NIL NIL NIL) (-604 1384966 1385048 1385264 "IRURPK" 1385671 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-603 1383902 1384103 1384343 "IRSN" 1384746 T IRSN (NIL) -7 NIL NIL NIL) (-602 1381973 1382328 1382757 "IRRF2F" 1383540 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-601 1381720 1381758 1381834 "IRREDFFX" 1381929 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-600 1380335 1380594 1380893 "IROOT" 1381453 NIL IROOT (NIL T) -7 NIL NIL NIL) (-599 1376939 1378019 1378711 "IR" 1379675 NIL IR (NIL T) -8 NIL NIL NIL) (-598 1376144 1376432 1376583 "IRFORM" 1376808 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1373757 1374252 1374818 "IR2" 1375622 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-596 1372857 1372970 1373184 "IR2F" 1373640 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-595 1372648 1372682 1372742 "IPRNTPK" 1372817 T IPRNTPK (NIL) -7 NIL NIL NIL) (-594 1369229 1372537 1372606 "IPF" 1372611 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-593 1367556 1369154 1369211 "IPADIC" 1369216 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-592 1366868 1367116 1367246 "IP4ADDR" 1367446 T IP4ADDR (NIL) -8 NIL NIL NIL) (-591 1366242 1366497 1366629 "IOMODE" 1366756 T IOMODE (NIL) -8 NIL NIL NIL) (-590 1365315 1365839 1365966 "IOBFILE" 1366135 T IOBFILE (NIL) -8 NIL NIL NIL) (-589 1364803 1365219 1365247 "IOBCON" 1365252 T IOBCON (NIL) -9 NIL 1365273 NIL) (-588 1364314 1364372 1364555 "INVLAPLA" 1364739 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-587 1353962 1356316 1358702 "INTTR" 1361978 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-586 1350297 1351039 1351904 "INTTOOLS" 1353147 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-585 1349883 1349974 1350091 "INTSLPE" 1350200 T INTSLPE (NIL) -7 NIL NIL NIL) (-584 1347836 1349806 1349865 "INTRVL" 1349870 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-583 1345438 1345950 1346525 "INTRF" 1347321 NIL INTRF (NIL T) -7 NIL NIL NIL) (-582 1344849 1344946 1345088 "INTRET" 1345336 NIL INTRET (NIL T) -7 NIL NIL NIL) (-581 1342846 1343235 1343705 "INTRAT" 1344457 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-580 1340109 1340692 1341311 "INTPM" 1342331 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-579 1336854 1337453 1338191 "INTPAF" 1339495 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-578 1332033 1332995 1334046 "INTPACK" 1335823 T INTPACK (NIL) -7 NIL NIL NIL) (-577 1328845 1331830 1331939 "INT" 1331944 T INT (NIL) -8 NIL NIL NIL) (-576 1328097 1328249 1328457 "INTHERTR" 1328687 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1327536 1327616 1327804 "INTHERAL" 1328011 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1325382 1325825 1326282 "INTHEORY" 1327099 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1316788 1318409 1320181 "INTG0" 1323734 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1297361 1302151 1306961 "INTFTBL" 1311998 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1296610 1296748 1296921 "INTFACT" 1297220 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1294037 1294483 1295040 "INTEF" 1296164 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1292390 1293129 1293157 "INTDOM" 1293458 T INTDOM (NIL) -9 NIL 1293665 NIL) (-568 1291759 1291933 1292175 "INTDOM-" 1292180 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1288119 1290048 1290102 "INTCAT" 1290901 NIL INTCAT (NIL T) -9 NIL 1291222 NIL) (-566 1287591 1287694 1287822 "INTBIT" 1288011 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1286290 1286444 1286751 "INTALG" 1287436 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1285773 1285863 1286020 "INTAF" 1286194 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1279122 1285583 1285723 "INTABL" 1285728 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1278455 1278921 1278986 "INT8" 1279020 T INT8 (NIL) -8 NIL NIL 1279065) (-561 1277787 1278253 1278318 "INT64" 1278352 T INT64 (NIL) -8 NIL NIL 1278397) (-560 1277119 1277585 1277650 "INT32" 1277684 T INT32 (NIL) -8 NIL NIL 1277729) (-559 1276451 1276917 1276982 "INT16" 1277016 T INT16 (NIL) -8 NIL NIL 1277061) (-558 1271146 1273999 1274027 "INS" 1274961 T INS (NIL) -9 NIL 1275626 NIL) (-557 1268386 1269157 1270131 "INS-" 1270204 NIL INS- (NIL T) -8 NIL NIL NIL) (-556 1267161 1267388 1267686 "INPSIGN" 1268139 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-555 1266279 1266396 1266593 "INPRODPF" 1267041 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-554 1265173 1265290 1265527 "INPRODFF" 1266159 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-553 1264173 1264325 1264585 "INNMFACT" 1265009 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-552 1263370 1263467 1263655 "INMODGCD" 1264072 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-551 1261878 1262123 1262447 "INFSP" 1263115 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-550 1261062 1261179 1261362 "INFPROD0" 1261758 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-549 1257917 1259127 1259642 "INFORM" 1260555 T INFORM (NIL) -8 NIL NIL NIL) (-548 1257527 1257587 1257685 "INFORM1" 1257852 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1257050 1257139 1257253 "INFINITY" 1257433 T INFINITY (NIL) -7 NIL NIL NIL) (-546 1256226 1256770 1256871 "INETCLTS" 1256969 T INETCLTS (NIL) -8 NIL NIL NIL) (-545 1254842 1255092 1255413 "INEP" 1255974 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-544 1254047 1254739 1254804 "INDE" 1254809 NIL INDE (NIL T) -8 NIL NIL NIL) (-543 1253611 1253679 1253796 "INCRMAPS" 1253974 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-542 1252429 1252880 1253086 "INBFILE" 1253425 T INBFILE (NIL) -8 NIL NIL NIL) (-541 1247728 1248665 1249609 "INBFF" 1251517 NIL INBFF (NIL T) -7 NIL NIL NIL) (-540 1246636 1246905 1246933 "INBCON" 1247446 T INBCON (NIL) -9 NIL 1247712 NIL) (-539 1245888 1246111 1246387 "INBCON-" 1246392 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-538 1245367 1245612 1245703 "INAST" 1245817 T INAST (NIL) -8 NIL NIL NIL) (-537 1244794 1245046 1245152 "IMPTAST" 1245281 T IMPTAST (NIL) -8 NIL NIL NIL) (-536 1241195 1244638 1244742 "IMATRIX" 1244747 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-535 1239903 1240026 1240342 "IMATQF" 1241051 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-534 1238123 1238350 1238687 "IMATLIN" 1239659 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-533 1232704 1238047 1238105 "ILIST" 1238110 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-532 1230612 1232564 1232677 "IIARRAY2" 1232682 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-531 1226010 1230523 1230587 "IFF" 1230592 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-530 1225357 1225627 1225743 "IFAST" 1225914 T IFAST (NIL) -8 NIL NIL NIL) (-529 1220355 1224649 1224837 "IFARRAY" 1225214 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-528 1219535 1220259 1220332 "IFAMON" 1220337 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-527 1219119 1219184 1219238 "IEVALAB" 1219445 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-526 1218794 1218862 1219022 "IEVALAB-" 1219027 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-525 1218241 1218709 1218771 "IDPO" 1218776 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-524 1217449 1218130 1218205 "IDPOAMS" 1218210 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1216714 1217338 1217413 "IDPOAM" 1217418 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1215260 1215721 1215773 "IDPC" 1216285 NIL IDPC (NIL T T) -9 NIL 1216566 NIL) (-521 1214688 1215152 1215225 "IDPAM" 1215230 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-520 1214023 1214580 1214653 "IDPAG" 1214658 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-519 1213668 1213859 1213934 "IDENT" 1213968 T IDENT (NIL) -8 NIL NIL NIL) (-518 1209923 1210771 1211666 "IDECOMP" 1212825 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-517 1202760 1203846 1204893 "IDEAL" 1208959 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-516 1201920 1202032 1202232 "ICDEN" 1202644 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-515 1200991 1201400 1201547 "ICARD" 1201793 T ICARD (NIL) -8 NIL NIL NIL) (-514 1199051 1199364 1199769 "IBPTOOLS" 1200668 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-513 1194658 1198671 1198784 "IBITS" 1198970 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-512 1191381 1191957 1192652 "IBATOOL" 1194075 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-511 1189160 1189622 1190155 "IBACHIN" 1190916 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-510 1186992 1189006 1189109 "IARRAY2" 1189114 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-509 1183101 1186918 1186975 "IARRAY1" 1186980 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-508 1176961 1181513 1181994 "IAN" 1182640 T IAN (NIL) -8 NIL NIL NIL) (-507 1176472 1176529 1176702 "IALGFACT" 1176898 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-506 1176000 1176113 1176141 "HYPCAT" 1176348 T HYPCAT (NIL) -9 NIL NIL NIL) (-505 1175538 1175655 1175841 "HYPCAT-" 1175846 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-504 1175133 1175333 1175416 "HOSTNAME" 1175475 T HOSTNAME (NIL) -8 NIL NIL NIL) (-503 1174978 1175015 1175056 "HOMOTOP" 1175061 NIL HOMOTOP (NIL T) -9 NIL 1175094 NIL) (-502 1171535 1172910 1172951 "HOAGG" 1173932 NIL HOAGG (NIL T) -9 NIL 1174661 NIL) (-501 1170129 1170528 1171054 "HOAGG-" 1171059 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-500 1163845 1169722 1169872 "HEXADEC" 1169999 T HEXADEC (NIL) -8 NIL NIL NIL) (-499 1162593 1162815 1163078 "HEUGCD" 1163622 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-498 1161669 1162430 1162560 "HELLFDIV" 1162565 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-497 1159851 1161446 1161534 "HEAP" 1161613 NIL HEAP (NIL T) -8 NIL NIL NIL) (-496 1159114 1159403 1159537 "HEADAST" 1159737 T HEADAST (NIL) -8 NIL NIL NIL) (-495 1152957 1159029 1159091 "HDP" 1159096 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-494 1146669 1152592 1152744 "HDMP" 1152858 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-493 1145993 1146133 1146297 "HB" 1146525 T HB (NIL) -7 NIL NIL NIL) (-492 1139385 1145839 1145943 "HASHTBL" 1145948 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-491 1138861 1139106 1139198 "HASAST" 1139313 T HASAST (NIL) -8 NIL NIL NIL) (-490 1136639 1138483 1138665 "HACKPI" 1138699 T HACKPI (NIL) -8 NIL NIL NIL) (-489 1132307 1136492 1136605 "GTSET" 1136610 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-488 1125728 1132185 1132283 "GSTBL" 1132288 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-487 1118115 1124893 1125149 "GSERIES" 1125528 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-486 1117242 1117659 1117687 "GROUP" 1117890 T GROUP (NIL) -9 NIL 1118024 NIL) (-485 1116608 1116767 1117018 "GROUP-" 1117023 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-484 1114975 1115296 1115683 "GROEBSOL" 1116285 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-483 1113875 1114163 1114214 "GRMOD" 1114743 NIL GRMOD (NIL T T) -9 NIL 1114911 NIL) (-482 1113643 1113679 1113807 "GRMOD-" 1113812 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-481 1108933 1109997 1110997 "GRIMAGE" 1112663 T GRIMAGE (NIL) -8 NIL NIL NIL) (-480 1107399 1107660 1107984 "GRDEF" 1108629 T GRDEF (NIL) -7 NIL NIL NIL) (-479 1106843 1106959 1107100 "GRAY" 1107278 T GRAY (NIL) -7 NIL NIL NIL) (-478 1106016 1106422 1106473 "GRALG" 1106626 NIL GRALG (NIL T T) -9 NIL 1106719 NIL) (-477 1105677 1105750 1105913 "GRALG-" 1105918 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-476 1102452 1105260 1105439 "GPOLSET" 1105583 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-475 1101806 1101863 1102121 "GOSPER" 1102389 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-474 1097538 1098244 1098770 "GMODPOL" 1101505 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-473 1096543 1096727 1096965 "GHENSEL" 1097350 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-472 1090699 1091542 1092562 "GENUPS" 1095627 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-471 1090396 1090447 1090536 "GENUFACT" 1090642 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-470 1089808 1089885 1090050 "GENPGCD" 1090314 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-469 1089282 1089317 1089530 "GENMFACT" 1089767 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-468 1087848 1088105 1088412 "GENEEZ" 1089025 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-467 1081720 1087459 1087621 "GDMP" 1087771 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-466 1071063 1075491 1076597 "GCNAALG" 1080703 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-465 1069376 1070238 1070266 "GCDDOM" 1070521 T GCDDOM (NIL) -9 NIL 1070678 NIL) (-464 1068846 1068973 1069188 "GCDDOM-" 1069193 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-463 1067518 1067703 1068007 "GB" 1068625 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-462 1056134 1058464 1060856 "GBINTERN" 1065209 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1053971 1054263 1054684 "GBF" 1055809 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1052752 1052917 1053184 "GBEUCLID" 1053787 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1052101 1052226 1052375 "GAUSSFAC" 1052623 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-458 1050468 1050770 1051084 "GALUTIL" 1051820 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-457 1048776 1049050 1049374 "GALPOLYU" 1050195 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-456 1046141 1046431 1046838 "GALFACTU" 1048473 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-455 1037947 1039446 1041054 "GALFACT" 1044573 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-454 1035335 1035993 1036021 "FVFUN" 1037177 T FVFUN (NIL) -9 NIL 1037897 NIL) (-453 1034601 1034783 1034811 "FVC" 1035102 T FVC (NIL) -9 NIL 1035285 NIL) (-452 1034244 1034426 1034494 "FUNDESC" 1034553 T FUNDESC (NIL) -8 NIL NIL NIL) (-451 1033859 1034041 1034122 "FUNCTION" 1034196 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-450 1031603 1032181 1032647 "FT" 1033413 T FT (NIL) -8 NIL NIL NIL) (-449 1030394 1030904 1031107 "FTEM" 1031420 T FTEM (NIL) -8 NIL NIL NIL) (-448 1028685 1028974 1029371 "FSUPFACT" 1030085 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-447 1027082 1027371 1027703 "FST" 1028373 T FST (NIL) -8 NIL NIL NIL) (-446 1026281 1026387 1026575 "FSRED" 1026964 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-445 1024980 1025236 1025583 "FSPRMELT" 1025996 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-444 1022286 1022724 1023210 "FSPECF" 1024543 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-443 1003351 1012060 1012101 "FS" 1015985 NIL FS (NIL T) -9 NIL 1018274 NIL) (-442 991994 994987 999044 "FS-" 999344 NIL FS- (NIL T T) -8 NIL NIL NIL) (-441 991522 991576 991746 "FSINT" 991935 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-440 989814 990515 990818 "FSERIES" 991301 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-439 988856 988972 989196 "FSCINT" 989694 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-438 985064 987800 987841 "FSAGG" 988211 NIL FSAGG (NIL T) -9 NIL 988470 NIL) (-437 982826 983427 984223 "FSAGG-" 984318 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 981868 982011 982238 "FSAGG2" 982679 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-435 979546 979826 980374 "FS2UPS" 981586 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-434 979180 979223 979352 "FS2" 979497 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 978058 978229 978531 "FS2EXPXP" 979005 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-432 977484 977599 977751 "FRUTIL" 977938 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-431 968897 972979 974337 "FR" 976158 NIL FR (NIL T) -8 NIL NIL NIL) (-430 963911 966586 966626 "FRNAALG" 967946 NIL FRNAALG (NIL T) -9 NIL 968544 NIL) (-429 959584 960660 961935 "FRNAALG-" 962685 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 959222 959265 959392 "FRNAAF2" 959535 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 957597 958071 958367 "FRMOD" 959034 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 955340 955972 956290 "FRIDEAL" 957388 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-425 954531 954618 954909 "FRIDEAL2" 955247 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-424 953664 954078 954119 "FRETRCT" 954124 NIL FRETRCT (NIL T) -9 NIL 954300 NIL) (-423 952776 953007 953358 "FRETRCT-" 953363 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 949850 951060 951119 "FRAMALG" 952001 NIL FRAMALG (NIL T T) -9 NIL 952293 NIL) (-421 947984 948439 949069 "FRAMALG-" 949292 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 941627 947457 947734 "FRAC" 947739 NIL FRAC (NIL T) -8 NIL NIL NIL) (-419 941263 941320 941427 "FRAC2" 941564 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-418 940899 940956 941063 "FR2" 941200 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 935384 938278 938306 "FPS" 939425 T FPS (NIL) -9 NIL 939982 NIL) (-416 934833 934942 935106 "FPS-" 935252 NIL FPS- (NIL T) -8 NIL NIL NIL) (-415 932121 933790 933818 "FPC" 934043 T FPC (NIL) -9 NIL 934185 NIL) (-414 931914 931954 932051 "FPC-" 932056 NIL FPC- (NIL T) -8 NIL NIL NIL) (-413 930704 931402 931443 "FPATMAB" 931448 NIL FPATMAB (NIL T) -9 NIL 931600 NIL) (-412 928943 929446 929793 "FPARFRAC" 930420 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-411 924337 924835 925517 "FORTRAN" 928375 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-410 922053 922553 923092 "FORT" 923818 T FORT (NIL) -7 NIL NIL NIL) (-409 919729 920291 920319 "FORTFN" 921379 T FORTFN (NIL) -9 NIL 922003 NIL) (-408 919493 919543 919571 "FORTCAT" 919630 T FORTCAT (NIL) -9 NIL 919692 NIL) (-407 917599 918109 918499 "FORMULA" 919123 T FORMULA (NIL) -8 NIL NIL NIL) (-406 917387 917417 917486 "FORMULA1" 917563 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-405 916910 916962 917135 "FORDER" 917329 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-404 916006 916170 916363 "FOP" 916737 T FOP (NIL) -7 NIL NIL NIL) (-403 914587 915286 915460 "FNLA" 915888 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-402 913302 913717 913745 "FNCAT" 914205 T FNCAT (NIL) -9 NIL 914465 NIL) (-401 912841 913261 913289 "FNAME" 913294 T FNAME (NIL) -8 NIL NIL NIL) (-400 911377 912340 912368 "FMTC" 912373 T FMTC (NIL) -9 NIL 912409 NIL) (-399 910123 911313 911359 "FMONOID" 911364 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-398 906910 908078 908119 "FMONCAT" 909336 NIL FMONCAT (NIL T) -9 NIL 909941 NIL) (-397 906060 906652 906801 "FM" 906806 NIL FM (NIL T T) -8 NIL NIL NIL) (-396 903484 904130 904158 "FMFUN" 905302 T FMFUN (NIL) -9 NIL 906010 NIL) (-395 902753 902934 902962 "FMC" 903252 T FMC (NIL) -9 NIL 903434 NIL) (-394 899818 900678 900732 "FMCAT" 901927 NIL FMCAT (NIL T T) -9 NIL 902422 NIL) (-393 898684 899584 899684 "FM1" 899763 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-392 896458 896874 897368 "FLOATRP" 