* algebra/catdef.spad.pamphlet (OrderedAbelianGroup): Export

	negative?, abs, sign, with default implementations.
	(OrderedAbelianMonoid): Export positive?, with default.
	(OrderedRing): Don't export them.

8 files changed, 25994 insertions, 25975 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index 8379f759..c303857e 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,10 @@
+2011-03-11  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
+	* algebra/catdef.spad.pamphlet (OrderedAbelianGroup): Export
+	negative?, abs, sign, with default implementations.
+	(OrderedAbelianMonoid): Export positive?, with default.
+	(OrderedRing): Don't export them.
+
 2011-03-10  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
 	* algebra/catdef.spad.pamphlet (CharacteristicNonZero)
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 554fbf18..2441b559 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -388,7 +388,8 @@ strap-1/TRANFUN.$(FASLEXT): strap-1/TRIGCAT.$(FASLEXT) \
 	strap-1/ATRIG.$(FASLEXT) strap-1/HYPCAT.$(FASLEXT) \
 	strap-1/AHYP.$(FASLEXT)
 strap-1/INS.$(FASLEXT): strap-1/DFLOAT.$(FASLEXT)
-strap-1/DFLOAT.$(FASLEXT): strap-1/FPS.$(FASLEXT) strap-1/TRANFUN.$(FASLEXT)
+strap-1/DFLOAT.$(FASLEXT): strap-1/FPS.$(FASLEXT) \
+	strap-1/TRANFUN.$(FASLEXT)
 strap-1/SEXCAT.$(FASLEXT): strap-1/KVTFROM.$(FASLEXT)
 strap-1/POLYCAT.$(FASLEXT): strap-1/SEXCAT.$(FASLEXT)
 strap-1/QFCAT.$(FASLEXT): strap-1/FEVALAB.$(FASLEXT) \
@@ -407,7 +408,7 @@ strap-1/FSAGG.$(FASLEXT): strap-1/DIAGG.$(FASLEXT)
 strap-1/CHAR.$(FASLEXT): strap-1/FSAGG.$(FASLEXT)
 strap-1/STRING.$(FASLEXT): strap-1/SRAGG.$(FASLEXT) strap-1/CHAR.$(FASLEXT) \
 	strap-1/ISTRING.$(FASLEXT)
-strap-1/INT.$(FASLEXT): strap-1/STRING.$(FASLEXT)
+strap-1/INT.$(FASLEXT): strap-1/STRING.$(FASLEXT) strap-1/ORDRING.$(FASLEXT)
 strap-1/SINT.$(FASLEXT): strap-1/INT.$(FASLEXT) strap-1/ORDFIN.$(FASLEXT) \
 	strap-1/BOOLE.$(FASLEXT)
 strap-1/LIST.$(FASLEXT): strap-1/ILIST.$(FASLEXT) strap-1/STRING.$(FASLEXT)
@@ -823,7 +824,8 @@ axiom_algebra_layer_0 = \
   BMODULE           BASTYPE  BASTYPE- STEP     LMODULE  \
   RMODULE  ALGEBRA  ALGEBRA- SGROUP   SGROUP-  ABELSG   \
   ABELSG-  ORDSET            OASGP    FILECAT  SEXCAT   \
-  MODULE   MODULE-  PID      OAGROUP  OCAMON   OAMON    \
+  MODULE   MODULE-  PID      OAGROUP  OAGROUP- OCAMON   \
+  OAMON    OAMON- \
   RNG      ORDFIN   LLINSET  RLINSET  LINSET   OAMONS   \
   MKBCFUNC MKRECORD MKUCFUNC DROPT1   PLOT1    ITFUN2   \
   ITFUN3   STREAM1  STREAM2  STREAM3  ANY1     SEGBIND2 \
@@ -915,7 +917,7 @@ axiom_algebra_layer_1 = \
   GCDDOM   GCDDOM-  UFD      UFD-     ES        ES-      \
   PATAB    PPCURVE  PSCURVE  CACHSET  RESLATC            \
   IDENT    OUTFORM  BINDING           BOOLEAN            \
-  ORDRING  ORDRING-          FEVALAB  FEVALAB-  IARRAY1  \
+  ORDRING                    FEVALAB  FEVALAB-  IARRAY1  \
   OSGROUP  MAYBE    DATAARY  PROPLOG  HOMOTOP   BYTEORD  \
   FIELD    FIELD-   VECTCAT  VECTCAT- \
   PROPERTY ARITY    OPERCAT  OPERCAT- PAIR      STREAM   \
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet
index 7dfc10fc..fdb915fa 100644
--- a/src/algebra/catdef.spad.pamphlet
+++ b/src/algebra/catdef.spad.pamphlet
@@ -1271,7 +1271,7 @@ Monoid(): Category == SemiGroup with
 )abbrev category OAGROUP OrderedAbelianGroup
 ++ Author:
 ++ Date Created:
-++ Date Last Updated:
+++ Date Last Updated: March 10, 2011
 ++ Basic Functions:
 ++ Related Constructors:
 ++ Also See:
@@ -1283,9 +1283,26 @@ Monoid(): Category == SemiGroup with
 ++ the ordering.
 
 OrderedAbelianGroup(): Category ==
-        Join(OrderedCancellationAbelianMonoid, AbelianGroup)
-
+    Join(OrderedCancellationAbelianMonoid, AbelianGroup) with
+      negative?: % -> Boolean
+        ++ \spad{negative?(x)} holds when \spad{x} is less than \spad{0}.
+      sign: % -> Integer
+        ++ \spad{sign(x)} is \spad{1} if \spad{x} is positive,
+        ++ \spad{-1} if \spad{x} is negative, and \spad{0} otherwise.
+      abs: % -> %
+        ++ \spad{abs(x)} returns the absolute value of \spad{x}.
+  add
+    negative? x == x < 0
+    sign x ==
+      positive? x => 1
+      negative? x => -1
+      0
+    abs x ==
+      positive? x => x
+      negative? x => -x
+      0
 @
+
 \section{category OAMON OrderedAbelianMonoid}
 <<category OAMON OrderedAbelianMonoid>>=
 )abbrev category OAMON OrderedAbelianMonoid
@@ -1303,7 +1320,12 @@ OrderedAbelianGroup(): Category ==
 ++ preserves the ordering.
 
 OrderedAbelianMonoid(): Category ==
-        Join(OrderedAbelianSemiGroup, AbelianMonoid)
+    Join(OrderedAbelianSemiGroup, AbelianMonoid) with
+      positive?: % -> Boolean
+        ++ \spad{positive?(x)} holds when \spad{x} is greater
+        ++ than \spad{0}.
+  add    
+    positive? x == 0 < x
 
 @
 \section{category OAMONS OrderedAbelianMonoidSup}
@@ -1456,7 +1478,7 @@ OrderedMonoid(): Category == Join(OrderedSemiGroup, Monoid)
 )abbrev category ORDRING OrderedRing
 ++ Author:
 ++ Date Created:
-++ Date Last Updated:
+++ Date Last Updated: March 10, 2011
 ++ Basic Functions:
 ++ Related Constructors:
 ++ Also See:
@@ -1470,28 +1492,7 @@ OrderedMonoid(): Category == Join(OrderedSemiGroup, Monoid)
 ++ Axiom:
 ++   \spad{0<a and b<c => ab< ac}
 
-OrderedRing(): Category == Join(OrderedAbelianGroup,Ring,Monoid) with
-     positive?: % -> Boolean
-       ++ positive?(x) tests whether x is strictly greater than 0.
-     negative?: % -> Boolean
-       ++ negative?(x) tests whether x is strictly less than 0.
-     sign     : % -> Integer
-       ++ sign(x) is 1 if x is positive, -1 if x is negative, 0 if x equals 0.
-     abs      : % -> %
-       ++ abs(x) returns the absolute value of x.
-  add
-     positive? x == x>0
-     negative? x == x<0
-     sign x ==
-       positive? x => 1
-       negative? x => -1
-       zero? x => 0
-       error "x satisfies neither positive?, negative? or zero?"
-     abs x ==
-       positive? x => x
-       negative? x => -x
-       zero? x => 0
-       error "x satisfies neither positive?, negative? or zero?"
+OrderedRing(): Category == Join(OrderedAbelianGroup,Ring,Monoid)
 
 @
 
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 1bdc25c0..2dc7e679 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2294602 . 3508766236)       
+(2294709 . 3508838145)       
 (-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."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
@@ -38,7 +38,7 @@ NIL
 NIL 
 (-27) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
@@ -46,7 +46,7 @@ NIL
 NIL 
 (-29 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4506 . T) (-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4502 . T) (-4507 . T) (-4501 . T)) 
+((-4507 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4503 . T) (-4508 . T) (-4502 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,14 +56,14 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -1610) 
+(-32 R -4346) 
 ((|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 -1069) (QUOTE (-560))))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4509))) 
+((|HasAttribute| |#1| (QUOTE -4510))) 
 (-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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
@@ -74,7 +74,7 @@ NIL
 NIL 
 (-36 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table.	It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . 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"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-39 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -1610 UP UPUP -3100) 
+(-40 -4346 UP UPUP -3043) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
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-(-41 R -1610) 
+((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2309 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) 
+(-41 R -4346) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-319)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-4506 |has| |#1| (-571)) (-4504 . T) (-4503 . T)) 
+((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) 
 (-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."))) 
-((-4509 . T) (-4510 . T)) 
-((-2191 (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|))))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|))))))) 
+((-4510 . T) (-4511 . T)) 
+((-2309 (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|))))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (QUOTE (-560))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-51) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -1610) 
+(-54 |Base| R -4346) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,77 +158,77 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
 (-58 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-59 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray's."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-61 -3952) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-61 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-62 -3952) 
+(-62 -2187) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-63 -3952) 
+(-63 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-64 -3952) 
+(-64 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-65 -3952) 
+(-65 -2187) 
 ((|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 -3952) 
+(-66 -2187) 
 ((|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 -3952) 
+(-67 -2187) 
 ((|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 -3952) 
+(-68 -2187) 
 ((|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 -3952) 
+(-69 -2187) 
 ((|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 -3952) 
+(-70 -2187) 
 ((|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 -3952) 
+(-71 -2187) 
 ((|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 -3952) 
+(-72 -2187) 
 ((|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 -3952) 
+(-73 -2187) 
 ((|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 -3952) 
+(-74 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-75 -3952) 
+(-75 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -240,51 +240,51 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives wrt \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-78 -3952) 
+(-78 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -3952) 
+(-79 -2187) 
 ((|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 -3952) 
+(-80 -2187) 
 ((|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 -3952) 
+(-81 -2187) 
 ((|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 -3952) 
+(-82 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -3952) 
+(-83 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -3952) 
+(-84 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -3952) 
+(-85 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -3952) 
+(-86 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -3952) 
+(-87 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-88 -3952) 
+(-88 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-89 -3952) 
+(-89 -2187) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -294,8 +294,8 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-376)))) 
 (-91 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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\"."))) 
-((-4509 . T)) 
+((-4510 . 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."))) 
-((-4509 . T) ((-4511 "*") . T) (-4510 . T) (-4506 . T) (-4504 . T) (-4503 . T) (-4502 . T) (-4507 . T) (-4501 . T) (-4500 . T) (-4499 . T) (-4498 . T) (-4497 . T) (-4505 . T) (-4508 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4496 . T)) 
+((-4510 . T) ((-4512 "*") . T) (-4511 . T) (-4507 . T) (-4505 . T) (-4504 . T) (-4503 . T) (-4508 . T) (-4502 . T) (-4501 . T) (-4500 . T) (-4499 . T) (-4498 . T) (-4506 . T) (-4509 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4497 . 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}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-100 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -342,15 +342,15 @@ NIL
 NIL 
 (-103 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|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 (-4511 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4512 "*")))) 
 (-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"))) 
-((-4509 . T)) 
+((-4510 . 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."))) 
-((-4510 . T)) 
+((-4511 . 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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) 
 (-109) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
 NIL 
 (-110) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| (-114) (QUOTE (-1132))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-871))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-114) (QUOTE (-1132))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-114) (QUOTE (-102)))) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-114) (QUOTE (-102)))) 
 (-111 R S) 
 ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-112 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
@@ -396,22 +396,22 @@ NIL
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-117 -1610 UP) 
+(-117 -4346 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
 (-118 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-119 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2191 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-2309 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) 
 (-120 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510))) 
+((|HasAttribute| |#1| (QUOTE -4511))) 
 (-121 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -422,15 +422,15 @@ NIL
 NIL 
 (-123 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-124 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-125) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
 (-126 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -438,24 +438,24 @@ NIL
 NIL 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
 (-128 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-129 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-130) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
 (-131) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2191 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2191 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2309 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-2309 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) 
 (-132) 
 ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) 
 NIL 
@@ -474,13 +474,13 @@ NIL
 NIL 
 (-136) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4511 "*") . T)) 
+(((-4512 "*") . T)) 
 NIL 
-(-137 |minix| -4350 R) 
+(-137 |minix| -3061 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
-(-138 |minix| -4350 S T$) 
+(-138 |minix| -3061 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
@@ -502,8 +502,8 @@ NIL
 NIL 
 (-143) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
-((-4509 . T) (-4499 . T) (-4510 . T)) 
-((-2191 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+((-4510 . T) (-4500 . T) (-4511 . T)) 
+((-2309 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
 (-144 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
@@ -518,7 +518,7 @@ NIL
 NIL 
 (-147) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-148 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) 
@@ -526,9 +526,9 @@ NIL
 NIL 
 (-149) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-150 -1610 UP UPUP) 
+(-150 -4346 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) 
 NIL 
 NIL 
@@ -539,14 +539,14 @@ NIL
 (-152 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasAttribute| |#1| (QUOTE -4509))) 
+((|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasAttribute| |#1| (QUOTE -4510))) 
 (-153 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
 (-154 |n| K Q) 
 ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) 
-((-4504 . T) (-4503 . T) (-4506 . T)) 
+((-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
 (-155) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -568,7 +568,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-160 R -1610) 
+(-160 R -4346) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -599,10 +599,10 @@ NIL
 (-167 S R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1234))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) 
+((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) 
 (-168 R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
-((-4502 -2191 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-2953 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 -2309 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-4437 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-169 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -614,8 +614,8 @@ NIL
 NIL 
 (-171 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-4502 -2191 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-2953 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
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+((-4503 -2309 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-4437 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2309 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4509)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-363))))) 
 (-172 R S) 
 ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 
 NIL 
@@ -630,7 +630,7 @@ NIL
 NIL 
 (-175) 
 ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) 
-(((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-176) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -638,7 +638,7 @@ NIL
 NIL 
 (-177 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) 
-(((-4511 "*") . T) (-4502 . T) (-4507 . T) (-4501 . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") . T) (-4503 . T) (-4508 . T) (-4502 . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-178) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -655,7 +655,7 @@ NIL
 (-181 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-975 |#2|) (|%list| (QUOTE -911) (|devaluate| |#1|)))) 
+((|HasCategory| (-976 |#2|) (|%list| (QUOTE -912) (|devaluate| |#1|)))) 
 (-182 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -692,7 +692,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) 
 NIL 
 NIL 
-(-191 R -1610) 
+(-191 R -4346) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -804,23 +804,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
 NIL 
 NIL 
-(-219 -1610 UP UPUP R) 
+(-219 -4346 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-220 -1610 FP) 
+(-220 -4346 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
 (-221) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) 
 (-222) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-223 R -1610) 
+(-223 R -4346) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -834,19 +834,19 @@ NIL
 NIL 
 (-226 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-227 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-228 R -1610) 
+(-228 R -4346) 
 ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) 
 NIL 
 NIL 
 (-229) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|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}."))) 