898235 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-391 890036 894187 894808 "FLOAT" 895857 T FLOAT (NIL) -8 NIL NIL NIL) (-390 887474 887974 888552 "FLOATCP" 889503 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-389 886122 887066 887107 "FLINEXP" 887112 NIL FLINEXP (NIL T) -9 NIL 887205 NIL) (-388 885276 885511 885839 "FLINEXP-" 885844 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-387 884352 884496 884720 "FLASORT" 885128 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-386 881454 882322 882374 "FLALG" 883601 NIL FLALG (NIL T T) -9 NIL 884068 NIL) (-385 875114 878863 878904 "FLAGG" 880166 NIL FLAGG (NIL T) -9 NIL 880818 NIL) (-384 873840 874179 874669 "FLAGG-" 874674 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 872882 873025 873252 "FLAGG2" 873693 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-382 869719 870727 870786 "FINRALG" 871914 NIL FINRALG (NIL T T) -9 NIL 872422 NIL) (-381 868879 869108 869447 "FINRALG-" 869452 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-380 868245 868484 868512 "FINITE" 868708 T FINITE (NIL) -9 NIL 868815 NIL) (-379 860588 862775 862815 "FINAALG" 866482 NIL FINAALG (NIL T) -9 NIL 867935 NIL) (-378 855920 856970 858114 "FINAALG-" 859493 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-377 855288 855675 855778 "FILE" 855850 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 853932 854270 854324 "FILECAT" 855008 NIL FILECAT (NIL T T) -9 NIL 855224 NIL) (-375 851634 853162 853190 "FIELD" 853230 T FIELD (NIL) -9 NIL 853310 NIL) (-374 850254 850639 851150 "FIELD-" 851155 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-373 848104 848889 849236 "FGROUP" 849940 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-372 847194 847358 847578 "FGLMICPK" 847936 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-371 843026 847119 847176 "FFX" 847181 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-370 842627 842688 842823 "FFSLPE" 842959 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-369 838617 839399 840195 "FFPOLY" 841863 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 838121 838157 838366 "FFPOLY2" 838575 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-367 833967 838040 838103 "FFP" 838108 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-366 829365 833878 833942 "FF" 833947 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-365 824491 828708 828898 "FFNBX" 829219 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-364 819419 823626 823884 "FFNBP" 824345 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-363 814052 818703 818914 "FFNB" 819252 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-362 812884 813082 813397 "FFINTBAS" 813849 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-361 808910 811131 811159 "FFIELDC" 811779 T FFIELDC (NIL) -9 NIL 812155 NIL) (-360 807572 807943 808440 "FFIELDC-" 808445 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-359 807141 807187 807311 "FFHOM" 807514 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-358 804836 805323 805840 "FFF" 806656 NIL FFF (NIL T) -7 NIL NIL NIL) (-357 800454 804578 804679 "FFCGX" 804779 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-356 796076 800186 800293 "FFCGP" 800397 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-355 791259 795803 795911 "FFCG" 796012 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-354 770788 780991 781077 "FFCAT" 786242 NIL FFCAT (NIL T T T) -9 NIL 787693 NIL) (-353 765985 767033 768347 "FFCAT-" 769577 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-352 765396 765439 765674 "FFCAT2" 765936 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-351 754719 758368 759588 "FEXPR" 764248 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-350 753681 754116 754157 "FEVALAB" 754241 NIL FEVALAB (NIL T) -9 NIL 754502 NIL) (-349 752840 753050 753388 "FEVALAB-" 753393 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-348 751406 752223 752426 "FDIV" 752739 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-347 748412 749153 749268 "FDIVCAT" 750836 NIL FDIVCAT (NIL T T T T) -9 NIL 751273 NIL) (-346 748174 748201 748371 "FDIVCAT-" 748376 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-345 747394 747481 747758 "FDIV2" 748081 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 746368 746689 746891 "FCTRDATA" 747212 T FCTRDATA (NIL) -8 NIL NIL NIL) (-343 745054 745313 745602 "FCPAK1" 746099 T FCPAK1 (NIL) -7 NIL NIL NIL) (-342 744153 744554 744695 "FCOMP" 744945 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-341 727858 731303 734841 "FC" 740635 T FC (NIL) -8 NIL NIL NIL) (-340 720151 724179 724219 "FAXF" 726021 NIL FAXF (NIL T) -9 NIL 726713 NIL) (-339 717428 718085 718910 "FAXF-" 719375 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-338 712483 716804 716980 "FARRAY" 717285 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-337 707363 709430 709483 "FAMR" 710506 NIL FAMR (NIL T T) -9 NIL 710966 NIL) (-336 706253 706555 706990 "FAMR-" 706995 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-335 705422 706175 706228 "FAMONOID" 706233 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-334 703194 703904 703957 "FAMONC" 704898 NIL FAMONC (NIL T T) -9 NIL 705284 NIL) (-333 701858 702948 703085 "FAGROUP" 703090 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-332 699653 699972 700375 "FACUTIL" 701539 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-331 698752 698937 699159 "FACTFUNC" 699463 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-330 691174 698055 698254 "EXPUPXS" 698608 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-329 688657 689197 689783 "EXPRTUBE" 690608 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-328 684928 685520 686250 "EXPRODE" 687996 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-327 670412 683577 684006 "EXPR" 684532 NIL EXPR (NIL T) -8 NIL NIL NIL) (-326 664966 665553 666359 "EXPR2UPS" 669710 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-325 664598 664655 664764 "EXPR2" 664903 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-324 655595 663749 664040 "EXPEXPAN" 664434 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-323 655395 655552 655581 "EXIT" 655586 T EXIT (NIL) -8 NIL NIL NIL) (-322 654875 655119 655210 "EXITAST" 655324 T EXITAST (NIL) -8 NIL NIL NIL) (-321 654502 654564 654677 "EVALCYC" 654807 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-320 654043 654161 654202 "EVALAB" 654372 NIL EVALAB (NIL T) -9 NIL 654476 NIL) (-319 653524 653646 653867 "EVALAB-" 653872 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-318 650878 652180 652208 "EUCDOM" 652763 T EUCDOM (NIL) -9 NIL 653113 NIL) (-317 649283 649725 650315 "EUCDOM-" 650320 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-316 636822 639581 642331 "ESTOOLS" 646553 T ESTOOLS (NIL) -7 NIL NIL NIL) (-315 636454 636511 636620 "ESTOOLS2" 636759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-314 636205 636247 636327 "ESTOOLS1" 636406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-313 630228 631836 631864 "ES" 634632 T ES (NIL) -9 NIL 636042 NIL) (-312 625175 626462 628279 "ES-" 628443 NIL ES- (NIL T) -8 NIL NIL NIL) (-311 621549 622310 623090 "ESCONT" 624415 T ESCONT (NIL) -7 NIL NIL NIL) (-310 621294 621326 621408 "ESCONT1" 621511 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-309 620969 621019 621119 "ES2" 621238 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-308 620599 620657 620766 "ES1" 620905 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-307 619815 619944 620120 "ERROR" 620443 T ERROR (NIL) -7 NIL NIL NIL) (-306 613213 619674 619765 "EQTBL" 619770 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-305 605716 608527 609976 "EQ" 611797 NIL -2155 (NIL T) -8 NIL NIL NIL) (-304 605348 605405 605514 "EQ2" 605653 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-303 600639 601686 602779 "EP" 604287 NIL EP (NIL T) -7 NIL NIL NIL) (-302 599239 599530 599836 "ENV" 600353 T ENV (NIL) -8 NIL NIL NIL) (-301 598319 598873 598901 "ENTIRER" 598906 T ENTIRER (NIL) -9 NIL 598952 NIL) (-300 595013 596501 596862 "EMR" 598127 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-299 594143 594328 594382 "ELTAGG" 594762 NIL ELTAGG (NIL T T) -9 NIL 594973 NIL) (-298 593862 593924 594065 "ELTAGG-" 594070 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-297 593626 593655 593709 "ELTAB" 593793 NIL ELTAB (NIL T T) -9 NIL 593845 NIL) (-296 592752 592898 593097 "ELFUTS" 593477 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-295 592494 592550 592578 "ELEMFUN" 592683 T ELEMFUN (NIL) -9 NIL NIL NIL) (-294 592364 592385 592453 "ELEMFUN-" 592458 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-293 587153 590406 590447 "ELAGG" 591387 NIL ELAGG (NIL T) -9 NIL 591850 NIL) (-292 585438 585872 586535 "ELAGG-" 586540 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-291 584750 584887 585043 "ELABOR" 585302 T ELABOR (NIL) -8 NIL NIL NIL) (-290 583411 583690 583984 "ELABEXPR" 584476 T ELABEXPR (NIL) -8 NIL NIL NIL) (-289 576245 578048 578877 "EFUPXS" 582686 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-288 569693 571494 572305 "EFULS" 575520 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-287 567178 567536 568008 "EFSTRUC" 569325 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-286 556969 558535 560083 "EF" 565693 NIL EF (NIL T T) -7 NIL NIL NIL) (-285 556043 556454 556603 "EAB" 556840 T EAB (NIL) -8 NIL NIL NIL) (-284 555225 556002 556030 "E04UCFA" 556035 T E04UCFA (NIL) -8 NIL NIL NIL) (-283 554407 555184 555212 "E04NAFA" 555217 T E04NAFA (NIL) -8 NIL NIL NIL) (-282 553589 554366 554394 "E04MBFA" 554399 T E04MBFA (NIL) -8 NIL NIL NIL) (-281 552771 553548 553576 "E04JAFA" 553581 T E04JAFA (NIL) -8 NIL NIL NIL) (-280 551955 552730 552758 "E04GCFA" 552763 T E04GCFA (NIL) -8 NIL NIL NIL) (-279 551139 551914 551942 "E04FDFA" 551947 T E04FDFA (NIL) -8 NIL NIL NIL) (-278 550321 551098 551126 "E04DGFA" 551131 T E04DGFA (NIL) -8 NIL NIL NIL) (-277 544494 545846 547210 "E04AGNT" 548977 T E04AGNT (NIL) -7 NIL NIL NIL) (-276 543252 543795 543835 "DVARCAT" 544176 NIL DVARCAT (NIL T) -9 NIL 544339 NIL) (-275 542456 542668 542982 "DVARCAT-" 542987 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-274 535317 542255 542384 "DSMP" 542389 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-273 533740 534459 534500 "DSEXT" 534863 NIL DSEXT (NIL T) -9 NIL 535157 NIL) (-272 532025 532453 533119 "DSEXT-" 533124 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-271 526806 527970 529038 "DROPT" 530977 T DROPT (NIL) -8 NIL NIL NIL) (-270 526471 526530 526628 "DROPT1" 526741 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-269 521586 522712 523849 "DROPT0" 525354 T DROPT0 (NIL) -7 NIL NIL NIL) (-268 519931 520256 520642 "DRAWPT" 521220 T DRAWPT (NIL) -7 NIL NIL NIL) (-267 514518 515441 516520 "DRAW" 518905 NIL DRAW (NIL T) -7 NIL NIL NIL) (-266 514151 514204 514322 "DRAWHACK" 514459 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-265 512882 513151 513442 "DRAWCX" 513880 T DRAWCX (NIL) -7 NIL NIL NIL) (-264 512397 512466 512617 "DRAWCURV" 512808 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-263 502865 504827 506942 "DRAWCFUN" 510302 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-262 499604 501530 501571 "DQAGG" 502200 NIL DQAGG (NIL T) -9 NIL 502474 NIL) (-261 487069 493815 493898 "DPOLCAT" 495750 NIL DPOLCAT (NIL T T T T) -9 NIL 496295 NIL) (-260 481906 483254 485212 "DPOLCAT-" 485217 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-259 475253 481767 481865 "DPMO" 481870 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-258 468503 475033 475200 "DPMM" 475205 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-257 468073 468287 468376 "DOMTMPLT" 468434 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-256 467506 467875 467955 "DOMCTOR" 468013 T DOMCTOR (NIL) -8 NIL NIL NIL) (-255 466718 466986 467137 "DOMAIN" 467375 T DOMAIN (NIL) -8 NIL NIL NIL) (-254 460430 466353 466505 "DMP" 466619 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-253 458375 459497 459538 "DMEXT" 459543 NIL DMEXT (NIL T) -9 NIL 459719 NIL) (-252 457975 458031 458175 "DLP" 458313 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 451800 457302 457492 "DLIST" 457817 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 448572 450625 450666 "DLAGG" 451216 NIL DLAGG (NIL T) -9 NIL 451446 NIL) (-249 447234 447898 447926 "DIVRING" 448018 T DIVRING (NIL) -9 NIL 448101 NIL) (-248 446471 446661 446961 "DIVRING-" 446966 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 444573 444930 445336 "DISPLAY" 446085 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 438436 444487 444550 "DIRPROD" 444555 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 437284 437487 437752 "DIRPROD2" 438229 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 425959 431995 432048 "DIRPCAT" 432306 NIL DIRPCAT (NIL NIL T) -9 NIL 433181 NIL) (-243 423285 423927 424808 "DIRPCAT-" 425145 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 422572 422732 422918 "DIOSP" 423119 T DIOSP (NIL) -7 NIL NIL NIL) (-241 419202 421456 421497 "DIOPS" 421931 NIL DIOPS (NIL T) -9 NIL 422160 NIL) (-240 418751 418865 419056 "DIOPS-" 419061 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 417802 418430 418458 "DIFRING" 418463 T DIFRING (NIL) -9 NIL 418485 NIL) (-238 417474 417548 417576 "DIFFSPC" 417695 T DIFFSPC (NIL) -9 NIL 417770 NIL) (-237 417119 417197 417349 "DIFFSPC-" 417354 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 416175 416653 416694 "DIFFMOD" 416699 NIL DIFFMOD (NIL T) -9 NIL 416797 NIL) (-235 415883 415928 415969 "DIFFDOM" 416090 NIL DIFFDOM (NIL T) -9 NIL 416158 NIL) (-234 415736 415760 415844 "DIFFDOM-" 415849 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 413668 414940 414981 "DIFEXT" 414986 NIL DIFEXT (NIL T) -9 NIL 415139 NIL) (-232 410918 413172 413213 "DIAGG" 413218 NIL DIAGG (NIL T) -9 NIL 413238 NIL) (-231 410302 410459 410711 "DIAGG-" 410716 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-230 405674 409261 409538 "DHMATRIX" 410071 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-229 401286 402195 403205 "DFSFUN" 404684 T DFSFUN (NIL) -7 NIL NIL NIL) (-228 396364 400217 400529 "DFLOAT" 400994 T DFLOAT (NIL) -8 NIL NIL NIL) (-227 394627 394908 395297 "DFINTTLS" 396072 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-226 391656 392648 393048 "DERHAM" 394293 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-225 389460 391431 391520 "DEQUEUE" 391600 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-224 388714 388847 389030 "DEGRED" 389322 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-223 385144 385889 386735 "DEFINTRF" 387942 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-222 382699 383168 383760 "DEFINTEF" 384663 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-221 382049 382319 382434 "DEFAST" 382604 T DEFAST (NIL) -8 NIL NIL NIL) (-220 375765 381642 381792 "DECIMAL" 381919 T DECIMAL (NIL) -8 NIL NIL NIL) (-219 373277 373735 374241 "DDFACT" 375309 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-218 372873 372916 373067 "DBLRESP" 373228 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-217 372176 372643 372734 "DBASIS" 372822 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 254936 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249600 251568 251609 "CLAGG" 252538 NIL CLAGG (NIL T) -9 NIL 253074 NIL) (-151 248022 248479 249062 "CLAGG-" 249067 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247566 247651 247791 "CINTSLPE" 247931 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 245067 245538 246086 "CHVAR" 247094 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 244227 244781 244809 "CHARZ" 244814 T CHARZ (NIL) -9 NIL 244829 NIL) (-147 243981 244021 244099 "CHARPOL" 244181 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 243025 243612 243640 "CHARNZ" 243687 T CHARNZ (NIL) -9 NIL 243743 NIL) (-145 240931 241679 242032 "CHAR" 242692 T CHAR (NIL) -8 NIL NIL NIL) (-144 240657 240718 240746 "CFCAT" 240857 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239898 240009 240192 "CDEN" 240541 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235863 239051 239331 "CCLASS" 239638 T CCLASS (NIL) -8 NIL NIL NIL) (-141 235114 235271 235448 "CATEGORY" 235706 T -10 (NIL) -8 NIL NIL NIL) (-140 234687 235033 235081 "CATCTOR" 235086 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 234138 234390 234488 "CATAST" 234609 T CATAST (NIL) -8 NIL NIL NIL) (-138 233614 233859 233951 "CASEAST" 234066 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228752 229771 230515 "CARTEN" 232926 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227860 228008 228229 "CARTEN2" 228599 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 226176 227010 227267 "CARD" 227623 T CARD (NIL) -8 NIL NIL NIL) (-134 225752 225980 226055 "CAPSLAST" 226121 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 225242 225450 225478 "CACHSET" 225610 T CACHSET (NIL) -9 NIL 225688 NIL) (-132 224698 225020 225048 "CABMON" 225098 T CABMON (NIL) -9 NIL 225154 NIL) (-131 224171 224402 224512 "BYTEORD" 224608 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 223148 223700 223842 "BYTE" 224005 T BYTE (NIL) -8 NIL NIL 224127) (-129 218501 222653 222825 "BYTEBUF" 222996 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 216013 218193 218300 "BTREE" 218427 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213465 215661 215783 "BTOURN" 215923 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210810 212907 212948 "BTCAT" 213016 NIL BTCAT (NIL T) -9 NIL 213093 NIL) (-125 210477 210557 210706 "BTCAT-" 210711 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205842 209723 209751 "BTAGG" 209865 T BTAGG (NIL) -9 NIL 209975 NIL) (-123 205332 205457 205663 "BTAGG-" 205668 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 202330 204610 204825 "BSTREE" 205149 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201468 201594 201778 "BRILL" 202186 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 198095 200166 200207 "BRAGG" 200856 NIL BRAGG (NIL T) -9 NIL 201114 NIL) (-119 196624 197030 197585 "BRAGG-" 197590 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189540 195968 196153 "BPADICRT" 196471 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187855 189477 189522 "BPADIC" 189527 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187553 187583 187697 "BOUNDZRO" 187819 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182781 183979 184891 "BOP" 186661 T BOP (NIL) -8 NIL NIL NIL) (-114 180562 180966 181441 "BOP1" 182339 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 180263 180324 180352 "BOOLE" 180463 T BOOLE (NIL) -9 NIL 180545 NIL) (-112 179088 179837 179986 "BOOLEAN" 180134 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 178353 178757 178811 "BMODULE" 178816 NIL BMODULE (NIL T T) -9 NIL 178881 NIL) (-110 174154 178151 178224 "BITS" 178300 T BITS (NIL) -8 NIL NIL NIL) (-109 173575 173694 173834 "BINDING" 174034 T BINDING (NIL) -8 NIL NIL NIL) (-108 167294 173170 173319 "BINARY" 173446 T BINARY (NIL) -8 