-((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-230) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -854,19 +854,19 @@ NIL
 NIL 
 (-231 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-232 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
 (-233 S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
 (-234 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-235 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -878,7 +878,7 @@ NIL
 NIL 
 (-237 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-238 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
@@ -890,33 +890,33 @@ NIL
 NIL 
 (-240) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-241 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4509))) 
+((|HasAttribute| |#1| (QUOTE -4510))) 
 (-242 S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
 (-243) 
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-244 S -4350 R) 
+(-244 S -3061 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4506)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1132)))) 
-(-245 -4350 R) 
+((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) 
+(-245 -3061 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"))) 
-((-4503 |has| |#2| (-1080)) (-4504 |has| |#2| (-1080)) (-4506 |has| |#2| (-6 -4506)) (-4509 . T)) 
+((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) 
 NIL 
-(-246 -4350 R) 
+(-246 -3061 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."))) 
-((-4503 |has| |#2| (-1080)) (-4504 |has| |#2| (-1080)) (-4506 |has| |#2| (-6 -4506)) (-4509 . T)) 
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+(-247 -3061 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
@@ -930,7 +930,7 @@ NIL
 NIL 
 (-250) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
-((-4502 . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-251 S) 
 ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) 
@@ -938,20 +938,20 @@ NIL
 NIL 
 (-252 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-253 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-254 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-255 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-256) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
@@ -966,23 +966,23 @@ NIL
 NIL 
 (-259 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4506 -2191 (-1383 (|has| |#4| (-1080)) (|has| |#4| (-240))) (|has| |#4| (-6 -4506)) (-1383 (|has| |#4| (-1080)) (|has| |#4| (-927 (-1208))))) (-4503 |has| |#4| (-1080)) (-4504 |has| |#4| (-1080)) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-240))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-748))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-815))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-871))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1080))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1132))) 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(|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-2191 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (-2191 (|HasAttribute| |#3| (QUOTE -4506)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -929) (QUOTE (-1208))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
+((-4507 -2309 (-2925 (|has| |#3| (-1081)) (|has| |#3| (-240))) (|has| |#3| (-6 -4507)) (-2925 (|has| |#3| (-1081)) (|has| |#3| (-928 (-1209))))) (-4504 |has| |#3| (-1081)) (-4505 |has| |#3| (-1081)) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#3| (QUOTE (-376))) (-2309 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1081)))) (-2309 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-817))) (-2309 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872)))) (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (QUOTE (-381))) (-2309 (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-175)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-240)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-376)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1081))))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081)))) (|HasCategory| |#3| (QUOTE (-240))) (-2309 (|HasCategory| |#3| (QUOTE (-240))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081))))) (-2309 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#3| (QUOTE (-1133))) (-2309 (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-21)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-175)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-240)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-376)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-381)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-748)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-817)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-872)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1133))))) (-2309 (-12 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1081))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-872))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1081)))) (-2309 (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (-2309 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-2309 (|HasCategory| |#3| (QUOTE (-1081))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1133)))) (-2309 (|HasAttribute| |#3| (QUOTE -4507)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
 (-261 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-240)))) 
 (-262 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
 (-263 S) 
 ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
 (-264 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -1023,15 +1023,15 @@ NIL
 (-273 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-239)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239)))) 
 (-274 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
 (-275 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-276 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -1076,11 +1076,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-287 R -1610) 
+(-287 R -4346) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the	inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-288 R -1610) 
+(-288 R -4346) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
@@ -1103,10 +1103,10 @@ NIL
 (-293 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132)))) 
+((|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133)))) 
 (-294 S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
 (-295 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
@@ -1127,18 +1127,18 @@ NIL
 (-299 S |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510))) 
+((|HasAttribute| |#1| (QUOTE -4511))) 
 (-300 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-301 S R |Mod| -4452 -4246 |exactQuo|) 
+(-301 S R |Mod| -2533 -1762 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-302) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4502 . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-303) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
@@ -1150,16 +1150,16 @@ NIL
 NIL 
 (-305 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-4506 -2191 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-1080)) (-4504 |has| |#1| (-1080))) 
-((|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) 
+((-4507 -2309 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) 
+((|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) 
 (-306 S R) 
 ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) 
 NIL 
 NIL 
 (-307 |Key| |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) 
 (-308) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
@@ -1167,16 +1167,16 @@ NIL
 (-309 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) 
 (-310) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
 NIL 
-(-311 -1610 S) 
+(-311 -4346 S) 
 ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) 
 NIL 
 NIL 
-(-312 E -1610) 
+(-312 E -4346) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) 
 NIL 
 NIL 
@@ -1206,7 +1206,7 @@ NIL
 NIL 
 (-319) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-320 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
@@ -1216,7 +1216,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-322 -1610) 
+(-322 -4346) 
 ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) 
 NIL 
 NIL 
@@ -1230,12 +1230,12 @@ NIL
 NIL 
 (-325 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-1051))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-871))) (-2191 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-1183))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))) (-2191 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-2309 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-2309 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))))) 
 (-326 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-4506 -2191 (-12 (|has| |#1| (-571)) (-2191 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) ((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-571)) (-4501 |has| |#1| (-571))) 
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+((-4507 -2309 (-12 (|has| |#1| (-571)) (-2309 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) 
+((-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-1081))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-147)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081))))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21)))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25)))) (-2309 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-327 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1244,7 +1244,7 @@ NIL
 ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) 
 NIL 
 NIL 
-(-329 R -1610) 
+(-329 R -4346) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
 NIL 
@@ -1254,8 +1254,8 @@ NIL
 NIL 
 (-331 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
 (-332 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1266,8 +1266,8 @@ NIL
 NIL 
 (-334 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) 
-((-4504 . T) (-4503 . T)) 
-((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| (-560) (QUOTE (-814)))) 
+((-4505 . T) (-4504 . T)) 
+((|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-816)))) 
 (-335 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1275,26 +1275,26 @@ NIL
 (-336 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-793) (QUOTE (-814)))) 
+((|HasCategory| (-793) (QUOTE (-816)))) 
 (-337 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-338 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-339 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-340 S -1610) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-340 S -4346) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381)))) 
-(-341 -1610) 
+(-341 -4346) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-342) 
 ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) 
@@ -1312,7 +1312,7 @@ NIL
 ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) 
 NIL 
 NIL 
-(-346 -1610 UP UPUP R) 
+(-346 -4346 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
@@ -1320,37 +1320,37 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-348 S -1610 UP UPUP R) 
+(-348 S -4346 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-349 -1610 UP UPUP R) 
+(-349 -4346 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-350 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-351 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-352 |basicSymbols| |subscriptedSymbols| R) 
 ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (QUOTE (-560))))) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-353 |p| |n|) 
 ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) 
-(-354 S -1610 UP UPUP) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) 
+(-354 S -4346 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-355 -1610 UP UPUP) 
+(-355 -4346 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
-((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-356 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
@@ -1358,16 +1358,16 @@ NIL
 NIL 
 (-357 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) 
 (-358 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-359 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-360 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1382,51 +1382,51 @@ NIL
 NIL 
 (-363) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-364 R UP -1610) 
+(-364 R UP -4346) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-365 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) 
 (-366 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-367 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-368 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-369 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-370 -1610 GF) 
+(-370 -4346 GF) 
 ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-371 -1610 FP FPP) 
+(-371 -4346 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
 (-372 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-373 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
 NIL 
 NIL 
 (-374 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-375 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1434,7 +1434,7 @@ NIL
 NIL 
 (-376) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-377 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
@@ -1450,7 +1450,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-571)))) 
 (-380 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4506 |has| |#1| (-571)) (-4504 . T) (-4503 . T)) 
+((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) 
 NIL 
 (-381) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
@@ -1462,15 +1462,15 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376)))) 
 (-383 R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-384 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132)))) 
+((|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133)))) 
 (-385 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4509 . T)) 
+((-4510 . T)) 
 NIL 
 (-386 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) 
@@ -1478,7 +1478,7 @@ NIL
 NIL 
 (-387 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4504 . T) (-4503 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) 
 NIL 
 (-388 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
@@ -1494,7 +1494,7 @@ NIL
 NIL 
 (-391) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4492 . T) (-4500 . T) (-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4493 . T) (-4501 . T) (-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-392 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
@@ -1506,11 +1506,11 @@ NIL
 NIL 
 (-394 R S) 
 ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-4504 . T) (-4503 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-4505 . T) (-4504 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-395 R S) 
 ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175)))) 
 (-396) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
@@ -1518,7 +1518,7 @@ NIL
 NIL 
 (-397 R |Basis|) 
 ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-398) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
@@ -1531,10 +1531,10 @@ NIL
 (-400 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-871)))) 
+((|HasCategory| |#1| (QUOTE (-872)))) 
 (-401) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-402) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
@@ -1546,13 +1546,13 @@ NIL
 NIL 
 (-404 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-405) 
 ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) 
 NIL 
 NIL 
-(-406 -1610 UP UPUP R) 
+(-406 -4346 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 
@@ -1576,11 +1576,11 @@ NIL
 ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-412 -3952 |returnType| -4118 |symbols|) 
+(-412 -2187 |returnType| -4401 |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 
-(-413 -1610 UP) 
+(-413 -4346 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1594,28 +1594,28 @@ NIL
 NIL 
 (-416) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-417 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4492)) (|HasAttribute| |#1| (QUOTE -4500))) 
+((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) 
 (-418) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-419 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "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."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1253))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1253)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) 
 (-420 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 
 (-421 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-4496 -12 (|has| |#1| (-6 -4507)) (|has| |#1| (-466)) (|has| |#1| (-6 -4496))) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4496)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-422 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 
@@ -1626,28 +1626,28 @@ NIL
 NIL 
 (-424 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-425 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-426 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-427 R -1610 UP A) 
+(-427 R -4346 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-428 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 
-(-429 R -1610 UP A |ibasis|) 
+(-429 R -4346 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -1069) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -1070) (|devaluate| |#2|)))) 
 (-430 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1658,7 +1658,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-432 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4506 |has| |#1| (-571)) (-4504 . T) (-4503 . T)) 
+((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) 
 NIL 
 (-433 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)}."))) 
@@ -1667,10 +1667,10 @@ NIL
 (-434 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) 
 (-435 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-4506 -2191 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) ((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-571)) (-4501 |has| |#1| (-571))) 
+((-4507 -2309 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) 
 NIL 
 (-436 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) 
@@ -1687,36 +1687,36 @@ NIL
 (-439 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 (-871))) (|HasCategory| |#2| (QUOTE (-381)))) 
+((|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-381)))) 
 (-440 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4509 . T) (-4499 . T) (-4510 . T)) 
+((-4510 . T) (-4500 . T) (-4511 . T)) 
 NIL 
 (-441 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-442 R -1610) 
+(-442 R -4346) 
 ((|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 
 (-443 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"))) 
-((-4496 -12 (|has| |#1| (-6 -4496)) (|has| |#2| (-6 -4496))) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4496)) (|HasAttribute| |#2| (QUOTE -4496)))) 
-(-444 R -1610) 
+((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) 
+(-444 R -4346) 
 ((|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 
-(-445 R -1610) 
+(-445 R -4346) 
 ((|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 
-(-446 R -1610) 
+(-446 R -4346) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-447 R -1610) 
+(-447 R -4346) 
 ((|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 
@@ -1724,10 +1724,10 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-449 R -1610 UP) 
+(-449 R -4346 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 -1069) (QUOTE (-48))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-48))))) 
 (-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 
@@ -1756,7 +1756,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-457 R UP -1610) 
+(-457 R UP -4346) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
@@ -1794,16 +1794,16 @@ NIL
 NIL 
 (-466) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-467 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"))) 
-((-4506 |has| (-421 (-975 |#1|)) (-571)) (-4504 . T) (-4503 . T)) 
-((|HasCategory| (-421 (-975 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-421 (-975 |#1|)) (QUOTE (-571)))) 
+((-4507 |has| (-421 (-976 |#1|)) (-571)) (-4505 . T) (-4504 . T)) 
+((|HasCategory| (-421 (-976 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-421 (-976 |#1|)) (QUOTE (-571)))) 
 (-468 |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"))) 
-(((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-469 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) 
 NIL 
@@ -1830,7 +1830,7 @@ NIL
 NIL 
 (-475 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-476 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1838,8 +1838,8 @@ NIL
 NIL 
 (-477 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) 
 (-478 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) 
 NIL 
@@ -1868,7 +1868,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-485 |lv| -1610 R) 
+(-485 |lv| -4346 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1878,23 +1878,23 @@ NIL
 NIL 
 (-487) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-488 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
 (-489 |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."))) 
-((-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132)))) 
+((-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133)))) 
 (-490 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)}"))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) 
 (-491) 
 ((|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}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-492) 
 ((|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'."))) 
@@ -1902,29 +1902,29 @@ NIL
 NIL 
 (-493 |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."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) 
 (-494) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
 NIL 
 (-495 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) 
-(-496 -4350 S) 
+(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(-496 -3061 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(-1209)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-175)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-240)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-381)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-872)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133))))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-872))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2309 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) 
 (-497) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
 NIL 
 (-498 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-499 -1610 UP UPUP R) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-499 -4346 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
@@ -1934,12 +1934,12 @@ NIL
 NIL 
 (-501) 
 ((|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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) 
 (-502 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 -4509)) (|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) 
+((|HasAttribute| |#1| (QUOTE -4510)) (|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) 
 (-503 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1960,34 +1960,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-508 -1610 UP |AlExt| |AlPol|) 
+(-508 -4346 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-509) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (QUOTE (-560))))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-510 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-511 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray's with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-512 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 
-(-513 R UP -1610) 
+(-513 R UP -4346) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-514 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| (-114) (QUOTE (-1132))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-871))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-114) (QUOTE (-1132))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-114) (QUOTE (-102)))) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-114) (QUOTE (-102)))) 
 (-515 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 
@@ -2000,10 +2000,10 @@ NIL
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-518 -1610 |Expon| |VarSet| |DPoly|) 
+(-518 -4346 |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 -633) (QUOTE (-1208))))) 
+((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) 
 (-519 |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 
@@ -2015,11 +2015,11 @@ NIL
 (-521 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 (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-522 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 (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-523 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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
@@ -2027,15 +2027,15 @@ NIL
 (-524 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-525 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-526 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) 
 (-527 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
@@ -2047,39 +2047,39 @@ NIL
 (-529 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-814)))) 
+((|HasCategory| |#2| (QUOTE (-816)))) 
 (-530 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-531) 
 ((|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 
 (-532 |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}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((-2191 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((-2309 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) 
 (-533 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-534 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."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-535 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
-((|HasAttribute| |#3| (QUOTE -4510))) 
+((|HasAttribute| |#3| (QUOTE -4511))) 
 (-536 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 -4510))) 
+((|HasAttribute| |#7| (QUOTE -4511))) 
 (-537 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."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-538) 
 ((|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 
@@ -2111,8 +2111,8 @@ NIL
 (-545 |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| (-793) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) 
-(-546 K -1610 |Par|) 
+((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) 
+(-546 K -4346 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
@@ -2136,7 +2136,7 @@ NIL
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-552 K -1610 |Par|) 
+(-552 K -4346 |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 
@@ -2166,11 +2166,11 @@ NIL
 NIL 
 (-559) 
 ((|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."))) 