NIL NIL NIL) (-107 165049 166521 166562 "BGAGG" 166822 NIL BGAGG (NIL T) -9 NIL 166959 NIL) (-106 164880 164912 165003 "BGAGG-" 165008 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163951 164264 164469 "BFUNCT" 164695 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162641 162819 163107 "BEZOUT" 163775 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 159113 161493 161823 "BBTREE" 162344 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158714 158792 158820 "BASTYPE" 158997 T BASTYPE (NIL) -9 NIL 159096 NIL) (-101 158390 158471 158606 "BASTYPE-" 158611 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157824 157900 158052 "BALFACT" 158301 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156680 157239 157425 "AUTOMOR" 157669 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156406 156411 156437 "ATTREG" 156442 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154658 155103 155455 "ATTRBUT" 156072 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154266 154486 154552 "ATTRAST" 154610 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153802 153915 153941 "ATRIG" 154142 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153611 153652 153739 "ATRIG-" 153744 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153242 153428 153454 "ASTCAT" 153459 T ASTCAT (NIL) -9 NIL 153489 NIL) (-92 152969 153028 153147 "ASTCAT-" 153152 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151121 152745 152833 "ASTACK" 152912 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149626 149923 150288 "ASSOCEQ" 150803 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148658 149285 149409 "ASP9" 149533 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148421 148606 148645 "ASP8" 148650 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147289 148026 148168 "ASP80" 148310 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146187 146924 147056 "ASP7" 147188 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145141 145864 145982 "ASP78" 146100 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144110 144821 144938 "ASP77" 145055 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 143022 143748 143879 "ASP74" 144010 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141922 142657 142789 "ASP73" 142921 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 141026 141748 141848 "ASP6" 141853 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139973 140703 140821 "ASP55" 140939 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138922 139647 139766 "ASP50" 139885 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138010 138623 138733 "ASP4" 138843 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137098 137711 137821 "ASP49" 137931 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135882 136637 136805 "ASP42" 136987 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134659 135415 135585 "ASP41" 135769 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133609 134336 134454 "ASP35" 134572 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133374 133557 133596 "ASP34" 133601 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133111 133178 133254 "ASP33" 133329 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132005 132746 132878 "ASP31" 133010 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131770 131953 131992 "ASP30" 131997 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131505 131574 131650 "ASP29" 131725 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131270 131453 131492 "ASP28" 131497 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131035 131218 131257 "ASP27" 131262 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130119 130733 130844 "ASP24" 130955 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129196 129921 130033 "ASP20" 130038 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128284 128897 129007 "ASP1" 129117 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127227 127958 128077 "ASP19" 128196 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126964 127031 127107 "ASP12" 127182 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125816 126563 126707 "ASP10" 126851 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123670 125660 125751 "ARRAY2" 125756 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119438 123318 123432 "ARRAY1" 123587 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118470 118643 118864 "ARRAY12" 119261 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112757 114672 114747 "ARR2CAT" 117377 NIL ARR2CAT (NIL T T T) -9 NIL 118135 NIL) (-56 110191 110935 111889 "ARR2CAT-" 111894 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109508 109818 109943 "ARITY" 110084 T ARITY (NIL) -8 NIL NIL NIL) (-54 108284 108436 108735 "APPRULE" 109344 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107935 107983 108102 "APPLYORE" 108230 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107289 107528 107648 "ANY" 107833 T ANY (NIL) -8 NIL NIL NIL) (-51 106567 106690 106847 "ANY1" 107163 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104097 105004 105331 "ANTISYM" 106291 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103589 103804 103900 "ANON" 104019 T ANON (NIL) -8 NIL NIL NIL) (-48 97589 102128 102582 "AN" 103153 T AN (NIL) -8 NIL NIL NIL) (-47 93473 94861 94912 "AMR" 95660 NIL AMR (NIL T T) -9 NIL 96260 NIL) (-46 92585 92806 93169 "AMR-" 93174 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 77030 92502 92563 "ALIST" 92568 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73835 76624 76793 "ALGSC" 76948 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70391 70945 71552 "ALGPKG" 73275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69668 69769 69953 "ALGMFACT" 70277 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65703 66282 66876 "ALGMANIP" 69252 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55914 65329 65479 "ALGFF" 65636 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55110 55241 55420 "ALGFACT" 55772 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54037 54637 54675 "ALGEBRA" 54680 NIL ALGEBRA (NIL T) -9 NIL 54721 NIL) (-37 53755 53814 53946 "ALGEBRA-" 53951 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35692 51592 51644 "ALAGG" 51780 NIL ALAGG (NIL T T) -9 NIL 51941 NIL) (-35 35228 35341 35367 "AHYP" 35568 T AHYP (NIL) -9 NIL NIL NIL) (-34 34159 34407 34433 "AGG" 34932 T AGG (NIL) -9 NIL 35211 NIL) (-33 33593 33755 33969 "AGG-" 33974 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31399 31822 32227 "AF" 33235 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30879 31124 31214 "ADDAST" 31327 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30147 30406 30562 "ACPLOT" 30741 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18770 27079 27117 "ACFS" 27724 NIL ACFS (NIL T) -9 NIL 27963 NIL) (-28 16797 17287 18049 "ACFS-" 18054 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12901 14830 14856 "ACF" 15735 T ACF (NIL) -9 NIL 16148 NIL) (-26 11605 11939 12432 "ACF-" 12437 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11163 11358 11384 "ABELSG" 11476 T ABELSG (NIL) -9 NIL 11541 NIL) (-24 11030 11055 11121 "ABELSG-" 11126 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10359 10646 10672 "ABELMON" 10842 T ABELMON (NIL) -9 NIL 10954 NIL) (-22 10023 10107 10245 "ABELMON-" 10250 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9357 9729 9755 "ABELGRP" 9827 T ABELGRP (NIL) -9 NIL 9902 NIL) (-20 8820 8949 9165 "ABELGRP-" 9170 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8082 8121 "A1AGG" 8126 NIL A1AGG (NIL T) -9 NIL 8166 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 436640d0..94992f9d 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,31 +1,54 @@
 
-(731775 . 3486967789)        
+(732177 . 3487133929)        
 (((*1 *2 *3)
-  (-12 (-4 *4 (-568)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -1701 *4)))
-   (-5 *1 (-991 *4 *3)) (-4 *3 (-1265 *4))))) 
-(((*1 *2 *3 *3)
-  (-12 (-5 *3 (-657 *4)) (-4 *4 (-374)) (-4 *2 (-1265 *4))
-   (-5 *1 (-942 *4 *2))))) 
-(((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862))
-      (-4 *7 (-1087 *4 *5 *6)) (-5 *2 (-112))
-      (-5 *1 (-1010 *4 *5 *6 *7 *3)) (-4 *3 (-1093 *4 *5 *6 *7))))
- ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-806)) (-4 *6 (-862))
-      (-4 *7 (-1087 *4 *5 *6)) (-5 *2 (-112))
-      (-5 *1 (-1129 *4 *5 *6 *7 *3)) (-4 *3 (-1093 *4 *5 *6 *7))))) 
-(((*1 *1) (-5 *1 (-816)))) 
-(((*1 *1 *1 *1 *2)
-  (|partial| -12 (-5 *2 (-112)) (-5 *1 (-607 *3)) (-4 *3 (-1071))))) 
+  (-12 (-4 *4 (-13 (-375) (-148) (-1063 (-420 (-577)))))
+   (-4 *5 (-1268 *4))
+   (-5 *2 (-660 (-2 (|:| |deg| (-787)) (|:| -3994 *5))))
+   (-5 *1 (-825 *4 *5 *3 *6)) (-4 *3 (-672 *5))
+   (-4 *6 (-672 (-420 *5)))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-354 *3 *4 *5)) (-4 *3 (-1246)) (-4 *4 (-1268 *3))
+   (-4 *5 (-1268 (-420 *4))) (-5 *2 (-705 (-420 *4)))))) 
+(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-420 (-975 *5))) (-5 *4 (-1201))
+   (-4 *5 (-13 (-318) (-148))) (-5 *2 (-660 (-305 (-327 *5))))
+   (-5 *1 (-1154 *5))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-420 (-975 *4))) (-4 *4 (-13 (-318) (-148)))
+   (-5 *2 (-660 (-305 (-327 *4)))) (-5 *1 (-1154 *4))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-305 (-420 (-975 *5)))) (-5 *4 (-1201))
+   (-4 *5 (-13 (-318) (-148))) (-5 *2 (-660 (-305 (-327 *5))))
+   (-5 *1 (-1154 *5))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-305 (-420 (-975 *4)))) (-4 *4 (-13 (-318) (-148)))