-((-4507 . T) (-4508 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-560) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \\spad{nothing}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4491 . T) (-4497 . T) (-4501 . T) (-4496 . T) (-4507 . T) (-4508 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4492 . T) (-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-561) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
@@ -2190,13 +2190,13 @@ NIL
 NIL 
 (-565 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) 
-(-566 R -1610) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) 
+(-566 R -4346) 
 ((|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 
-(-567 R0 -1610 UP UPUP R) 
+(-567 R0 -4346 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 
@@ -2206,7 +2206,7 @@ NIL
 NIL 
 (-569 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-2941 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4430 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-570 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."))) 
@@ -2214,9 +2214,9 @@ NIL
 NIL 
 (-571) 
 ((|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."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-572 R -1610) 
+(-572 R -4346) 
 ((|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},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "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 
@@ -2228,7 +2228,7 @@ NIL
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-575 R -1610 L) 
+(-575 R -4346 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}'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}'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 -680) (|devaluate| |#2|)))) 
@@ -2236,11 +2236,11 @@ NIL
 ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) 
 NIL 
 NIL 
-(-577 -1610 UP UPUP R) 
+(-577 -4346 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 
-(-578 -1610 UP) 
+(-578 -4346 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 
@@ -2248,15 +2248,15 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) 
 NIL 
 NIL 
-(-580 R -1610 L) 
+(-580 R -4346 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}'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 -680) (|devaluate| |#2|)))) 
-(-581 R -1610) 
+(-581 R -4346) 
 ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) 
-(-582 -1610 UP) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) 
+(-582 -4346 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
@@ -2264,27 +2264,27 @@ NIL
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-584 -1610) 
+(-584 -4346) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
 (-585 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."))) 
-((-2941 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4430 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-586) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
-(-587 R -1610) 
+(-587 R -4346) 
 ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) 
-(-588 -1610 UP) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) 
+(-588 -4346 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 
-(-589 R -1610) 
+(-589 R -4346) 
 ((|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 
@@ -2306,25 +2306,25 @@ NIL
 NIL 
 (-594 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-595 |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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) 
 (-596) 
 ((|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 
-(-597 -1610) 
+(-597 -4346) 
 ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) 
-((-4504 . T) (-4503 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1208))))) 
-(-598 E -1610) 
+((-4505 . T) (-4504 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) 
+(-598 E -4346) 
 ((|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 
-(-599 R -1610) 
+(-599 R -4346) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 NIL 
@@ -2358,19 +2358,19 @@ NIL
 NIL 
 (-607 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2191 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2191 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2309 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2309 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
 (-608 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 
 (-609 |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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) 
 (-610 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 ((|HasCategory| |#1| (QUOTE (-571)))) 
 (-611) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) 
@@ -2384,7 +2384,7 @@ NIL
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-614 R -1610 FG) 
+(-614 R -4346 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
@@ -2394,12 +2394,12 @@ NIL
 NIL 
 (-616 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-617 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#2| (QUOTE (-871))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#3| (QUOTE (-1132)))) 
+((|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (QUOTE (-872))) (|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#3| (QUOTE (-1133)))) 
 (-618 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
@@ -2410,8 +2410,8 @@ NIL
 NIL 
 (-620 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4506 -2191 (-1383 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) 
-((-2191 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
+((-4507 -2309 (-2925 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) 
+((-2309 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
 (-621) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
@@ -2438,20 +2438,20 @@ NIL
 NIL 
 (-627 |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."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102)))) 
 (-628 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 
 (-629 |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}."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
 (-630 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 -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) 
+((|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) 
 (-631 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 
@@ -2464,7 +2464,7 @@ NIL
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-634 -1610 UP) 
+(-634 -4346 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
@@ -2482,24 +2482,24 @@ NIL
 NIL 
 (-638 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}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-870)))) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-871)))) 
 (-639 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 
 (-640 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."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-641 R -1610) 
+(-641 R -4346) 
 ((|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 
 (-642 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"))) 
-((-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4502 . T) (-4506 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) 
+((-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4503 . T) (-4507 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) 
 (-643 R E V P TS ST) 
 ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) 
 NIL 
@@ -2514,13 +2514,13 @@ NIL
 NIL 
 (-646 |VarSet| R |Order|) 
 ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-647 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) 
 NIL 
 NIL 
-(-648 R -1610) 
+(-648 R -4346) 
 ((|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 
@@ -2528,25 +2528,25 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-650 |lv| -1610) 
+(-650 |lv| -4346) 
 ((|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 
 (-651) 
 ((|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."))) 
-((-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (QUOTE (-51))))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1190) (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132)))) 
+((-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 (-51))) (QUOTE (-1133)))) 
 (-652 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)."))) 
-((-4506 -2191 (-1383 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) 
-((-2191 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
+((-4507 -2309 (-2925 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) 
+((-2309 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
 (-653 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-654 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4504 . T) (-4503 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) 
 NIL 
 (-655 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))}."))) 
@@ -2563,18 +2563,18 @@ NIL
 (-658 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-1372 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-2912 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-659 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}."))) 
-((-4504 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-657 |#2|) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) 
+((-4505 . T) (-4504 . T)) 
+((-12 (|HasCategory| (-657 |#2|) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) 
 (-660 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 
 (-661 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}."))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-662 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."))) 
@@ -2582,8 +2582,8 @@ NIL
 NIL 
 (-663 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."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-664 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 
@@ -2606,8 +2606,8 @@ NIL
 NIL 
 (-669 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-670 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
@@ -2619,40 +2619,40 @@ NIL
 (-672 A S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510))) 
+((|HasAttribute| |#1| (QUOTE -4511))) 
 (-673 S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
 (-674 M R S) 
 ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4504 . T) (-4503 . T)) 
-((|HasCategory| |#1| (QUOTE (-813)))) 
-(-675 R -1610 L) 
+((-4505 . T) (-4504 . T)) 
+((|HasCategory| |#1| (QUOTE (-814)))) 
+(-675 R -4346 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 
-(-676 A -2018) 
+(-676 A -4463) 
 ((|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}}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-677 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}}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-678 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-679 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-680 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}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-681 -1610 UP) 
+(-681 -4346 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)))) 
@@ -2674,7 +2674,7 @@ NIL
 NIL 
 (-686 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4504 . T) (-4503 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) 
 ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-687 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}."))) 
@@ -2682,13 +2682,13 @@ NIL
 NIL 
 (-688 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}."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-689 -1610 |Row| |Col| M) 
+(-689 -4346 |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 
-(-690 -1610) 
+(-690 -4346) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "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 
@@ -2698,8 +2698,8 @@ NIL
 NIL 
 (-692 |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."))) 
-((-4506 . T) (-4509 . T) (-4503 . T) (-4504 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2191 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
+((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2309 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-693) 
 ((|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 
@@ -2719,7 +2719,7 @@ NIL
 (-697 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 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-698) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -2759,10 +2759,10 @@ NIL
 (-707 S R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571)))) 
+((|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571)))) 
 (-708 R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
 (-709 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}."))) 
@@ -2774,8 +2774,8 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571)))) 
 (-711 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."))) 
-((-4509 . T) (-4510 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4510 . T) (-4511 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-712 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
@@ -2784,7 +2784,7 @@ NIL
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) 
 NIL 
 NIL 
-(-714 S -1610 FLAF FLAS) 
+(-714 S -4346 FLAF FLAS) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 
 NIL 
 NIL 
@@ -2794,11 +2794,11 @@ NIL
 NIL 
 (-716) 
 ((|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"))) 
-((-4502 . T) (-4507 |has| (-721) (-376)) (-4501 |has| (-721) (-376)) (-2953 . T) (-4508 |has| (-721) (-6 -4508)) (-4505 |has| (-721) (-6 -4505)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
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+((-4503 . T) (-4508 |has| (-721) (-376)) (-4502 |has| (-721) (-376)) (-4437 . T) (-4509 |has| (-721) (-6 -4509)) (-4506 |has| (-721) (-6 -4506)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2309 (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2309 (-12 (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2309 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (|%list| (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2309 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1052))) (|HasCategory| (-721) (QUOTE (-1235))) (-12 (|HasCategory| (-721) (QUOTE (-1034))) (|HasCategory| (-721) (QUOTE (-1235)))) (-2309 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940))))) (-2309 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-1235)))) (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940))) (-2309 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2309 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2309 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4509)) (|HasAttribute| (-721) (QUOTE -4506)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-363))))) 
 (-717 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}."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
 (-718 U) 
 ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
@@ -2808,13 +2808,13 @@ NIL
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "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 
-(-720 OV E -1610 PG) 
+(-720 OV E -4346 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 
 (-721) 
 ((|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}"))) 
-((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4430 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-722 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."))) 
@@ -2822,7 +2822,7 @@ NIL
 NIL 
 (-723) 
 ((|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}"))) 
-((-4508 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4509 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-724 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"))) 
@@ -2840,7 +2840,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) 
 NIL 
 NIL 
-(-728 S -4324 I) 
+(-728 S -3095 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 
@@ -2850,7 +2850,7 @@ NIL
 NIL 
 (-730 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)}.}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-731 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}."))) 
@@ -2860,25 +2860,25 @@ NIL
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-733 R |Mod| -4452 -4246 |exactQuo|) 
+(-733 R |Mod| -2533 -1762 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-734 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4505 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-735 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
 (-736 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) 
+((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) 
-(-737 R |Mod| -4452 -4246 |exactQuo|) 
+(-737 R |Mod| -2533 -1762 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-738 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
@@ -2886,11 +2886,11 @@ NIL
 NIL 
 (-739 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
-(-740 -1610) 
+(-740 -4346) 
 ((|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]]}."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
 (-741 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."))) 
@@ -2914,7 +2914,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) 
 (-746 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."))) 
-((-4502 |has| |#1| (-376)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 (-747 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."))) 
@@ -2924,7 +2924,7 @@ NIL
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-749 -1610 UP) 
+(-749 -4346 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 
@@ -2942,8 +2942,8 @@ NIL
 NIL 
 (-753 |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."))) 
-(((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-940))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-754 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
@@ -2958,15 +2958,15 @@ NIL
 NIL 
 (-757 R M) 
 ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) 
-((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-871)))) 
+((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-872)))) 
 (-758 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}."))) 
-((-4509 . T) (-4499 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4510 . T) (-4500 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-759 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4499 . T) (-4510 . T)) 
+((-4500 . T) (-4511 . T)) 
 NIL 
 (-760) 
 ((|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."))) 
@@ -2978,7 +2978,7 @@ NIL
 NIL 
 (-762 |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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
 (-763 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"))) 
@@ -2994,7 +2994,7 @@ NIL
 NIL 
 (-766 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
 (-767) 
 ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{\\spad{manpageXXc02}}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) 
@@ -3076,11 +3076,11 @@ NIL
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-787 -1610) 
+(-787 -4346) 
 ((|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 
-(-788 P -1610) 
+(-788 P -4346) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) 
 NIL 
 NIL 
@@ -3088,7 +3088,7 @@ NIL
 NIL 
 NIL 
 NIL 
-(-790 UP -1610) 
+(-790 UP -4346) 
 ((|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 
@@ -3102,9 +3102,9 @@ NIL
 NIL 
 (-793) 
 ((|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."))) 
-(((-4511 "*") . T)) 
+(((-4512 "*") . T)) 
 NIL 
-(-794 R -1610) 
+(-794 R -4346) 
 ((|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 
@@ -3124,7 +3124,7 @@ NIL
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-799 -1610 |ExtF| |SUEx| |ExtP| |n|) 
+(-799 -4346 |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 
@@ -3138,12 +3138,12 @@ NIL
 NIL 
 (-802 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
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 (-803 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4505 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
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+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
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 (-804 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 
@@ -3154,12 +3154,12 @@ NIL
 ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) 
 (-806 R E V P) 
 ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
 (-807 S) 
 ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-175)))) 
+((-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-175)))) 
 (-808) 
 ((|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 
@@ -3180,2069 +3180,2073 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-813) 
-((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) 
+(-813 S) 
+((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
 (-814) 
-((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) 
+((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-815) 
-((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
+(-815 S) 
+((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
 (-816) 
+((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
+NIL 
+NIL 
+(-817) 
+((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
+NIL 
+NIL 
+(-818) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-817 S R) 
+(-819 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381)))) 
-(-818 R) 
+((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-381)))) 
+(-820 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-819) 
+(-821) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-820 R) 
+(-822 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2191 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) 
-(-821 -2191 R OS S) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2309 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) 
+(-823 -2309 R OS S) 
 ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-822) 
+(-824) 
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-823 R -1610 L) 
+(-825 R -4346 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-824 R -1610) 
+(-826 R -4346) 
 ((|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 
-(-825) 
+(-827) 
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) 
 NIL 
 NIL 
-(-826 R -1610) 
+(-828 R -4346) 
 ((|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 
-(-827) 
+(-829) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
 NIL 
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-(-828 -1610 UP UPUP R) 
+(-830 -4346 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
 NIL 
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-(-829 -1610 UP L LQ) 
+(-831 -4346 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
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-(-830) 
+(-832) 
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
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-(-831 -1610 UP L LQ) 
+(-833 -4346 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
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-(-832 -1610 UP) 
+(-834 -4346 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}'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}'s form a basis for the rational solutions of the homogeneous equation."))) 
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-(-833 -1610 L UP A LO) 
+(-835 -4346 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
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-(-834 -1610 UP) 
+(-836 -4346 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-835 -1610 LO) 
+(-837 -4346 LO) 
 ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) 
 NIL 
 NIL 
-(-836 -1610 LODO) 
+(-838 -4346 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-837 -4350 S |f|) 
+(-839 -3061 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}."))) 
-((-4503 |has| |#2| (-1080)) (-4504 |has| |#2| (-1080)) (-4506 |has| |#2| (-6 -4506)) (-4509 . T)) 
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-(-839 |Kernels| R |var|) 
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+((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-841 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4511 "*") |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 . T) (-4504 . T) (-4503 . T)) 
+(((-4512 "*") |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 . T) (-4505 . T) (-4504 . T)) 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
-(-840 S) 
+(-842 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 
-(-841 S) 
+(-843 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-871)))) 
-(-842) 
+((|HasCategory| |#1| (QUOTE (-872)))) 
+(-844) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-843) 
+(-845) 
 ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath XML encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) 
 NIL 
 NIL 
-(-844) 
+(-846) 
 ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) 
 NIL 
 NIL 
-(-845) 
+(-847) 
 ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,cd,s)} writes the symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,mode,enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \"r\",{} \"w\" or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) 
 NIL 
 NIL 
-(-846) 
+(-848) 
 ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath XML encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) 
 NIL 
 NIL 
-(-847) 
+(-849) 
 ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
 NIL 
 NIL 
-(-848) 
+(-850) 
 ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown CD or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown CD error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) 
 NIL 
 NIL 
-(-849 R) 
+(-851 R) 
 ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
 NIL 
 NIL 
-(-850 P R) 
+(-852 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) 
-(-851) 
+(-853) 
 ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the CDs supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) 
 NIL 
 NIL 
-(-852 S) 
+(-854 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4509 . T) (-4499 . T) (-4510 . T)) 
+((-4510 . T) (-4500 . T) (-4511 . T)) 
 NIL 
-(-853) 
+(-855) 
 ((|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 
-(-854 R) 
+(-856 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."))) 
-((-4506 |has| |#1| (-870))) 
-((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) 
-(-855 R S) 
+((-4507 |has| |#1| (-871))) 
+((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) 
+(-857 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 
-(-856 R) 
+(-858 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) 
+((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) 
-(-857 A S) 
+(-859 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 
-(-858 S) 
+(-860 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-859) 
+(-861) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-860) 
+(-862) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) 
 NIL 
 NIL 
-(-861) 
+(-863) 
 ((|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 
-(-862) 
+(-864) 
 ((|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 
-(-863) 
+(-865) 
 ((|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 
-(-864 R) 
+(-866 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4506 |has| |#1| (-870))) 
-((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) 
-(-865 R S) 
+((-4507 |has| |#1| (-871))) 
+((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2309 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) 
+(-867 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-866) 
+(-868) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-867 -4350 S) 
+(-869 -3061 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-868) 
+(-870) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-869 S) 
-((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-NIL 
-NIL 
-(-870) 
-((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4506 . T)) 
-NIL 
 (-871) 
+((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
+((-4507 . T)) 
+NIL 
+(-872) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-872 T$ |f|) 
+(-873 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 -632) (QUOTE (-887))))) 
-(-873 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) 
+(-874 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-874) 
+(-875) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-875 S R) 
+(-876 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175)))) 
-(-876 R) 
+(-877 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-877 R C) 
+(-878 R C) 
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) 
-(-878 R |sigma| -3708) 
+(-879 R |sigma| -3286) 
 ((|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."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-879 |x| R |sigma| -3708) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-880 |x| R |sigma| -3286) 
 ((|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}."))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-880 R) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) 
+(-881 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 -421) (QUOTE (-560)))))) 
-(-881) 
+(-882) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-882) 
+(-883) 
 ((|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 
-(-883) 
+(-884) 
 ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-884 S) 
+(-885 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-885) 
+(-886) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-886) 
+(-887) 
 ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-887) 
+(-888) 
 ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) 
 NIL 
 NIL 
-(-888 |VariableList|) 
+(-889 |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 
-(-889) 
+(-890) 
 ((|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 
-(-890 R |vl| |wl| |wtlevel|) 
+(-891 R |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) 
+((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-891 R PS UP) 
+(-892 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 
-(-892 R |x| |pt|) 
+(-893 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 
-(-893 |p|) 
+(-894 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-894 |p|) 
+(-895 |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}."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-895 |p|) 
+(-896 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2191 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1183))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) 
-(-896 |p| PADIC) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-2309 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) 
+(-897 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2191 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) 
-(-897 S T$) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-2309 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(-898 S T$) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) 
-(-898) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) 
+(-899) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) 
 NIL 
 NIL 
-(-899) 
+(-900) 
 ((|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 
-(-900) 
+(-901) 
 ((|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 
-(-901 CF1 CF2) 
+(-902 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-902 |ComponentFunction|) 
+(-903 |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 
-(-903 CF1 CF2) 
+(-904 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-904 |ComponentFunction|) 
+(-905 |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 
-(-905) 
+(-906) 
 ((|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 
-(-906 CF1 CF2) 
+(-907 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-907 |ComponentFunction|) 
+(-908 |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 
-(-908) 
+(-909) 
 ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-909 R) 
+(-910 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 
-(-910 R S L) 
+(-911 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 
-(-911 S) 
+(-912 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 
-(-912 |Base| |Subject| |Pat|) 
+(-913 |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 (-1372 (|HasCategory| |#2| (QUOTE (-1080)))) (-1372 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-1372 (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208))))) 
-(-913 R S) 
+((-12 (-2912 (|HasCategory| |#2| (QUOTE (-1081)))) (-2912 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2912 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) 
+(-914 R S) 
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-914 R A B) 
+(-915 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-915 R) 
+(-916 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) 
 NIL 
 NIL 
-(-916 R -4324) 
+(-917 R -3095) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
-(-917 R S) 
+(-918 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 
-(-918 |VarSet|) 
+(-919 |VarSet|) 
 ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) 
 NIL 
 NIL 
-(-919 UP R) 
+(-920 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-920 A T$ S) 
+(-921 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 
-(-921 T$ S) 
+(-922 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 
-(-922) 
+(-923) 
 ((|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 
-(-923 UP -1610) 
+(-924 UP -4346) 
 ((|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 
-(-924) 
+(-925) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **"))) 
 NIL 
 NIL 
-(-925) 
+(-926) 
 ((|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 
-(-926 R S) 
+(-927 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
-(-927 S) 
+(-928 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-928 A S) 
+(-929 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 
-(-929 S) 
+(-930 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 
-(-930 S) 
+(-931 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-931 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-932 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-4506 . T)) 
-((-2191 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) 
-(-932 |n| R) 
+((-4507 . T)) 
+((-2309 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) 
+(-933 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
 NIL 
-(-933 S) 
+(-934 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."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-934 S) 
+(-935 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 
-(-935 |p|) 
+(-936 |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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) 
-(-936 R E |VarSet| S) 
+(-937 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 
-(-937 R S) 
+(-938 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 
-(-938 S) 
+(-939 S) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-147)))) 
-(-939) 
+(-940) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-940 R0 -1610 UP UPUP R) 
+(-941 R0 -4346 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 
-(-941 UP UPUP R) 
+(-942 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 
-(-942 UP UPUP) 
+(-943 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 
-(-943 R) 
+(-944 R) 
 ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-944 R) 
+(-945 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 
-(-945 E OV R P) 
+(-946 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-946) 
+(-947) 
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) 
 NIL 
 NIL 
-(-947 -1610) 
+(-948 -4346) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
-(-948) 
+(-949) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4511 "*") . T)) 
+(((-4512 "*") . T)) 
 NIL 
-(-949 R) 
+(-950 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 
-(-950) 
+(-951) 
 ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-951 |xx| -1610) 
+(-952 |xx| -4346) 
 ((|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 
-(-952 -1610 P) 
+(-953 -4346 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-953 R |Var| |Expon| GR) 
+(-954 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) 
 NIL 
 NIL 
-(-954) 
+(-955) 
 ((|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 
-(-955 S) 
+(-956 S) 
 ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) 
 NIL 
 NIL 
-(-956) 
+(-957) 
 ((|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 
-(-957) 
+(-958) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-958) 
+(-959) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-959 R -1610) 
+(-960 R -4346) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-960 S A B) 
+(-961 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 
-(-961 S R -1610) 
+(-962 S R -4346) 
 ((|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 
-(-962 I) 
+(-963 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 
-(-963 S E) 
+(-964 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 
-(-964 S R L) 
+(-965 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 
-(-965 S E V R P) 
+(-966 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 -911) (|devaluate| |#1|)))) 
-(-966 -4324) 
+((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) 
+(-967 -3095) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-967 R -1610 -4324) 
+(-968 R -4346 -3095) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-968 S R Q) 
+(-969 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 
-(-969 S) 
+(-970 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 
-(-970 S R P) 
+(-971 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 
-(-971) 
+(-972) 
 ((|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 
-(-972 R) 
+(-973 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-973 |lv| R) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-974 |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 
-(-974 |TheField| |ThePols|) 
+(-975 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-870)))) 
-(-975 R) 
+((|HasCategory| |#1| (QUOTE (-871)))) 
+(-976 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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-976 R S) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-977 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 
-(-977 |x| R) 
+(-978 |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 
-(-978 S R E |VarSet|) 
+(-979 S R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-939))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) 
-(-979 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-940))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) 
+(-980 R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
-(-980 E V R P -1610) 
+(-981 E V R P -4346) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-981 E |Vars| R P S) 
+(-982 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 
-(-982 E V R P -1610) 
+(-983 E V R P -4346) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-466)))) 
-(-983) 
+(-984) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-984) 
+(-985) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-985 R E) 
+(-986 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4507))) 
-(-986 R L) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) 
+(-987 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 
-(-987 S) 
+(-988 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-988 A B) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-989 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 
-(-989) 
+(-990) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) 
 NIL 
 NIL 
-(-990 -1610) 
+(-991 -4346) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-991 I) 
+(-992 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-992) 
+(-993) 
 ((|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 
-(-993 A B) 
+(-994 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"))) 
-((-4506 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) 
-(-994) 
+((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) 
+(-995) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-995 T$) 
+(-996 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-996 T$) 
+(-997 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-997 S T$) 
+(-998 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-998) 
+(-999) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-999 S) 
+(-1000 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
-(-1000 R |polR|) 
+(-1001 R |polR|) 
 ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-466)))) 
-(-1001) 
+(-1002) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-1002) 
+(-1003) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-1003 S |Coef| |Expon| |Var|) 
+(-1004 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 
-(-1004 |Coef| |Expon| |Var|) 
+(-1005 |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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1005) 
+(-1006) 
 ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-1006 S R E |VarSet| P) 
+(-1007 S R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-571)))) 
-(-1007 R E |VarSet| P) 
+(-1008 R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((-4509 . T)) 
+((-4510 . T)) 
 NIL 
-(-1008 R E V P) 
+(-1009 R E V P) 
 ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-466)))) 
-(-1009 K) 
+(-1010 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 
-(-1010 |VarSet| E RC P) 
+(-1011 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
 NIL 
 NIL 
-(-1011 R) 
+(-1012 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}."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1012 R1 R2) 
+(-1013 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-1013 R) 
+(-1014 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 
-(-1014 K) 
+(-1015 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-1015 R E OV PPR) 
+(-1016 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 
-(-1016 K R UP -1610) 
+(-1017 K R UP -4346) 
 ((|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 
-(-1017 R |Var| |Expon| |Dpoly|) 
+(-1018 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "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} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319))))) 
-(-1018 |vl| |nv|) 
+(-1019 |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 
-(-1019 R E V P TS) 
+(-1020 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1020) 
+(-1021) 
 ((|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 
-(-1021 A S) 
+(-1022 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 (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1183)))) 
-(-1022 S) 
+((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184)))) 
+(-1023 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}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1023 A B R S) 
+(-1024 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 
-(-1024 |n| K) 
+(-1025 |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 
-(-1025) 
+(-1026) 
 ((|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 
-(-1026 S) 
+(-1027 S) 
 ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
-(-1027 R) 
+(-1028 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.}"))) 
-((-4502 |has| |#1| (-302)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) 
-(-1028 S R) 
+((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) 
+(-1029 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 (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-302)))) 
-(-1029 R) 
+((|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-302)))) 
+(-1030 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-4502 |has| |#1| (-302)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1030 QR R QS S) 
+(-1031 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-1031 S) 
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-1032 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}."))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1033 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1033) 
+(-1034) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-1034 -1610 UP UPUP |radicnd| |n|) 
+(-1035 -4346 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2191 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2191 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2191 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2191 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2191 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2191 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) 
-(-1035 |bb|) 
+((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2309 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2309 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2309 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) 
+(-1036 |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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) 
-(-1036) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2309 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) 
+(-1037) 
 ((|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 
-(-1037) 
+(-1038) 
 ((|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 
-(-1038 RP) 
+(-1039 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 
-(-1039 S) 
+(-1040 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 
-(-1040 A S) 
+(-1041 A S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#2| (QUOTE (-1132)))) 
-(-1041 S) 
+((|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (QUOTE (-1133)))) 
+(-1042 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
 NIL 
-(-1042 S) 
+(-1043 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-1043) 
+(-1044) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
-((-4502 . T) (-4507 . T) (-4501 . T) (-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4506 . T)) 
+((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) 
 NIL 
-(-1044 R -1610) 
+(-1045 R -4346) 
 ((|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 
-(-1045 R -1610) 
+(-1046 R -4346) 
 ((|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 
-(-1046 -1610 UP) 
+(-1047 -4346 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 
-(-1047 -1610 UP) 
+(-1048 -4346 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 
-(-1048 S) 
+(-1049 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 
-(-1049 F1 UP UPUP R F2) 
+(-1050 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 
-(-1050) 
+(-1051) 
 ((|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 
-(-1051) 
+(-1052) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1052 |Pol|) 
+(-1053 |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 
-(-1053 |Pol|) 
+(-1054 |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 
-(-1054) 
+(-1055) 
 ((|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 
-(-1055 |TheField|) 
+(-1056 |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"))) 
-((-4502 . T) (-4507 . T) (-4501 . T) (-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4506 . T)) 
-((-2191 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) 
-(-1056 -1610 L) 
+((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) 
+((-2309 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) 
+(-1057 -4346 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 
-(-1057 S) 
+(-1058 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 (-1132)))) 
-(-1058 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1133)))) 
+(-1059 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1059) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1060) 
 ((|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 
-(-1060 R) 
+(-1061 R) 
 ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4511 "*")))) 
-(-1061 R) 
+((|HasAttribute| |#1| (QUOTE (-4512 "*")))) 
+(-1062 R) 
 ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319)))) 
-(-1062 S) 
+(-1063 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-1063 S) 
+(-1064 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-1064 S) 
+(-1065 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 
-(-1065 -1610 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1066 -4346 |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"))) 
-(((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1066) 
-((|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.}"))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1208))) (|%list| (QUOTE |:|) (QUOTE -2660) (QUOTE (-51))))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-1208) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102)))) 
 (-1067) 
+((|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.}"))) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102)))) 
+(-1068) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1068 A S) 
+(-1069 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 
-(-1069 S) 
+(-1070 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 
-(-1070 Q R) 
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 ((|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 
-(-1071 R) 
+(-1072 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-1072) 
+(-1073) 
 ((|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 
-(-1073 UP) 
+(-1074 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 
-(-1074 R) 
+(-1075 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 
-(-1075 T$) 
+(-1076 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-1076 T$) 
+(-1077 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-1077 R |ls|) 
+(-1078 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1132))) (|HasCategory| (-802 |#1| (-888 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -802) (|devaluate| |#1|) (|%list| (QUOTE -888) (|devaluate| |#2|)))))) (|HasCategory| (-802 |#1| (-888 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-888 |#2|) (QUOTE (-381))) (|HasCategory| (-802 |#1| (-888 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-102)))) 
-(-1078) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-1133))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -802) (|devaluate| |#1|) (|%list| (QUOTE -889) (|devaluate| |#2|)))))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-889 |#2|) (QUOTE (-381))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-102)))) 
+(-1079) 
 ((|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 
-(-1079 S) 
+(-1080 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 
-(-1080) 
+(-1081) 
 ((|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."))) 