+   (-5 *2 (-660 (-305 (-327 *4)))) (-5 *1 (-1154 *4))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-660 (-420 (-975 *5)))) (-5 *4 (-660 (-1201)))
+   (-4 *5 (-13 (-318) (-148))) (-5 *2 (-660 (-660 (-305 (-327 *5)))))
+   (-5 *1 (-1154 *5))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-660 (-420 (-975 *4)))) (-4 *4 (-13 (-318) (-148)))
+   (-5 *2 (-660 (-660 (-305 (-327 *4))))) (-5 *1 (-1154 *4))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-660 (-305 (-420 (-975 *5))))) (-5 *4 (-660 (-1201)))
+   (-4 *5 (-13 (-318) (-148))) (-5 *2 (-660 (-660 (-305 (-327 *5)))))
+   (-5 *1 (-1154 *5))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-660 (-305 (-420 (-975 *4)))))
+   (-4 *4 (-13 (-318) (-148))) (-5 *2 (-660 (-660 (-305 (-327 *4)))))
+   (-5 *1 (-1154 *4))))) 
 (((*1 *2 *3 *4 *3 *4 *3)
-  (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *2 (-1057))
-   (-5 *1 (-769))))) 
+  (-12 (-5 *3 (-577)) (-5 *4 (-705 (-228))) (-5 *2 (-1060))
+   (-5 *1 (-772))))) 
+(((*1 *2) (-12 (-5 *2 (-927 (-577))) (-5 *1 (-940))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227)))
-     (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227))
-     (|:| |relerr| (-227))))
+    (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228)))
+     (|:| -4071 (-1119 (-859 (-228)))) (|:| |abserr| (-228))
+     (|:| |relerr| (-228))))
    (-5 *2
     (-2
      (|:| |endPointContinuity|
@@ -39,10476 +62,9980 @@
            (|:| |notEvaluated|
                 "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1179 (-227)))
+          (-3 (|:| |str| (-1182 (-228)))
            (|:| |notEvaluated|
                 "Internal singularities not yet evaluated")))
-     (|:| -1685
+     (|:| -4071
           (-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 *3 *3 *4 *5 *5 *5 *3)
-  (-12 (-5 *3 (-576)) (-5 *4 (-1180)) (-5 *5 (-702 (-227)))
-   (-5 *2 (-1057)) (-5 *1 (-760))))) 
+   (-5 *1 (-572))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *1 (-692 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-1122))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2))
-   (-4 *2 (-13 (-442 *3) (-1024)))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-336 *3 *2)) (-4 *3 (-1071)) (-4 *2 (-805))))
- ((*1 *2 *1) (-12 (-4 *1 (-721 *3)) (-4 *3 (-1071)) (-5 *2 (-784))))
- ((*1 *2 *1) (-12 (-4 *1 (-867 *3)) (-4 *3 (-1071)) (-5 *2 (-784))))
- ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-657 *6)) (-4 *1 (-969 *4 *5 *6)) (-4 *4 (-1071))
-   (-4 *5 (-806)) (-4 *6 (-862)) (-5 *2 (-657 (-784)))))
+  (-12 (-5 *1 (-695 *2 *3)) (-4 *2 (-1125)) (-4 *3 (-1125))))) 
+(((*1 *2 *3 *2)
+  (-12 (-5 *2 (-660 (-1119 (-391)))) (-5 *3 (-660 (-271)))
+   (-5 *1 (-269))))
+ ((*1 *1 *2) (-12 (-5 *2 (-660 (-1119 (-391)))) (-5 *1 (-271))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-660 (-1119 (-391)))) (-5 *1 (-481))))
+ ((*1 *2 *1) (-12 (-5 *2 (-660 (-1119 (-391)))) (-5 *1 (-481))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-944)) (-5 *2 (-1203 (-420 (-577)))) (-5 *1 (-192))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1237 *3)) (-4 *3 (-999))))) 
+(((*1 *1 *1 *2) (-12 (-4 *1 (-1037)) (-5 *2 (-880))))) 
+(((*1 *2 *1 *1)
+  (-12 (-5 *2 (-660 (-305 *4))) (-5 *1 (-640 *3 *4 *5)) (-4 *3 (-865))
+   (-4 *4 (-13 (-174) (-733 (-420 (-577))))) (-14 *5 (-944))))) 
+(((*1 *2 *3)
+  (-12 (-4 *2 (-1268 *4)) (-5 *1 (-825 *4 *2 *3 *5))
+   (-4 *4 (-13 (-375) (-148) (-1063 (-420 (-577))))) (-4 *3 (-672 *2))
+   (-4 *5 (-672 (-420 *2)))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-354 *3 *4 *5)) (-4 *3 (-1246)) (-4 *4 (-1268 *3))
+   (-4 *5 (-1268 (-420 *4))) (-5 *2 (-705 (-420 *4)))))) 
+(((*1 *2 *2 *2 *2 *2 *2)
+  (-12 (-4 *2 (-13 (-375) (-10 -8 (-15 ** ($ $ (-420 (-577)))))))
+   (-5 *1 (-1153 *3 *2)) (-4 *3 (-1268 *2))))) 
+(((*1 *2 *3 *4 *3 *3 *3 *3 *4 *3)
+  (-12 (-5 *3 (-577)) (-5 *4 (-705 (-171 (-228)))) (-5 *2 (-1060))
+   (-5 *1 (-772))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-660 (-577))) (-5 *2 (-927 (-577))) (-5 *1 (-940))))
+ ((*1 *2) (-12 (-5 *2 (-927 (-577))) (-5 *1 (-940))))) 
+(((*1 *2 *1 *3 *4 *4 *5)
+  (-12 (-5 *3 (-966 (-228))) (-5 *4 (-892)) (-5 *5 (-944))
+   (-5 *2 (-1297)) (-5 *1 (-481))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-969 *4 *5 *3)) (-4 *4 (-1071)) (-4 *5 (-806))
-   (-4 *3 (-862)) (-5 *2 (-784))))) 
-(((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-657 *6)) (-4 *6 (-1087 *3 *4 *5))
-      (-4 *3 (-568)) (-4 *4 (-806)) (-4 *5 (-862))
-      (-5 *1 (-1302 *3 *4 *5 *6))))
- ((*1 *1 *2 *3 *4)
-  (|partial| -12 (-5 *2 (-657 *8)) (-5 *3 (-1 (-112) *8 *8))
-      (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1087 *5 *6 *7)) (-4 *5 (-568))
-      (-4 *6 (-806)) (-4 *7 (-862)) (-5 *1 (-1302 *5 *6 *7 *8))))) 
-(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *3)
-  (-12 (-5 *3 (-576)) (-5 *4 (-702 (-227))) (-5 *2 (-1057))
-   (-5 *1 (-765))))) 
+  (-12 (-5 *3 (-966 (-228))) (-5 *2 (-1297)) (-5 *1 (-481))))
+ ((*1 *2 *1 *3 *4 *4 *5)
+  (-12 (-5 *3 (-660 (-966 (-228)))) (-5 *4 (-892)) (-5 *5 (-944))
+   (-5 *2 (-1297)) (-5 *1 (-481))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1292 (-705 *4))) (-4 *4 (-174))
+   (-5 *2 (-1292 (-705 (-975 *4)))) (-5 *1 (-191 *4))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-1129)) (-5 *3 (-790)) (-5 *1 (-52))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-52))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-250 *2)) (-4 *2 (-1242))))
+ ((*1 *1 *1)
+  (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809))
+   (-4 *4 (-865))))
+ ((*1 *1 *1) (-12 (-4 *1 (-1280 *2)) (-4 *2 (-1242))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173))))
+ ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1237 *3)) (-4 *3 (-999))))) 
 (((*1 *2 *1)
-  (-12 (-4 *2 (-969 *3 *5 *4)) (-5 *1 (-1009 *3 *4 *5 *2))
-   (-4 *3 (-464)) (-4 *4 (-862)) (-4 *5 (-806))))) 
-(((*1 *2 *3 *2)
-  (-12 (-5 *2 (-112)) (-5 *3 (-657 (-270))) (-5 *1 (-268))))
- ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-270))))) 
-(((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-731 *2)) (-4 *2 (-374))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-565))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-419 *5)) (-4 *5 (-1265 *4)) (-4 *4 (-568))
-   (-4 *4 (-1071)) (-4 *2 (-1280 *4)) (-5 *1 (-1283 *4 *5 *6 *2))
-   (-4 *6 (-669 *5))))) 
+  (-12 (-4 *3 (-1242)) (-5 *2 (-660 *1)) (-4 *1 (-1035 *3))))) 
+(((*1 *2 *3 *4 *5 *6 *7 *6)
+  (|partial| -12
+      (-5 *5
+       (-2 (|:| |contp| *3)
+        (|:| -3363 (-660 (-2 (|:| |irr| *10) (|:| -3504 (-577)))))))
+      (-5 *6 (-660 *3)) (-5 *7 (-660 *8)) (-4 *8 (-865)) (-4 *3 (-318))
+      (-4 *10 (-972 *3 *9 *8)) (-4 *9 (-809))
+      (-5 *2
+       (-2 (|:| |polfac| (-660 *10)) (|:| |correct| *3)
+        (|:| |corrfact| (-660 (-1197 *3)))))
+      (-5 *1 (-638 *8 *9 *3 *10)) (-5 *4 (-660 (-1197 *3)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-374))
-   (-5 *2
-    (-2 (|:| A (-702 *5))
-     (|:| |eqs|
-          (-657
-           (-2 (|:| C (-702 *5)) (|:| |g| (-1289 *5)) (|:| -3989 *6)
-            (|:| |rh| *5))))))
-   (-5 *1 (-826 *5 *6)) (-5 *3 (-702 *5)) (-5 *4 (-1289 *5))
-   (-4 *6 (-669 *5))))
+  (-12 (-4 *2 (-1268 *4)) (-5 *1 (-823 *4 *2 *3 *5))
+   (-4 *4 (-13 (-375) (-148) (-1063 (-420 (-577))))) (-4 *3 (-672 *2))
+   (-4 *5 (-672 (-420 *2)))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-374)) (-4 *6 (-669 *5))
-   (-5 *2 (-2 (|:| -3750 (-702 *6)) (|:| |vec| (-1289 *5))))
-   (-5 *1 (-826 *5 *6)) (-5 *3 (-702 *6)) (-5 *4 (-1289 *5))))) 
+  (-12 (-4 *2 (-1268 *4)) (-5 *1 (-823 *4 *2 *5 *3))
+   (-4 *4 (-13 (-375) (-148) (-1063 (-420 (-577))))) (-4 *5 (-672 *2))
+   (-4 *3 (-672 (-420 *2)))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-354 *3 *4 *5)) (-4 *3 (-1246)) (-4 *4 (-1268 *3))
+   (-4 *5 (-1268 (-420 *4))) (-5 *2 (-705 (-420 *4)))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-660 (-271))) (-5 *1 (-1293))))
+ ((*1 *2 *1) (-12 (-5 *2 (-660 (-271))) (-5 *1 (-1293))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-660 (-271))) (-5 *1 (-1294))))
+ ((*1 *2 *1) (-12 (-5 *2 (-660 (-271))) (-5 *1 (-1294))))) 
+(((*1 *2 *2 *2 *2 *2)
+  (-12 (-4 *2 (-13 (-375) (-10 -8 (-15 ** ($ $ (-420 (-577)))))))
+   (-5 *1 (-1153 *3 *2)) (-4 *3 (-1268 *2))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1289 *1)) (-4 *1 (-378 *4)) (-4 *4 (-174))
-   (-5 *2 (-702 *4))))
- ((*1 *2)
-  (-12 (-4 *4 (-174)) (-5 *2 (-702 *4)) (-5 *1 (-428 *3 *4))
-   (-4 *3 (-429 *4))))
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-(((*1 *2 *1) (-12 (-5 *2 (-1126)) (-5 *1 (-52))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-249 *2)) (-4 *2 (-1239))))
- ((*1 *1 *1)
-  (-12 (-4 *1 (-1087 *2 *3 *4)) (-4 *2 (-1071)) (-4 *3 (-806))
-   (-4 *4 (-862))))
- ((*1 *1 *1) (-12 (-4 *1 (-1277 *2)) (-4 *2 (-1239))))) 
-(((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1198)) (-4 *4 (-568)) (-5 *1 (-159 *4 *2))
-   (-4 *2 (-442 *4))))
- ((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1114 *2)) (-4 *2 (-442 *4)) (-4 *4 (-568))
-   (-5 *1 (-159 *4 *2))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1114 *1)) (-4 *1 (-161))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1198))))) 
-(((*1 *1 *2 *3)
-  (-12 (-5 *2 (-480)) (-5 *3 (-657 (-270))) (-5 *1 (-1290))))
- ((*1 *1 *1) (-5 *1 (-1290)))) 
-(((*1 *2 *3 *3 *3 *4 *5 *5 *6)
-  (-12 (-5 *3 (-1 (-227) (-227) (-227)))
-   (-5 *4 (-3 (-1 (-227) (-227) (-227) (-227)) "undefined"))
-   (-5 *5 (-1116 (-227))) (-5 *6 (-657 (-270))) (-5 *2 (-1155 (-227)))
-   (-5 *1 (-710))))
- ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *3 (-1 (-963 (-227)) (-227) (-227))) (-5 *4 (-1116 (-227)))
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- ((*1 *2 *2 *3 *4 *4 *5)
-  (-12 (-5 *2 (-1155 (-227))) (-5 *3 (-1 (-963 (-227)) (-227) (-227)))
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-(((*1 *1 *1 *1) (-4 *1 (-989)))) 
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-(((*1 *1 *1 *2) (-12 (-5 *2 (-657 (-270))) (-5 *1 (-1290))))
- ((*1 *2 *1) (-12 (-5 *2 (-657 (-270))) (-5 *1 (-1290))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-657 (-270))) (-5 *1 (-1291))))
- ((*1 *2 *1) (-12 (-5 *2 (-657 (-270))) (-5 *1 (-1291))))) 
+  (-12 (-5 *3 (-660 (-577))) (-5 *2 (-927 (-577))) (-5 *1 (-940))))
+ ((*1 *2) (-12 (-5 *2 (-927 (-577))) (-5 *1 (-940))))) 
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+  (-12 (-5 *3 (-577)) (-5 *4 (-112)) (-5 *5 (-705 (-171 (-228))))
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+(((*1 *2 *1 *3)
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+   (-4 *3 (-999))))) 
+(((*1 *2 *1 *1)
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 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-59 *6)) (-4 *6 (-1239))
-   (-4 *5 (-1239)) (-5 *2 (-59 *5)) (-5 *1 (-58 *6 *5))))
- ((*1 *2 *3 *4 *5)
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- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *5 *6 *5)) (-4 *6 (-1239)) (-4 *5 (-1239))
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- ((*1 *2 *3 *4 *5)
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-   (-4 *2 (-437 *5)) (-5 *1 (-435 *6 *4 *5 *2)) (-4 *4 (-437 *6))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-657 *6)) (-4 *6 (-1239))
-   (-4 *5 (-1239)) (-5 *2 (-657 *5)) (-5 *1 (-655 *6 *5))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-978 *6)) (-4 *6 (-1239))
-   (-4 *5 (-1239)) (-5 *2 (-978 *5)) (-5 *1 (-977 *6 *5))))
- ((*1 *2 *3 *4 *5)
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-(((*1 *2 *3 *4 *4 *5 *3 *3)
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-(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-712))))
- ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-712))))) 
+  (-12 (-5 *4 (-787)) (-5 *5 (-660 *3)) (-4 *3 (-318)) (-4 *6 (-865))
+   (-4 *7 (-809)) (-5 *2 (-112)) (-5 *1 (-638 *6 *7 *3 *8))
+   (-4 *8 (-972 *3 *7 *6))))) 
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+   (-5 *1 (-823 *4 *5 *3 *6)) (-4 *3 (-672 *5))
+   (-4 *6 (-672 (-420 *5)))))
+ ((*1 *2 *3 *4)
+  (-12 (-4 *5 (-13 (-375) (-148) (-1063 (-420 (-577)))))
+   (-4 *4 (-1268 *5)) (-5 *2 (-660 (-2 (|:| -3693 *4) (|:| -2448 *4))))
+   (-5 *1 (-823 *5 *4 *3 *6)) (-4 *3 (-672 *4))
+   (-4 *6 (-672 (-420 *4)))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-13 (-375) (-148) (-1063 (-420 (-577)))))
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+   (-5 *1 (-823 *4 *5 *6 *3)) (-4 *6 (-672 *5))
+   (-4 *3 (-672 (-420 *5)))))
+ ((*1 *2 *3 *4)
+  (-12 (-4 *5 (-13 (-375) (-148) (-1063 (-420 (-577)))))
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+   (-4 *3 (-672 (-420 *4)))))) 
+(((*1 *2)
+  (-12 (-4 *1 (-354 *3 *4 *5)) (-4 *3 (-1246)) (-4 *4 (-1268 *3))
+   (-4 *5 (-1268 (-420 *4))) (-5 *2 (-705 (-420 *4)))))) 
+(((*1 *2 *2 *2 *2)
+  (-12 (-4 *2 (-13 (-375) (-10 -8 (-15 ** ($ $ (-420 (-577)))))))
+   (-5 *1 (-1153 *3 *2)) (-4 *3 (-1268 *2))))) 
+(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3)
+  (-12 (-5 *3 (-577)) (-5 *4 (-112)) (-5 *5 (-705 (-228)))
+   (-5 *2 (-1060)) (-5 *1 (-771))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-660 (-577))) (-5 *2 (-927 (-577))) (-5 *1 (-940))))
+ ((*1 *2) (-12 (-5 *2 (-927 (-577))) (-5 *1 (-940))))) 
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+(((*1 *2 *1 *1)
+  (-12 (-4 *1 (-1035 *3)) (-4 *3 (-1242)) (-4 *3 (-1125))
+   (-5 *2 (-112))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-112)) (-5 *1 (-350 *3 *4 *5)) (-14 *3 (-657 (-1198)))
-   (-14 *4 (-657 (-1198))) (-4 *5 (-399))))
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-   (-14 *4 (-657 (-1198))) (-4 *5 (-399))))) 
+  (-12 (-4 *3 (-465)) (-4 *4 (-809)) (-4 *5 (-865))
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 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-657 (-326 (-227)))) (-5 *4 (-784))
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-(((*1 *2 *1 *3) (-12 (-4 *1 (-312)) (-5 *3 (-1198)) (-5 *2 (-112))))
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 (((*1 *2 *1)
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 (((*1 *2 *1)
-  (-12 (-4 *1 (-700 *3 *4 *5)) (-4 *3 (-1071)) (-4 *4 (-384 *3))
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+  (-12
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+            (|:| -4071 (-1119 (-859 (-228)))) (|:| |abserr| (-228))
+            (|:| |relerr| (-228))))
+      (|:| -4444
+           (-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| (-1182 (-228)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -4071
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
+   (-5 *1 (-572))))
  ((*1 *2 *1)
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-(((*1 *2 *2 *3)
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-     (|:| |endPointContinuity|
-          (-3 (|:| |continuous| "Continuous at the end points")
-           (|:| |lowerSingular|
-                "There is a singularity at the lower end point")
-           (|:| |upperSingular|
-                "There is a singularity at the upper end point")
-           (|:| |bothSingular|
-                "There are singularities at both end points")
-           (|:| |notEvaluated|
-                "End point continuity not yet evaluated")))
-     (|:| |singularitiesStream|
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-           (|:| |notEvaluated|
-                "Internal singularities not yet evaluated")))
-     (|:| -1685
-          (-3 (|:| |finite| "The range is finite")
-           (|:| |lowerInfinite| "The bottom of range is infinite")
-           (|:| |upperInfinite| "The top of range is infinite")
-           (|:| |bothInfinite|
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-           (|:| |notEvaluated| "Range not yet evaluated")))))
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-(((*1 *2 *2 *3)
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+            (|:| -4071 (-1119 (-859 (-228)))) (|:| |abserr| (-228))
+            (|:| |relerr| (-228))))
+      (|:| -4444
+           (-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| (-1182 (-228)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -4071
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
+   (-5 *1 (-572))))) 
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+                 (|:| |upperSingular|
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+                 (|:| |bothSingular|
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+                 (|:| |notEvaluated|
+                      "End point continuity not yet evaluated")))
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+                 (|:| |notEvaluated|
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+                 (|:| |lowerInfinite|
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+                 (|:| |upperInfinite| "The top of range is infinite")
+                 (|:| |bothInfinite|
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+                 (|:| |notEvaluated| "Range not yet evaluated")))))))
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+   (-5 *2 (-2 (|:| |goodPols| (-660 *7)) (|:| |badPols| (-660 *7))))
+   (-5 *1 (-1002 *4 *5 *6 *7)) (-5 *3 (-660 *7))))) 
+(((*1 *2 *3 *4 *5 *3)
+  (-12 (-5 *4 (-1 *7 *7))
+   (-5 *5
+    (-1 (-2 (|:| |ans| *6) (|:| -4239 *6) (|:| |sol?| (-112))) (-577)
+     *6))
+   (-4 *6 (-375)) (-4 *7 (-1268 *6))
+   (-5 *2
+    (-3 (-2 (|:| |answer| (-420 *7)) (|:| |a0| *6))
+     (-2 (|:| -2898 (-420 *7)) (|:| |coeff| (-420 *7))) "failed"))
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+(((*1 *2 *1) (-12 (-4 *1 (-313)) (-5 *2 (-660 (-115)))))) 
+(((*1 *1 *2)
+  (|partial| -12 (-5 *2 (-660 *6)) (-4 *6 (-1090 *3 *4 *5))
+      (-4 *3 (-569)) (-4 *4 (-809)) (-4 *5 (-865))
+      (-5 *1 (-1305 *3 *4 *5 *6))))
+ ((*1 *1 *2 *3 *4)
+  (|partial| -12 (-5 *2 (-660 *8)) (-5 *3 (-1 (-112) *8 *8))
+      (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1090 *5 *6 *7)) (-4 *5 (-569))
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+(((*1 *2 *1) (-12 (-5 *2 (-660 (-177))) (-5 *1 (-1110))))) 
+(((*1 *2 *3 *4 *5 *4)
+  (-12 (-5 *3 (-705 (-228))) (-5 *4 (-577)) (-5 *5 (-112))
+   (-5 *2 (-1060)) (-5 *1 (-761))))) 
+(((*1 *2 *3 *3)
+  (-12 (-5 *2 (-1182 (-660 (-577)))) (-5 *1 (-902))
+   (-5 *3 (-660 (-577)))))) 
 (((*1 *2 *3)
   (|partial| -12
       (-5 *3
-       (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-227)))
-        (|:| -1685 (-1116 (-856 (-227)))) (|:| |abserr| (-227))
-        (|:| |relerr| (-227))))
+       (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228)))
+        (|:| -4071 (-1119 (-859 (-228)))) (|:| |abserr| (-228))
+        (|:| |relerr| (-228))))
       (-5 *2
        (-2
         (|:| |endPointContinuity|
@@ -10522,4734 +10049,5003 @@
               (|:| |notEvaluated|
                    "End point continuity not yet evaluated")))
         (|:| |singularitiesStream|
-             (-3 (|:| |str| (-1179 (-227)))
+             (-3 (|:| |str| (-1182 (-228)))
               (|:| |notEvaluated|