-((-4506 . T)) 
+((-4507 . T)) 
 NIL 
-(-1081 |xx| -1610) 
+(-1082 |xx| -4346) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1082 S) 
+(-1083 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 
-(-1083 S |m| |n| R |Row| |Col|) 
+(-1084 S |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-571))) (|HasCategory| |#4| (QUOTE (-175)))) 
-(-1084 |m| |n| R |Row| |Col|) 
+(-1085 |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"))) 
-((-4509 . T) (-4504 . T) (-4503 . T)) 
+((-4510 . T) (-4505 . T) (-4504 . T)) 
 NIL 
-(-1085 |m| |n| R) 
+(-1086 |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}."))) 
-((-4509 . T) (-4504 . T) (-4503 . T)) 
-((|HasCategory| |#3| (QUOTE (-175))) (-2191 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) 
-(-1086 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4510 . T) (-4505 . T) (-4504 . T)) 
+((|HasCategory| |#3| (QUOTE (-175))) (-2309 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) 
+(-1087 |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 
-(-1087 R) 
+(-1088 R) 
 ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-1088) 
+(-1089) 
 ((|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 
-(-1089 S T$) 
+(-1090 S T$) 
 ((|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 (-1132)))) 
-(-1090 S) 
+((|HasCategory| |#1| (QUOTE (-1133)))) 
+(-1091 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1091) 
+(-1092) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1092 |TheField| |ThePolDom|) 
+(-1093 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1093) 
+(-1094) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-4497 . T) (-4501 . T) (-4496 . T) (-4507 . T) (-4508 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1094) 
+(-1095) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1208))) (|%list| (QUOTE |:|) (QUOTE -2660) (QUOTE (-51))))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-1208) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102)))) 
-(-1095 S R E V) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3529) (QUOTE (-51))))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1209)) (|:| -3529 (-51))) (QUOTE (-102)))) 
+(-1096 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1022) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-1208))))) 
-(-1096 R E V) 
+((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1023) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-1209))))) 
+(-1097 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
-(-1097) 
+(-1098) 
 ((|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 
-(-1098 S |TheField| |ThePols|) 
+(-1099 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 
-(-1099 |TheField| |ThePols|) 
+(-1100 |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 
-(-1100 R E V P TS) 
+(-1101 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1101 S R E V P) 
+(-1102 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-1102 R E V P) 
+(-1103 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1103 R E V P TS) 
+(-1104 R E V P TS) 
 ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1104) 
+(-1105) 
 ((|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 
-(-1105) 
+(-1106) 
 ((|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 
-(-1106 |Base| R -1610) 
+(-1107 |Base| R -4346) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-1107 |f|) 
+(-1108 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1108 |Base| R -1610) 
+(-1109 |Base| R -4346) 
 ((|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 
-(-1109 R |ls|) 
+(-1110 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 
-(-1110 R UP M) 
+(-1111 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."))) 
-((-4502 |has| |#1| (-376)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) 
-(-1111 UP SAE UPA) 
+((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
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+(-1112 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 
-(-1112 UP SAE UPA) 
+(-1113 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 
-(-1113) 
+(-1114) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1114) 
+(-1115) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1115 S) 
+(-1116 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 
-(-1116) 
+(-1117) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-1117 R) 
+(-1118 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 
-(-1118 R) 
+(-1119 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"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1119 (-1208)) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1119 (-1208)) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1119 (-1208)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1119 (-1208)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1119 (-1208)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-1119 S) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1120 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 
-(-1120 S) 
+(-1121 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1132)))) 
-(-1121 R S) 
+((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1133)))) 
+(-1122 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 (-870)))) 
-(-1122) 
+((|HasCategory| |#1| (QUOTE (-871)))) 
+(-1123) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1123 S) 
+(-1124 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1120 |#1|) (QUOTE (-1132)))) 
-(-1124 R S) 
+((|HasCategory| (-1121 |#1|) (QUOTE (-1133)))) 
+(-1125 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1125 S) 
+(-1126 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1126 S L) 
+(-1127 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 
-(-1127) 
+(-1128) 
 ((|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 
-(-1128 S) 
+(-1129 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)}}"))) 
-((-4509 . T) (-4499 . T) (-4510 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-1129 A S) 
+((-4510 . T) (-4500 . T) (-4511 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-1130 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1130 S) 
+(-1131 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-4499 . T)) 
+((-4500 . T)) 
 NIL 
-(-1131 S) 
+(-1132 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 
-(-1132) 
+(-1133) 
 ((|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 
-(-1133 |m| |n|) 
+(-1134 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1134) 
+(-1135) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1135 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1136 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1136 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1137 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1137 R FS) 
+(-1138 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 
-(-1138 R E V P TS) 
+(-1139 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1139 R E V P TS) 
+(-1140 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1140 R E V P) 
+(-1141 R E V P) 
 ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1141) 
+(-1142) 
 ((|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 
-(-1142 S) 
+(-1143 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1143) 
+(-1144) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1144 |dimtot| |dim1| S) 
+(-1145 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-4503 |has| |#3| (-1080)) (-4504 |has| |#3| (-1080)) (-4506 |has| |#3| (-6 -4506)) (-4509 . T)) 
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|#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-872))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2309 (|HasCategory| |#3| (QUOTE (-1081))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1133)))) (|HasAttribute| |#3| (QUOTE -4507)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
+(-1146 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-466)))) 
-(-1146) 
+(-1147) 
 ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) 
 NIL 
 NIL 
-(-1147) 
+(-1148) 
 ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) 
 NIL 
 NIL 
-(-1148 R -1610) 
+(-1149 R -4346) 
 ((|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 
-(-1149 R) 
+(-1150 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 
-(-1150) 
+(-1151) 
 ((|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 
-(-1151) 
+(-1152) 
 ((|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."))) 
-((-4497 . T) (-4501 . T) (-4496 . T) (-4507 . T) (-4508 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1152 S) 
+(-1153 S) 
 ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4509 . T) (-4510 . T)) 
+((-4510 . T) (-4511 . T)) 
 NIL 
-(-1153 S |ndim| R |Row| |Col|) 
+(-1154 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4511 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) 
-(-1154 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4512 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) 
+(-1155 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
-((-4509 . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4510 . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1155 R |Row| |Col| M) 
+(-1156 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 
-(-1156 R |VarSet|) 
+(-1157 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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-1157 |Coef| |Var| SMP) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-940))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1158 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1158 R E V P) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-1159 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}"))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1159 UP -1610) 
+(-1160 UP -4346) 
 ((|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 
-(-1160 R) 
+(-1161 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 
-(-1161 R) 
+(-1162 R) 
 ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1162 R) 
+(-1163 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 
-(-1163 S A) 
+(-1164 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 (-871)))) 
-(-1164 R) 
+((|HasCategory| |#1| (QUOTE (-872)))) 
+(-1165 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 
-(-1165 R) 
+(-1166 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1166) 
+(-1167) 
 ((|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 
-(-1167) 
+(-1168) 
 ((|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 
-(-1168) 
+(-1169) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) 
 NIL 
 NIL 
-(-1169) 
+(-1170) 
 ((|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 
-(-1170) 
+(-1171) 
 ((|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 
-(-1171 V C) 
+(-1172 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1172 V C) 
+(-1173 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2191 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2191 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) 
-(-1173 |ndim| R) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-2309 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-2309 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) 
+(-1174 |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}."))) 
-((-4506 . T) (-4498 |has| |#2| (-6 (-4511 "*"))) (-4509 . T) (-4503 . T) (-4504 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2191 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
-(-1174 S) 
+((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-2309 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
+(-1175 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1175) 
+(-1176) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1176 R E V P TS) 
+(-1177 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1177 R E V P) 
+(-1178 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1178) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1179) 
 ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) 
 NIL 
 NIL 
-(-1179 S) 
+(-1180 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}."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1180 A S) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1181 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 
-(-1181 S) 
+(-1182 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 
-(-1182 |Key| |Ent| |dent|) 
+(-1183 |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."))) 
-((-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132)))) 
-(-1183) 
+((-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133)))) 
+(-1184) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1184) 
+(-1185) 
 ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1185 |Coef|) 
+(-1186 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1186 S) 
-((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) 
-((-4510 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-1187 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."))) 
+((-4511 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1188 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 
-(-1188 A B) 
+(-1189 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 
-(-1189 A B C) 
+(-1190 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 
-(-1190) 
+(-1191) 
 ((|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"))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2191 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2191 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
-(-1191 |Entry|) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2309 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2309 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+(-1192 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#1|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102)))) 
-(-1192 A) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#1|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 (-1191)) (|:| -3529 |#1|)) (QUOTE (-102)))) 
+(-1193 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) 
-(-1193 |Coef|) 
+(-1194 |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 
-(-1194 |Coef|) 
+(-1195 |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 
-(-1195 R UP) 
+(-1196 R UP) 
 ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-319)))) 
-(-1196 |n| R) 
+(-1197 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1197 S1 S2) 
+(-1198 S1 S2) 
 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) 
 NIL 
 NIL 
-(-1198) 
+(-1199) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1199 |Coef| |var| |cen|) 
+(-1200 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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|#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-147))) (-2309 (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1207 |#1| |#2| |#3|) (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1201 R -4346) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
 NIL 
-(-1201 R) 
+(-1202 R) 
 ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) 
 NIL 
 NIL 
-(-1202 R) 
+(-1203 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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4505 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-1203 R S) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
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+(-1204 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 
-(-1204 E OV R P) 
+(-1205 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 
-(-1205 |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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
 (-1206 |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."))) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
+(-1207 |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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
-(-1207) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
+(-1208) 
 ((|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 
-(-1208) 
+(-1209) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1209 R) 
+(-1210 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 
-(-1210 R) 
+(-1211 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4507))) 
-(-1211) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2309 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) 
+(-1212) 
 ((|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 
-(-1212) 
+(-1213) 
 ((|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 
-(-1213) 
+(-1214) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1214 N) 
+(-1215 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1215 N) 
+(-1216 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) 
 NIL 
 NIL 
-(-1216) 
+(-1217) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1217 R) 
+(-1218 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 
-(-1218) 
+(-1219) 
 ((|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 
-(-1219 S) 
+(-1220 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1220 |Key| |Entry|) 
+(-1221 |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}"))) 
-((-4509 . T) (-4510 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) 
-(-1221 S) 
+((-4510 . T) (-4511 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1919) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3529) (|devaluate| |#2|)))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2309 (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (QUOTE (-102)))) 
+(-1222 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 
-(-1222 S) 
+(-1223 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 
-(-1223 R) 
+(-1224 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 
-(-1224 S |Key| |Entry|) 
+(-1225 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1225 |Key| |Entry|) 
+(-1226 |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-4510 . T)) 
+((-4511 . T)) 
 NIL 
-(-1226 |Key| |Entry|) 
+(-1227 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) 
 NIL 
 NIL 
-(-1227) 
+(-1228) 
 ((|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 
-(-1228) 
+(-1229) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1229 S) 
+(-1230 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 
-(-1230) 
+(-1231) 
 ((|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 
-(-1231 R) 
+(-1232 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 
-(-1232) 
+(-1233) 
 ((|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 
-(-1233 S) 
+(-1234 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1234) 
+(-1235) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1235 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}."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-1236 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1237 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1237) 
+(-1238) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1238 R -1610) 
+(-1239 R -4346) 
 ((|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 
-(-1239 R |Row| |Col| M) 
+(-1240 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 
-(-1240 R -1610) 
+(-1241 R -4346) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (|devaluate| |#1|))))) 
-(-1241 |Coef|) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) 
+(-1242 |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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1242 S R E V P) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-1243 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-381)))) 
-(-1243 R E V P) 
+(-1244 R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1244 |Curve|) 
+(-1245 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 
-(-1245) 
+(-1246) 
 ((|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 
-(-1246 S) 
+(-1247 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) 
-(-1247 -1610) 
+((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) 
+(-1248 -4346) 
 ((|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 
-(-1248) 
+(-1249) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1249) 
+(-1250) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1250 S) 
+(-1251 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-871)))) 
-(-1251) 
+((|HasCategory| |#1| (QUOTE (-872)))) 
+(-1252) 
 ((|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 
-(-1252 S) 
+(-1253 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 
-(-1253) 
+(-1254) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1254) 
+(-1255) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1255) 
+(-1256) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1256) 
+(-1257) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1257) 
+(-1258) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1258 |Coef| |var| |cen|) 
+(-1259 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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(QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1260 |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 
-(-1260 |Coef|) 
+(-1261 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1261 S |Coef| UTS) 
+(-1262 S |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
-(-1262 |Coef| UTS) 
+(-1263 |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)}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
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 NIL 
-(-1263 |Coef| UTS) 
+(-1264 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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 ((|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."))) 
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 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
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-(-1268 |x| R |y| S) 
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+((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2309 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2309 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2309 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(-1269 |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 
-(-1269 R Q UP) 
+(-1270 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1270 R UP) 
+(-1271 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1271 R UP) 
+(-1272 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 
-(-1272 R U) 
+(-1273 R U) 
 ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) 
 NIL 
 NIL 
-(-1273 S R) 
+(-1274 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1183)))) 
-(-1274 R) 
+((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1184)))) 
+(-1275 R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4505 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
-(-1275 R PR S PS) 
+(-1276 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 
-(-1276 S |Coef| |Expon|) 
+(-1277 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#2|) (QUOTE (-1208)))))) 
-(-1277 |Coef| |Expon|) 
+((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) 
+(-1278 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1278 RC P) 
+(-1279 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1279 |Coef| |var| |cen|) 
+(-1280 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
-(-1280 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
+(-1281 |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 
-(-1281 |Coef|) 
+(-1282 |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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1282 S |Coef| ULS) 
+(-1283 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 
-(-1283 |Coef| ULS) 
+(-1284 |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)}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1284 |Coef| ULS) 
+(-1285 |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)}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) 
-(-1285 R FE |var| |cen|) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2309 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) 
+(-1286 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))}."))) 
-(((-4511 "*") |has| (-1279 |#2| |#3| |#4|) (-175)) (-4502 |has| (-1279 |#2| |#3| |#4|) (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-175))) (-2191 (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-571)))) 
-(-1286 A S) 
+(((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-2309 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) 
+(-1287 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4510))) 
-(-1287 S) 
+((|HasAttribute| |#1| (QUOTE -4511))) 
+(-1288 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1288 |Coef| |var| |cen|) 
+(-1289 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) 
-(-1289 |Coef1| |Coef2| UTS1 UTS2) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2309 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3834) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2309 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) 
+(-1290 |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 
-(-1290 S |Coef|) 
+(-1291 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 (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1234))) (|HasSignature| |#2| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1208))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-1291 |Coef|) 
+((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -2712) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3671) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) 
+(-1292 |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."))) 
-(((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1292 |Coef| UTS) 
+(-1293 |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 
-(-1293 -1610 UP L UTS) 
+(-1294 -4346 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 (-571)))) 
-(-1294) 
+(-1295) 
 ((|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 
-(-1295 |sym|) 
+(-1296 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1296 S R) 
+(-1297 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1297 R) 
+((|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1298 R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4510 . T) (-4509 . T)) 
+((-4511 . T) (-4510 . T)) 
 NIL 
-(-1298 R) 
+(-1299 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4510 . T) (-4509 . T)) 
-((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-1299 A B) 
+((-4511 . T) (-4510 . T)) 
+((-2309 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2309 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2309 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2309 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-1300 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 
-(-1300) 
+(-1301) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1301) 
+(-1302) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1302) 
+(-1303) 
 ((|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 
-(-1303) 
+(-1304) 
 ((|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 
-(-1304) 
+(-1305) 
 ((|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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1305 A S) 
+(-1306 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1306 S) 
+(-1307 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}."))) 
-((-4504 . T) (-4503 . T)) 
+((-4505 . T) (-4504 . T)) 
 NIL 
-(-1307 R) 
+(-1308 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1308 K R UP -1610) 
+(-1309 K R UP -4346) 
 ((|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 
-(-1309) 
+(-1310) 
 ((|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 
-(-1310) 
+(-1311) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1311 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1312 R |VarSet| E P |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) 
+((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1312 R E V P) 
+(-1313 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) 
-((-4510 . T) (-4509 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1313 R) 
+((-4511 . T) (-4510 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1314 R) 
 ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) 
-((-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1314 |vl| R) 
+(-1315 |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."))) 
-((-4506 . T) (-4502 |has| |#2| (-6 -4502)) (-4504 . T) (-4503 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4502))) 
-(-1315 R |VarSet| XPOLY) 
+((-4507 . T) (-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4503))) 
+(-1316 R |VarSet| XPOLY) 
 ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) 
 NIL 
 NIL 
-(-1316 S -1610) 
+(-1317 S -4346) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) 
-(-1317 -1610) 
+(-1318 -4346) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
-(-1318 |vl| R) 
+(-1319 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4502 |has| |#2| (-6 -4502)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
-(-1319 |VarSet| R) 
+(-1320 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) 
-((-4502 |has| |#2| (-6 -4502)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -739) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasAttribute| |#2| (QUOTE -4502))) 
-(-1320 R) 
+((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -739) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasAttribute| |#2| (QUOTE -4503))) 
+(-1321 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."))) 
-((-4502 |has| |#1| (-6 -4502)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4502))) 
-(-1321 |vl| R) 
+((-4503 |has| |#1| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4503))) 
+(-1322 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4502 |has| |#2| (-6 -4502)) (-4504 . T) (-4503 . T) (-4506 . T)) 
+((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) 
 NIL 
-(-1322 R E) 
+(-1323 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-4506 . T) (-4507 |has| |#1| (-6 -4507)) (-4502 |has| |#1| (-6 -4502)) (-4504 . T) (-4503 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4502))) 
-(-1323 |VarSet| R) 
+((-4507 . T) (-4508 |has| |#1| (-6 -4508)) (-4503 |has| |#1| (-6 -4503)) (-4505 . T) (-4504 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4503))) 
+(-1324 |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."))) 
-((-4502 |has| |#2| (-6 -4502)) (-4504 . T) (-4503 . T) (-4506 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4502))) 
-(-1324) 
+((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4503))) 
+(-1325) 
 ((|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 
-(-1325 A) 
+(-1326 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 
-(-1326 R |ls| |ls2|) 
+(-1327 R |ls| |ls2|) 
 ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.	") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1327 R) 
+(-1328 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1328 |p|) 
+(-1329 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) 
+(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5260,4 +5264,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2294582 2294587 2294592 2294597) (-2 NIL 2294562 2294567 2294572 2294577) (-1 NIL 2294542 2294547 2294552 2294557) (0 NIL 2294522 2294527 2294532 2294537) (-1328 "ZMOD.spad" 2294331 2294344 2294460 2294517) (-1327 "ZLINDEP.spad" 2293429 2293440 2294321 2294326) (-1326 "ZDSOLVE.spad" 2283389 2283411 2293419 2293424) (-1325 "YSTREAM.spad" 2282884 2282895 2283379 2283384) (-1324 "YDIAGRAM.spad" 2282518 2282527 2282874 2282879) (-1323 "XRPOLY.spad" 2281738 2281758 2282374 2282443) (-1322 "XPR.spad" 2279533 2279546 2281456 2281555) (-1321 "XPOLYC.spad" 2278852 2278868 2279459 2279528) (-1320 "XPOLY.spad" 2278407 2278418 2278708 2278777) (-1319 "XPBWPOLY.spad" 2276846 2276866 2278181 2278250) (-1318 "XFALG.spad" 2273894 2273910 2276772 2276841) (-1317 "XF.spad" 2272357 2272372 2273796 2273889) (-1316 "XF.spad" 2270800 2270817 2272241 2272246) (-1315 "XEXPPKG.spad" 2270059 2270085 2270790 2270795) (-1314 "XDPOLY.spad" 2269673 2269689 2269915 2269984) (-1313 "XALG.spad" 2269341 2269352 2269629 2269668) (-1312 "WUTSET.spad" 2265311 2265328 2268942 2268969) (-1311 "WP.spad" 2264518 2264562 2265169 2265236) (-1310 "WHILEAST.spad" 2264316 2264325 2264508 2264513) (-1309 "WHEREAST.spad" 2263987 2263996 2264306 2264311) (-1308 "WFFINTBS.spad" 2261650 2261672 2263977 2263982) (-1307 "WEIER.spad" 2259872 2259883 2261640 2261645) (-1306 "VSPACE.spad" 2259545 2259556 2259840 2259867) (-1305 "VSPACE.spad" 2259238 2259251 2259535 2259540) (-1304 "VOID.spad" 2258915 2258924 2259228 2259233) (-1303 "VIEWDEF.spad" 2254116 2254125 2258905 2258910) (-1302 "VIEW3D.spad" 2238077 2238086 2254106 2254111) (-1301 "VIEW2D.spad" 2225976 2225985 2238067 2238072) (-1300 "VIEW.spad" 2223696 2223705 2225966 2225971) (-1299 "VECTOR2.spad" 2222335 2222348 2223686 2223691) (-1298 "VECTOR.spad" 2220835 2220846 2221086 2221113) (-1297 "VECTCAT.spad" 2218747 2218758 2220803 2220830) (-1296 "VECTCAT.spad" 2216466 2216479 2218524 2218529) (-1295 "VARIABLE.spad" 2216246 2216261 2216456 2216461) (-1294 "UTYPE.spad" 2215890 2215899 2216236 2216241) (-1293 "UTSODETL.spad" 2215185 2215209 2215846 2215851) (-1292 "UTSODE.spad" 2213401 2213421 2215175 2215180) (-1291 "UTSCAT.spad" 2210880 2210896 2213299 2213396) (-1290 "UTSCAT.spad" 2207979 2207997 2210400 2210405) (-1289 "UTS2.spad" 2207574 2207609 2207969 2207974) (-1288 "UTS.spad" 2202452 2202480 2205972 2206069) (-1287 "URAGG.spad" 2197173 2197184 2202442 2202447) (-1286 "URAGG.spad" 2191858 2191871 2197129 2197134) (-1285 "UPXSSING.spad" 2189476 2189502 2190912 2191045) (-1284 "UPXSCONS.spad" 2187154 2187174 2187527 2187676) (-1283 "UPXSCCA.spad" 2185725 2185745 2187000 2187149) (-1282 "UPXSCCA.spad" 2184438 2184460 2185715 2185720) (-1281 "UPXSCAT.spad" 2183027 2183043 2184284 2184433) (-1280 "UPXS2.spad" 2182570 2182623 2183017 2183022) (-1279 "UPXS.spad" 2179785 2179813 2180621 2180770) (-1278 "UPSQFREE.spad" 2178199 2178213 2179775 2179780) (-1277 "UPSCAT.spad" 2175994 2176018 2178097 2178194) (-1276 "UPSCAT.spad" 2173474 2173500 2175579 2175584) (-1275 "UPOLYC2.spad" 2172945 2172964 2173464 2173469) (-1274 "UPOLYC.spad" 2168025 2168036 2172787 2172940) (-1273 "UPOLYC.spad" 2162991 2163004 2167755 2167760) (-1272 "UPMP.spad" 2161923 2161936 2162981 2162986) (-1271 "UPDIVP.spad" 2161488 2161502 2161913 2161918) (-1270 "UPDECOMP.spad" 2159749 2159763 2161478 2161483) (-1269 "UPCDEN.spad" 2158966 2158982 2159739 2159744) (-1268 "UP2.spad" 2158330 2158351 2158956 2158961) (-1267 "UP.spad" 2155358 2155373 2155745 2155898) (-1266 "UNISEG2.spad" 2154855 2154868 2155314 2155319) (-1265 "UNISEG.spad" 2154208 2154219 2154774 2154779) (-1264 "UNIFACT.spad" 2153311 2153323 2154198 2154203) (-1263 "ULSCONS.spad" 2144223 2144243 2144593 2144742) (-1262 "ULSCCAT.spad" 2141960 2141980 2144069 2144218) (-1261 "ULSCCAT.spad" 2139805 2139827 2141916 2141921) (-1260 "ULSCAT.spad" 2138045 2138061 2139651 2139800) (-1259 "ULS2.spad" 2137559 2137612 2138035 2138040) (-1258 "ULS.spad" 2127130 2127158 2128075 2128504) (-1257 "UINT8.spad" 2127007 2127016 2127120 2127125) (-1256 "UINT64.spad" 2126883 2126892 2126997 2127002) (-1255 "UINT32.spad" 2126759 2126768 2126873 2126878) (-1254 "UINT16.spad" 2126635 2126644 2126749 2126754) (-1253 "UFD.spad" 2125700 2125709 2126561 2126630) (-1252 "UFD.spad" 2124827 2124838 2125690 2125695) (-1251 "UDVO.spad" 2123708 2123717 2124817 2124822) (-1250 "UDPO.spad" 2121289 2121300 2123664 2123669) (-1249 "TYPEAST.spad" 2121208 2121217 2121279 2121284) (-1248 "TYPE.spad" 2121140 2121149 2121198 2121203) (-1247 "TWOFACT.spad" 2119792 2119807 2121130 2121135) (-1246 "TUPLE.spad" 2119283 2119294 2119688 2119693) (-1245 "TUBETOOL.spad" 2116150 2116159 2119273 2119278) (-1244 "TUBE.spad" 2114797 2114814 2116140 2116145) (-1243 "TSETCAT.spad" 2102868 2102885 2114765 2114792) (-1242 "TSETCAT.spad" 2090925 2090944 2102824 2102829) (-1241 "TS.spad" 2089518 2089534 2090484 2090581) (-1240 "TRMANIP.spad" 2083882 2083899 2089206 2089211) (-1239 "TRIMAT.spad" 2082845 2082870 2083872 2083877) (-1238 "TRIGMNIP.spad" 2081372 2081389 2082835 2082840) (-1237 "TRIGCAT.spad" 2080884 2080893 2081362 2081367) (-1236 "TRIGCAT.spad" 2080394 2080405 2080874 2080879) (-1235 "TREE.spad" 2078840 2078851 2079872 2079899) (-1234 "TRANFUN.spad" 2078679 2078688 2078830 2078835) (-1233 "TRANFUN.spad" 2078516 2078527 2078669 2078674) (-1232 "TOPSP.spad" 2078190 2078199 2078506 2078511) (-1231 "TOOLSIGN.spad" 2077853 2077864 2078180 2078185) (-1230 "TEXTFILE.spad" 2076414 2076423 2077843 2077848) (-1229 "TEX1.spad" 2075970 2075981 2076404 2076409) (-1228 "TEX.spad" 2073164 2073173 2075960 2075965) (-1227 "TEMUTL.spad" 2072719 2072728 2073154 2073159) (-1226 "TBCMPPK.spad" 2070820 2070843 2072709 2072714) (-1225 "TBAGG.spad" 2069878 2069901 2070800 2070815) (-1224 "TBAGG.spad" 2068944 2068969 2069868 2069873) (-1223 "TANEXP.spad" 2068352 2068363 2068934 2068939) (-1222 "TALGOP.spad" 2068076 