                    "Internal singularities not yet evaluated")))
-        (|:| -1685
+        (|:| -4071
              (-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 *3) (-12 (-5 *3 (-400)) (-5 *2 (-1294)) (-5 *1 (-403))))
- ((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-403))))) 
-(((*1 *2 *3)
-  (-12 (-5 *2 (-1 (-963 *3) (-963 *3))) (-5 *1 (-178 *3))
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- ((*1 *2)
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-      (-4 *3 (-353 *4 *2 *5))))
- ((*1 *2)
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-(((*1 *2 *2 *3)
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-(((*1 *2 *3)
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- ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-941)) (-5 *2 (-1289 *3)) (-5 *1 (-1199 *3))
-   (-4 *3 (-1071))))) 
+      (-5 *1 (-572))))) 
+(((*1 *2 *1)
+  (-12 (-4 *1 (-1159 *3)) (-4 *3 (-1074)) (-5 *2 (-660 (-966 *3)))))) 
+(((*1 *2 *1)
+  (-12 (-5 *2 (-3 (|:| |fst| (-447)) (|:| -2963 "void")))
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+(((*1 *2 *2)
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 (((*1 *2 *3)
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-(((*1 *2 *1) (-12 (-4 *1 (-1017 *2)) (-4 *2 (-1239))))) 
+  (-12 (-5 *3 (-660 (-327 (-228)))) (-5 *2 (-112)) (-5 *1 (-277))))
+ ((*1 *2 *3) (-12 (-5 *3 (-327 (-228))) (-5 *2 (-112)) (-5 *1 (-277))))
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+    (-3 (-2 (|:| |answer| (-420 *7)) (|:| |a0| *6))
+     (-2 (|:| -2898 (-420 *7)) (|:| |coeff| (-420 *7))) "failed"))
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+(((*1 *2 *1 *3) (-12 (-4 *1 (-313)) (-5 *3 (-1201)) (-5 *2 (-112))))
+ ((*1 *2 *1 *1) (-12 (-4 *1 (-313)) (-5 *2 (-112))))) 
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+  (-12 (-5 *3 (-660 *7)) (-4 *7 (-1090 *4 *5 *6)) (-4 *4 (-569))
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 (((*1 *2 *3 *1)
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-(((*1 *1 *1)
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-   (-4 *4 (-862)) (-4 *2 (-464))))
+  (-12 (-5 *3 (-519)) (-5 *2 (-707 (-109))) (-5 *1 (-177))))
  ((*1 *2 *3 *1)
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-   (-4 *2 (-13 (-1265 *3) (-568) (-10 -8 (-15 -3436 ($ $ $)))))))) 
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-      (-4 *2
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-        (-10 -8 (-15 -3501 ($ *7)) (-15 -1621 (*7 $))
-         (-15 -1635 (*7 $)))))))) 
-(((*1 *2 *3 *4 *5)
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-   (-4 *4 (-1071))))) 
-(((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-835))))) 
+  (-12 (-5 *3 (-519)) (-5 *2 (-707 (-109))) (-5 *1 (-1110))))) 
+(((*1 *2 *3 *4 *5 *4)
+  (-12 (-5 *3 (-705 (-228))) (-5 *4 (-577)) (-5 *5 (-112))
+   (-5 *2 (-1060)) (-5 *1 (-761))))) 
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+(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-450))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-865)) (-5 *2 (-1213 (-660 *4))) (-5 *1 (-1212 *4))
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+  (-12 (-4 *4 (-569)) (-4 *5 (-809)) (-4 *6 (-865))
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+   (-5 *2 (-2 (|:| |goodPols| (-660 *7)) (|:| |badPols| (-660 *7))))
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 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9))
-      (-4 *9 (-1087 *6 *7 *8)) (-4 *6 (-568)) (-4 *7 (-806))
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-      (-5 *3 (-657 *9)) (-4 *1 (-1232 *6 *7 *8 *9))))
- ((*1 *2 *3 *4)
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-   (-4 *2 (-13 (-862) (-21)))))) 
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+   (-4 *7 (-1268 *6))
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+   (-5 *1 (-587 *6 *7)) (-5 *3 (-420 *7))))) 
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+   (-4 *4 (-569)) (-5 *2 (-1197 *5)) (-5 *1 (-32 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-625 *1)) (-4 *1 (-1074)) (-4 *1 (-313))
+   (-5 *2 (-1197 *1))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-787)) (-5 *2 (-1297)) (-5 *1 (-884 *4 *5 *6 *7))
+   (-4 *4 (-1074)) (-14 *5 (-660 (-1201))) (-14 *6 (-660 *3))
+   (-14 *7 *3)))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-787)) (-4 *4 (-1074)) (-4 *5 (-865)) (-4 *6 (-809))
+   (-14 *8 (-660 *5)) (-5 *2 (-1297))
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+ ((*1 *2 *1 *3) (-12 (-5 *3 (-787)) (-5 *1 (-901 *2)) (-4 *2 (-1242))))) 
+(((*1 *1) (-5 *1 (-450)))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-657 (-2 (|:| -4291 (-1198)) (|:| -4440 (-449)))))
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-   (-5 *1 (-769))))) 
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+(((*1 *2 *3)
+  (-12 (-4 *4 (-865)) (-5 *2 (-660 (-660 (-660 *4))))
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 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-657 (-270))) (-5 *4 (-1198))
-      (-5 *1 (-269 *2)) (-4 *2 (-1239))))
+  (|partial| -12 (-5 *3 (-660 (-271))) (-5 *4 (-1201))
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  ((*1 *2 *3 *4)
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 (((*1 *2 *3)
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-   (-4 *4 (-568))))) 
+  (-12 (-4 *4 (-569)) (-4 *5 (-809)) (-4 *6 (-865)) (-5 *2 (-112))
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+(((*1 *2 *3 *4 *5)
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+   (-5 *5
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+     *6))
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 (((*1 *2 *3 *4 *5)
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-(((*1 *1 *1 *2) (-12 (-4 *1 (-733)) (-5 *2 (-941))))
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-            (|:| |endPointContinuity|
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-                  (|:| |lowerSingular|
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-                  (|:| |upperSingular|
-                       "There is a singularity at the upper end point")
-                  (|:| |bothSingular|
-                       "There are singularities at both end points")
-                  (|:| |notEvaluated|
-                       "End point continuity not yet evaluated")))
-            (|:| |singularitiesStream|
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-                  (|:| |notEvaluated|
-                       "Internal singularities not yet evaluated")))
-            (|:| -1685
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-                  (|:| |lowerInfinite|
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-                  (|:| |upperInfinite| "The top of range is infinite")
-                  (|:| |bothInfinite|
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-                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+           (|:| |lowerSingular|
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+           (|:| |upperSingular|
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+           (|:| |bothSingular|
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+           (|:| |notEvaluated|
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+           (|:| |notEvaluated|
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+     (|:| -4071
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+           (|:| |lowerInfinite| "The bottom of range is infinite")
+           (|:| |upperInfinite| "The top of range is infinite")
+           (|:| |bothInfinite|
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+           (|:| |notEvaluated| "Range not yet evaluated")))))
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@@ -15261,3046 +15057,3260 @@
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 (((*1 *2 *2)
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 (((*1 *2 *3)
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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")))
+   (-5 *1 (-194))))) 
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 (((*1 *2)
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 (((*1 *2 *1)
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+  (-12 (-5 *3 (-1183)) (-5 *4 (-577)) (-5 *5 (-705 (-228)))
+   (-5 *2 (-1060)) (-5 *1 (-773))))) 
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+(((*1 *2 *3)
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 (((*1 *2 *3)
   (-12
    (-5 *3
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-(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *3 *3 *5 *6 *3 *6 *6 *5 *6 *6 *6 *6
-      *5 *3 *3 *3 *3 *3 *6 *6 *6 *3 *3 *3 *3 *3 *7 *4 *4 *4 *4 *3 *8
-      *9)
-  (-12 (-5 *4 (-702 (-227))) (-5 *5 (-112)) (-5 *6 (-227))
-   (-5 *7 (-702 (-576)))
-   (-5 *8 (-3 (|:| |fn| (-400)) (|:| |fp| (-80 CONFUN))))
-   (-5 *9 (-3 (|:| |fn| (-400)) (|:| |fp| (-77 OBJFUN))))
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-(((*1 *2 *1)
-  (-12 (-4 *1 (-1306 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1071))
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-(((*1 *1 *2)
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+    (-2 (|:| |var| (-1201)) (|:| |fn| (-327 (-228)))
+     (|:| -4071 (-1119 (-859 (-228)))) (|:| |abserr| (-228))
+     (|:| |relerr| (-228))))
+   (-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))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4)
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\ No newline at end of file