2068087 2068342 2068347) (-1221 "TABLEAU.spad" 2067557 2067568 2068066 2068071) (-1220 "TABLE.spad" 2065490 2065513 2065760 2065787) (-1219 "TABLBUMP.spad" 2062269 2062280 2065480 2065485) (-1218 "SYSTEM.spad" 2061497 2061506 2062259 2062264) (-1217 "SYSSOLP.spad" 2058980 2058991 2061487 2061492) (-1216 "SYSPTR.spad" 2058879 2058888 2058970 2058975) (-1215 "SYSNNI.spad" 2058102 2058113 2058869 2058874) (-1214 "SYSINT.spad" 2057506 2057517 2058092 2058097) (-1213 "SYNTAX.spad" 2053840 2053849 2057496 2057501) (-1212 "SYMTAB.spad" 2051908 2051917 2053830 2053835) (-1211 "SYMS.spad" 2047931 2047940 2051898 2051903) (-1210 "SYMPOLY.spad" 2046910 2046921 2046992 2047119) (-1209 "SYMFUNC.spad" 2046411 2046422 2046900 2046905) (-1208 "SYMBOL.spad" 2043906 2043915 2046401 2046406) (-1207 "SWITCH.spad" 2040677 2040686 2043896 2043901) (-1206 "SUTS.spad" 2037656 2037684 2039075 2039172) (-1205 "SUPXS.spad" 2034858 2034886 2035707 2035856) (-1204 "SUPFRACF.spad" 2033963 2033981 2034848 2034853) (-1203 "SUP2.spad" 2033355 2033368 2033953 2033958) (-1202 "SUP.spad" 2029997 2030008 2030770 2030923) (-1201 "SUMRF.spad" 2028971 2028982 2029987 2029992) (-1200 "SUMFS.spad" 2028600 2028617 2028961 2028966) (-1199 "SULS.spad" 2018158 2018186 2019116 2019545) (-1198 "SUCHTAST.spad" 2017927 2017936 2018148 2018153) (-1197 "SUCH.spad" 2017617 2017632 2017917 2017922) (-1196 "SUBSPACE.spad" 2009748 2009763 2017607 2017612) (-1195 "SUBRESP.spad" 2008918 2008932 2009704 2009709) (-1194 "STTFNC.spad" 2005386 2005402 2008908 2008913) (-1193 "STTF.spad" 2001485 2001501 2005376 2005381) (-1192 "STTAYLOR.spad" 1994130 1994141 2001360 2001365) (-1191 "STRTBL.spad" 1992145 1992162 1992294 1992321) (-1190 "STRING.spad" 1990911 1990920 1991132 1991159) (-1189 "STREAM3.spad" 1990484 1990499 1990901 1990906) (-1188 "STREAM2.spad" 1989612 1989625 1990474 1990479) (-1187 "STREAM1.spad" 1989318 1989329 1989602 1989607) (-1186 "STREAM.spad" 1986104 1986115 1988711 1988726) (-1185 "STINPROD.spad" 1985040 1985056 1986094 1986099) (-1184 "STEPAST.spad" 1984274 1984283 1985030 1985035) (-1183 "STEP.spad" 1983483 1983492 1984264 1984269) (-1182 "STBL.spad" 1981531 1981559 1981698 1981713) (-1181 "STAGG.spad" 1980606 1980617 1981521 1981526) (-1180 "STAGG.spad" 1979679 1979692 1980596 1980601) (-1179 "STACK.spad" 1978907 1978918 1979157 1979184) (-1178 "SRING.spad" 1978667 1978676 1978897 1978902) (-1177 "SREGSET.spad" 1976366 1976383 1978268 1978295) (-1176 "SRDCMPK.spad" 1974943 1974963 1976356 1976361) (-1175 "SRAGG.spad" 1970126 1970135 1974911 1974938) (-1174 "SRAGG.spad" 1965329 1965340 1970116 1970121) (-1173 "SQMATRIX.spad" 1962824 1962842 1963740 1963827) (-1172 "SPLTREE.spad" 1957290 1957303 1962086 1962113) (-1171 "SPLNODE.spad" 1953910 1953923 1957280 1957285) (-1170 "SPFCAT.spad" 1952719 1952728 1953900 1953905) (-1169 "SPECOUT.spad" 1951271 1951280 1952709 1952714) (-1168 "SPADXPT.spad" 1943362 1943371 1951261 1951266) (-1167 "spad-parser.spad" 1942827 1942836 1943352 1943357) (-1166 "SPADAST.spad" 1942528 1942537 1942817 1942822) (-1165 "SPACEC.spad" 1926743 1926754 1942518 1942523) (-1164 "SPACE3.spad" 1926519 1926530 1926733 1926738) (-1163 "SORTPAK.spad" 1926068 1926081 1926475 1926480) (-1162 "SOLVETRA.spad" 1923831 1923842 1926058 1926063) (-1161 "SOLVESER.spad" 1922287 1922298 1923821 1923826) (-1160 "SOLVERAD.spad" 1918313 1918324 1922277 1922282) (-1159 "SOLVEFOR.spad" 1916775 1916793 1918303 1918308) (-1158 "SNTSCAT.spad" 1916375 1916392 1916743 1916770) (-1157 "SMTS.spad" 1914657 1914683 1915934 1916031) (-1156 "SMP.spad" 1912060 1912080 1912450 1912577) (-1155 "SMITH.spad" 1910905 1910930 1912050 1912055) (-1154 "SMATCAT.spad" 1909023 1909053 1910849 1910900) (-1153 "SMATCAT.spad" 1907073 1907105 1908901 1908906) (-1152 "SKAGG.spad" 1906042 1906053 1907041 1907068) (-1151 "SINT.spad" 1904982 1904991 1905908 1906037) (-1150 "SIMPAN.spad" 1904710 1904719 1904972 1904977) (-1149 "SIGNRF.spad" 1903828 1903839 1904700 1904705) (-1148 "SIGNEF.spad" 1903107 1903124 1903818 1903823) (-1147 "SIGAST.spad" 1902524 1902533 1903097 1903102) (-1146 "SIG.spad" 1901886 1901895 1902514 1902519) (-1145 "SHP.spad" 1899830 1899845 1901842 1901847) (-1144 "SHDP.spad" 1887185 1887212 1887702 1887801) (-1143 "SGROUP.spad" 1886793 1886802 1887175 1887180) (-1142 "SGROUP.spad" 1886399 1886410 1886783 1886788) (-1141 "SGCF.spad" 1879538 1879547 1886389 1886394) (-1140 "SFRTCAT.spad" 1878484 1878501 1879506 1879533) (-1139 "SFRGCD.spad" 1877547 1877567 1878474 1878479) (-1138 "SFQCMPK.spad" 1872360 1872380 1877537 1877542) (-1137 "SFORT.spad" 1871799 1871813 1872350 1872355) (-1136 "SEXOF.spad" 1871642 1871682 1871789 1871794) (-1135 "SEXCAT.spad" 1869470 1869510 1871632 1871637) (-1134 "SEX.spad" 1869362 1869371 1869460 1869465) (-1133 "SETMN.spad" 1867820 1867837 1869352 1869357) (-1132 "SETCAT.spad" 1867305 1867314 1867810 1867815) (-1131 "SETCAT.spad" 1866788 1866799 1867295 1867300) (-1130 "SETAGG.spad" 1863337 1863348 1866768 1866783) (-1129 "SETAGG.spad" 1859894 1859907 1863327 1863332) (-1128 "SET.spad" 1858167 1858178 1859264 1859303) (-1127 "SEQAST.spad" 1857870 1857879 1858157 1858162) (-1126 "SEGXCAT.spad" 1857026 1857039 1857860 1857865) (-1125 "SEGCAT.spad" 1855951 1855962 1857016 1857021) (-1124 "SEGBIND2.spad" 1855649 1855662 1855941 1855946) (-1123 "SEGBIND.spad" 1855407 1855418 1855596 1855601) (-1122 "SEGAST.spad" 1855137 1855146 1855397 1855402) (-1121 "SEG2.spad" 1854572 1854585 1855093 1855098) (-1120 "SEG.spad" 1854385 1854396 1854491 1854496) (-1119 "SDVAR.spad" 1853661 1853672 1854375 1854380) (-1118 "SDPOL.spad" 1850916 1850927 1851207 1851334) (-1117 "SCPKG.spad" 1849005 1849016 1850906 1850911) (-1116 "SCOPE.spad" 1848182 1848191 1848995 1849000) (-1115 "SCACHE.spad" 1846878 1846889 1848172 1848177) (-1114 "SASTCAT.spad" 1846787 1846796 1846868 1846873) (-1113 "SAOS.spad" 1846659 1846668 1846777 1846782) (-1112 "SAERFFC.spad" 1846372 1846392 1846649 1846654) (-1111 "SAEFACT.spad" 1846073 1846093 1846362 1846367) (-1110 "SAE.spad" 1843507 1843523 1844118 1844253) (-1109 "RURPK.spad" 1841166 1841182 1843497 1843502) (-1108 "RULESET.spad" 1840619 1840643 1841156 1841161) (-1107 "RULECOLD.spad" 1840471 1840484 1840609 1840614) (-1106 "RULE.spad" 1838719 1838743 1840461 1840466) (-1105 "RTVALUE.spad" 1838454 1838463 1838709 1838714) (-1104 "RSTRCAST.spad" 1838171 1838180 1838444 1838449) (-1103 "RSETGCD.spad" 1834613 1834633 1838161 1838166) (-1102 "RSETCAT.spad" 1824581 1824598 1834581 1834608) (-1101 "RSETCAT.spad" 1814569 1814588 1824571 1824576) (-1100 "RSDCMPK.spad" 1813069 1813089 1814559 1814564) (-1099 "RRCC.spad" 1811453 1811483 1813059 1813064) (-1098 "RRCC.spad" 1809835 1809867 1811443 1811448) (-1097 "RPTAST.spad" 1809537 1809546 1809825 1809830) (-1096 "RPOLCAT.spad" 1789041 1789056 1809405 1809532) (-1095 "RPOLCAT.spad" 1768240 1768257 1788606 1788611) (-1094 "ROUTINE.spad" 1763641 1763650 1766389 1766416) (-1093 "ROMAN.spad" 1762969 1762978 1763507 1763636) (-1092 "ROIRC.spad" 1762049 1762081 1762959 1762964) (-1091 "RNS.spad" 1760952 1760961 1761951 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146508 146935 146940) (-132 "BYTEORD.spad" 146175 146183 146490 146495) (-131 "BYTEBUF.spad" 143876 143884 145162 145189) (-130 "BYTE.spad" 143351 143359 143866 143871) (-129 "BTREE.spad" 142295 142305 142829 142856) (-128 "BTOURN.spad" 141171 141181 141773 141800) (-127 "BTCAT.spad" 140563 140573 141139 141166) (-126 "BTCAT.spad" 139975 139987 140553 140558) (-125 "BTAGG.spad" 139441 139449 139943 139970) (-124 "BTAGG.spad" 138927 138937 139431 139436) (-123 "BSTREE.spad" 137539 137549 138405 138432) (-122 "BRILL.spad" 135744 135755 137529 137534) (-121 "BRAGG.spad" 134700 134710 135734 135739) (-120 "BRAGG.spad" 133620 133632 134656 134661) (-119 "BPADICRT.spad" 131445 131457 131692 131785) (-118 "BPADIC.spad" 131117 131129 131371 131440) (-117 "BOUNDZRO.spad" 130773 130790 131107 131112) (-116 "BOP1.spad" 128231 128241 130763 130768) (-115 "BOP.spad" 123365 123373 128221 128226) (-114 "BOOLEAN.spad" 122803 122811 123355 123360) (-113 "BOOLE.spad" 122453 122461 122793 122798) (-112 "BOOLE.spad" 122101 122111 122443 122448) (-111 "BMODULE.spad" 121813 121825 122069 122096) (-110 "BITS.spad" 121187 121195 121402 121429) (-109 "BINDING.spad" 120608 120616 121177 121182) (-108 "BINARY.spad" 118577 118585 118933 119026) (-107 "BGAGG.spad" 117782 117792 118557 118572) (-106 "BGAGG.spad" 116995 117007 117772 117777) (-105 "BFUNCT.spad" 116559 116567 116975 116990) (-104 "BEZOUT.spad" 115699 115726 116509 116514) (-103 "BBTREE.spad" 112447 112457 115177 115204) (-102 "BASTYPE.spad" 111946 111954 112437 112442) (-101 "BASTYPE.spad" 111443 111453 111936 111941) (-100 "BALFACT.spad" 110902 110915 111433 111438) (-99 "AUTOMOR.spad" 110353 110362 110882 110897) (-98 "ATTREG.spad" 107076 107083 110105 110348) (-97 "ATTRBUT.spad" 103099 103106 107056 107071) (-96 "ATTRAST.spad" 102816 102823 103089 103094) (-95 "ATRIG.spad" 102286 102293 102806 102811) (-94 "ATRIG.spad" 101754 101763 102276 102281) (-93 "ASTCAT.spad" 101658 101665 101744 101749) (-92 "ASTCAT.spad" 101560 101569 101648 101653) (-91 "ASTACK.spad" 100770 100779 101038 101065) (-90 "ASSOCEQ.spad" 99604 99615 100726 100731) (-89 "ASP9.spad" 98685 98698 99594 99599) (-88 "ASP80.spad" 98007 98020 98675 98680) (-87 "ASP8.spad" 97050 97063 97997 98002) (-86 "ASP78.spad" 96501 96514 97040 97045) (-85 "ASP77.spad" 95870 95883 96491 96496) (-84 "ASP74.spad" 94962 94975 95860 95865) (-83 "ASP73.spad" 94233 94246 94952 94957) (-82 "ASP7.spad" 93393 93406 94223 94228) (-81 "ASP6.spad" 92260 92273 93383 93388) (-80 "ASP55.spad" 90769 90782 92250 92255) (-79 "ASP50.spad" 88586 88599 90759 90764) (-78 "ASP49.spad" 87585 87598 88576 88581) (-77 "ASP42.spad" 86000 86039 87575 87580) (-76 "ASP41.spad" 84587 84626 85990 85995) (-75 "ASP4.spad" 83882 83895 84577 84582) (-74 "ASP35.spad" 82870 82883 83872 83877) (-73 "ASP34.spad" 82171 82184 82860 82865) (-72 "ASP33.spad" 81731 81744 82161 82166) (-71 "ASP31.spad" 80871 80884 81721 81726) (-70 "ASP30.spad" 79763 79776 80861 80866) (-69 "ASP29.spad" 79229 79242 79753 79758) (-68 "ASP28.spad" 70502 70515 79219 79224) (-67 "ASP27.spad" 69399 69412 70492 70497) (-66 "ASP24.spad" 68486 68499 69389 69394) (-65 "ASP20.spad" 67950 67963 68476 68481) (-64 "ASP19.spad" 62636 62649 67940 67945) (-63 "ASP12.spad" 62050 62063 62626 62631) (-62 "ASP10.spad" 61321 61334 62040 62045) (-61 "ASP1.spad" 60702 60715 61311 61316) (-60 "ARRAY2.spad" 59941 59950 60180 60207) (-59 "ARRAY12.spad" 58654 58665 59931 59936) (-58 "ARRAY1.spad" 57317 57326 57663 57690) (-57 "ARR2CAT.spad" 53099 53120 57285 57312) (-56 "ARR2CAT.spad" 48901 48924 53089 53094) (-55 "ARITY.spad" 48273 48280 48891 48896) (-54 "APPRULE.spad" 47557 47579 48263 48268) (-53 "APPLYORE.spad" 47176 47189 47547 47552) (-52 "ANY1.spad" 46247 46256 47166 47171) (-51 "ANY.spad" 45098 45105 46237 46242) (-50 "ANTISYM.spad" 43543 43559 45078 45093) (-49 "ANON.spad" 43252 43259 43533 43538) (-48 "AN.spad" 41558 41565 43065 43158) (-47 "AMR.spad" 39743 39754 41456 41553) (-46 "AMR.spad" 37759 37772 39474 39479) (-45 "ALIST.spad" 34599 34620 34949 34976) (-44 "ALGSC.spad" 33734 33760 34471 34524) (-43 "ALGPKG.spad" 29517 29528 33690 33695) (-42 "ALGMFACT.spad" 28710 28724 29507 29512) (-41 "ALGMANIP.spad" 26194 26209 28537 28542) (-40 "ALGFF.spad" 23799 23826 24016 24172) (-39 "ALGFACT.spad" 22918 22928 23789 23794) (-38 "ALGEBRA.spad" 22751 22760 22874 22913) (-37 "ALGEBRA.spad" 22616 22627 22741 22746) (-36 "ALAGG.spad" 22128 22149 22584 22611) (-35 "AHYP.spad" 21509 21516 22118 22123) (-34 "AGG.spad" 19842 19849 21499 21504) (-33 "AGG.spad" 18139 18148 19798 19803) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-3 NIL 2294689 2294694 2294699 2294704) (-2 NIL 2294669 2294674 2294679 2294684) (-1 NIL 2294649 2294654 2294659 2294664) (0 NIL 2294629 2294634 2294639 2294644) (-1329 "ZMOD.spad" 2294438 2294451 2294567 2294624) (-1328 "ZLINDEP.spad" 2293536 2293547 2294428 2294433) (-1327 "ZDSOLVE.spad" 2283496 2283518 2293526 2293531) (-1326 "YSTREAM.spad" 2282991 2283002 2283486 2283491) (-1325 "YDIAGRAM.spad" 2282625 2282634 2282981 2282986) (-1324 "XRPOLY.spad" 2281845 2281865 2282481 2282550) (-1323 "XPR.spad" 2279640 2279653 2281563 2281662) (-1322 "XPOLYC.spad" 2278959 2278975 2279566 2279635) (-1321 "XPOLY.spad" 2278514 2278525 2278815 2278884) (-1320 "XPBWPOLY.spad" 2276953 2276973 2278288 2278357) (-1319 "XFALG.spad" 2274001 2274017 2276879 2276948) (-1318 "XF.spad" 2272464 2272479 2273903 2273996) (-1317 "XF.spad" 2270907 2270924 2272348 2272353) (-1316 "XEXPPKG.spad" 2270166 2270192 2270897 2270902) (-1315 "XDPOLY.spad" 2269780 2269796 2270022 2270091) (-1314 "XALG.spad" 2269448 2269459 2269736 2269775) (-1313 "WUTSET.spad" 2265418 2265435 2269049 2269076) (-1312 "WP.spad" 2264625 2264669 2265276 2265343) (-1311 "WHILEAST.spad" 2264423 2264432 2264615 2264620) (-1310 "WHEREAST.spad" 2264094 2264103 2264413 2264418) (-1309 "WFFINTBS.spad" 2261757 2261779 2264084 2264089) (-1308 "WEIER.spad" 2259979 2259990 2261747 2261752) (-1307 "VSPACE.spad" 2259652 2259663 2259947 2259974) (-1306 "VSPACE.spad" 2259345 2259358 2259642 2259647) (-1305 "VOID.spad" 2259022 2259031 2259335 2259340) (-1304 "VIEWDEF.spad" 2254223 2254232 2259012 2259017) (-1303 "VIEW3D.spad" 2238184 2238193 2254213 2254218) (-1302 "VIEW2D.spad" 2226083 2226092 2238174 2238179) (-1301 "VIEW.spad" 2223803 2223812 2226073 2226078) (-1300 "VECTOR2.spad" 2222442 2222455 2223793 2223798) (-1299 "VECTOR.spad" 2220942 2220953 2221193 2221220) (-1298 "VECTCAT.spad" 2218854 2218865 2220910 2220937) (-1297 "VECTCAT.spad" 2216573 2216586 2218631 2218636) (-1296 "VARIABLE.spad" 2216353 2216368 2216563 2216568) (-1295 "UTYPE.spad" 2215997 2216006 2216343 2216348) (-1294 "UTSODETL.spad" 2215292 2215316 2215953 2215958) (-1293 "UTSODE.spad" 2213508 2213528 2215282 2215287) (-1292 "UTSCAT.spad" 2210987 2211003 2213406 2213503) (-1291 "UTSCAT.spad" 2208086 2208104 2210507 2210512) (-1290 "UTS2.spad" 2207681 2207716 2208076 2208081) (-1289 "UTS.spad" 2202559 2202587 2206079 2206176) (-1288 "URAGG.spad" 2197280 2197291 2202549 2202554) (-1287 "URAGG.spad" 2191965 2191978 2197236 2197241) (-1286 "UPXSSING.spad" 2189583 2189609 2191019 2191152) (-1285 "UPXSCONS.spad" 2187261 2187281 2187634 2187783) (-1284 "UPXSCCA.spad" 2185832 2185852 2187107 2187256) (-1283 "UPXSCCA.spad" 2184545 2184567 2185822 2185827) (-1282 "UPXSCAT.spad" 2183134 2183150 2184391 2184540) (-1281 "UPXS2.spad" 2182677 2182730 2183124 2183129) (-1280 "UPXS.spad" 2179892 2179920 2180728 2180877) (-1279 "UPSQFREE.spad" 2178306 2178320 2179882 2179887) (-1278 "UPSCAT.spad" 2176101 2176125 2178204 2178301) (-1277 "UPSCAT.spad" 2173581 2173607 2175686 2175691) (-1276 "UPOLYC2.spad" 2173052 2173071 2173571 2173576) (-1275 "UPOLYC.spad" 2168132 2168143 2172894 2173047) (-1274 "UPOLYC.spad" 2163098 2163111 2167862 2167867) (-1273 "UPMP.spad" 2162030 2162043 2163088 2163093) (-1272 "UPDIVP.spad" 2161595 2161609 2162020 2162025) (-1271 "UPDECOMP.spad" 2159856 2159870 2161585 2161590) (-1270 "UPCDEN.spad" 2159073 2159089 2159846 2159851) (-1269 "UP2.spad" 2158437 2158458 2159063 2159068) (-1268 "UP.spad" 2155465 2155480 2155852 2156005) (-1267 "UNISEG2.spad" 2154962 2154975 2155421 2155426) (-1266 "UNISEG.spad" 2154315 2154326 2154881 2154886) (-1265 "UNIFACT.spad" 2153418 2153430 2154305 2154310) (-1264 "ULSCONS.spad" 2144330 2144350 2144700 2144849) (-1263 "ULSCCAT.spad" 2142067 2142087 2144176 2144325) (-1262 "ULSCCAT.spad" 2139912 2139934 2142023 2142028) (-1261 "ULSCAT.spad" 2138152 2138168 2139758 2139907) (-1260 "ULS2.spad" 2137666 2137719 2138142 2138147) (-1259 "ULS.spad" 2127237 2127265 2128182 2128611) (-1258 "UINT8.spad" 2127114 2127123 2127227 2127232) (-1257 "UINT64.spad" 2126990 2126999 2127104 2127109) (-1256 "UINT32.spad" 2126866 2126875 2126980 2126985) (-1255 "UINT16.spad" 2126742 2126751 2126856 2126861) (-1254 "UFD.spad" 2125807 2125816 2126668 2126737) (-1253 "UFD.spad" 2124934 2124945 2125797 2125802) (-1252 "UDVO.spad" 2123815 2123824 2124924 2124929) (-1251 "UDPO.spad" 2121396 2121407 2123771 2123776) (-1250 "TYPEAST.spad" 2121315 2121324 2121386 2121391) (-1249 "TYPE.spad" 2121247 2121256 2121305 2121310) (-1248 "TWOFACT.spad" 2119899 2119914 2121237 2121242) (-1247 "TUPLE.spad" 2119390 2119401 2119795 2119800) (-1246 "TUBETOOL.spad" 2116257 2116266 2119380 2119385) (-1245 "TUBE.spad" 2114904 2114921 2116247 2116252) (-1244 "TSETCAT.spad" 2102975 2102992 2114872 2114899) (-1243 "TSETCAT.spad" 2091032 2091051 2102931 2102936) (-1242 "TS.spad" 2089625 2089641 2090591 2090688) (-1241 "TRMANIP.spad" 2083989 2084006 2089313 2089318) (-1240 "TRIMAT.spad" 2082952 2082977 2083979 2083984) (-1239 "TRIGMNIP.spad" 2081479 2081496 2082942 2082947) (-1238 "TRIGCAT.spad" 2080991 2081000 2081469 2081474) (-1237 "TRIGCAT.spad" 2080501 2080512 2080981 2080986) (-1236 "TREE.spad" 2078947 2078958 2079979 2080006) (-1235 "TRANFUN.spad" 2078786 2078795 2078937 2078942) (-1234 "TRANFUN.spad" 2078623 2078634 2078776 2078781) (-1233 "TOPSP.spad" 2078297 2078306 2078613 2078618) (-1232 "TOOLSIGN.spad" 2077960 2077971 2078287 2078292) (-1231 "TEXTFILE.spad" 2076521 2076530 2077950 2077955) (-1230 "TEX1.spad" 2076077 2076088 2076511 2076516) (-1229 "TEX.spad" 2073271 2073280 2076067 2076072) (-1228 "TEMUTL.spad" 2072826 2072835 2073261 2073266) (-1227 "TBCMPPK.spad" 2070927 2070950 2072816 2072821) (-1226 "TBAGG.spad" 2069985 2070008 2070907 2070922) (-1225 "TBAGG.spad" 2069051 2069076 2069975 2069980) (-1224 "TANEXP.spad" 2068459 2068470 2069041 2069046) (-1223 "TALGOP.spad" 2068183 2068194 2068449 2068454) (-1222 "TABLEAU.spad" 2067664 2067675 2068173 2068178) (-1221 "TABLE.spad" 2065597 2065620 2065867 2065894) (-1220 "TABLBUMP.spad" 2062376 2062387 2065587 2065592) (-1219 "SYSTEM.spad" 2061604 2061613 2062366 2062371) (-1218 "SYSSOLP.spad" 2059087 2059098 2061594 2061599) (-1217 "SYSPTR.spad" 2058986 2058995 2059077 2059082) (-1216 "SYSNNI.spad" 2058209 2058220 2058976 2058981) (-1215 "SYSINT.spad" 2057613 2057624 2058199 2058204) (-1214 "SYNTAX.spad" 2053947 2053956 2057603 2057608) (-1213 "SYMTAB.spad" 2052015 2052024 2053937 2053942) (-1212 "SYMS.spad" 2048038 2048047 2052005 2052010) (-1211 "SYMPOLY.spad" 2047017 2047028 2047099 2047226) (-1210 "SYMFUNC.spad" 2046518 2046529 2047007 2047012) (-1209 "SYMBOL.spad" 2044013 2044022 2046508 2046513) (-1208 "SWITCH.spad" 2040784 2040793 2044003 2044008) (-1207 "SUTS.spad" 2037763 2037791 2039182 2039279) (-1206 "SUPXS.spad" 2034965 2034993 2035814 2035963) (-1205 "SUPFRACF.spad" 2034070 2034088 2034955 2034960) (-1204 "SUP2.spad" 2033462 2033475 2034060 2034065) (-1203 "SUP.spad" 2030104 2030115 2030877 2031030) (-1202 "SUMRF.spad" 2029078 2029089 2030094 2030099) (-1201 "SUMFS.spad" 2028707 2028724 2029068 2029073) (-1200 "SULS.spad" 2018265 2018293 2019223 2019652) (-1199 "SUCHTAST.spad" 2018034 2018043 2018255 2018260) (-1198 "SUCH.spad" 2017724 2017739 2018024 2018029) (-1197 "SUBSPACE.spad" 2009855 2009870 2017714 2017719) (-1196 "SUBRESP.spad" 2009025 2009039 2009811 2009816) (-1195 "STTFNC.spad" 2005493 2005509 2009015 2009020) (-1194 "STTF.spad" 2001592 2001608 2005483 2005488) (-1193 "STTAYLOR.spad" 1994237 1994248 2001467 2001472) (-1192 "STRTBL.spad" 1992252 1992269 1992401 1992428) (-1191 "STRING.spad" 1991018 1991027 1991239 1991266) (-1190 "STREAM3.spad" 1990591 1990606 1991008 1991013) (-1189 "STREAM2.spad" 1989719 1989732 1990581 1990586) (-1188 "STREAM1.spad" 1989425 1989436 1989709 1989714) (-1187 "STREAM.spad" 1986211 1986222 1988818 1988833) (-1186 "STINPROD.spad" 1985147 1985163 1986201 1986206) (-1185 "STEPAST.spad" 1984381 1984390 1985137 1985142) (-1184 "STEP.spad" 1983590 1983599 1984371 1984376) (-1183 "STBL.spad" 1981638 1981666 1981805 1981820) (-1182 "STAGG.spad" 1980713 1980724 1981628 1981633) (-1181 "STAGG.spad" 1979786 1979799 1980703 1980708) (-1180 "STACK.spad" 1979014 1979025 1979264 1979291) (-1179 "SRING.spad" 1978774 1978783 1979004 1979009) (-1178 "SREGSET.spad" 1976473 1976490 1978375 1978402) (-1177 "SRDCMPK.spad" 1975050 1975070 1976463 1976468) (-1176 "SRAGG.spad" 1970233 1970242 1975018 1975045) (-1175 "SRAGG.spad" 1965436 1965447 1970223 1970228) (-1174 "SQMATRIX.spad" 1962931 1962949 1963847 1963934) (-1173 "SPLTREE.spad" 1957397 1957410 1962193 1962220) (-1172 "SPLNODE.spad" 1954017 1954030 1957387 1957392) (-1171 "SPFCAT.spad" 1952826 1952835 1954007 1954012) (-1170 "SPECOUT.spad" 1951378 1951387 1952816 1952821) (-1169 "SPADXPT.spad" 1943469 1943478 1951368 1951373) (-1168 "spad-parser.spad" 1942934 1942943 1943459 1943464) (-1167 "SPADAST.spad" 1942635 1942644 1942924 1942929) (-1166 "SPACEC.spad" 1926850 1926861 1942625 1942630) (-1165 "SPACE3.spad" 1926626 1926637 1926840 1926845) (-1164 "SORTPAK.spad" 1926175 1926188 1926582 1926587) (-1163 "SOLVETRA.spad" 1923938 1923949 1926165 1926170) (-1162 "SOLVESER.spad" 1922394 1922405 1923928 1923933) (-1161 "SOLVERAD.spad" 1918420 1918431 1922384 1922389) (-1160 "SOLVEFOR.spad" 1916882 1916900 1918410 1918415) (-1159 "SNTSCAT.spad" 1916482 1916499 1916850 1916877) (-1158 "SMTS.spad" 1914764 1914790 1916041 1916138) (-1157 "SMP.spad" 1912167 1912187 1912557 1912684) (-1156 "SMITH.spad" 1911012 1911037 1912157 1912162) (-1155 "SMATCAT.spad" 1909130 1909160 1910956 1911007) (-1154 "SMATCAT.spad" 1907180 1907212 1909008 1909013) (-1153 "SKAGG.spad" 1906149 1906160 1907148 1907175) (-1152 "SINT.spad" 1905089 1905098 1906015 1906144) (-1151 "SIMPAN.spad" 1904817 1904826 1905079 1905084) (-1150 "SIGNRF.spad" 1903935 1903946 1904807 1904812) (-1149 "SIGNEF.spad" 1903214 1903231 1903925 1903930) (-1148 "SIGAST.spad" 1902631 1902640 1903204 1903209) (-1147 "SIG.spad" 1901993 1902002 1902621 1902626) (-1146 "SHP.spad" 1899937 1899952 1901949 1901954) (-1145 "SHDP.spad" 1887292 1887319 1887809 1887908) (-1144 "SGROUP.spad" 1886900 1886909 1887282 1887287) (-1143 "SGROUP.spad" 1886506 1886517 1886890 1886895) (-1142 "SGCF.spad" 1879645 1879654 1886496 1886501) (-1141 "SFRTCAT.spad" 1878591 1878608 1879613 1879640) (-1140 "SFRGCD.spad" 1877654 1877674 1878581 1878586) (-1139 "SFQCMPK.spad" 1872467 1872487 1877644 1877649) (-1138 "SFORT.spad" 1871906 1871920 1872457 1872462) (-1137 "SEXOF.spad" 1871749 1871789 1871896 1871901) (-1136 "SEXCAT.spad" 1869577 1869617 1871739 1871744) (-1135 "SEX.spad" 1869469 1869478 1869567 1869572) (-1134 "SETMN.spad" 1867927 1867944 1869459 1869464) (-1133 "SETCAT.spad" 1867412 1867421 1867917 1867922) (-1132 "SETCAT.spad" 1866895 1866906 1867402 1867407) (-1131 "SETAGG.spad" 1863444 1863455 1866875 1866890) (-1130 "SETAGG.spad" 1860001 1860014 1863434 1863439) (-1129 "SET.spad" 1858274 1858285 1859371 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 2ab83e9f..3c47c0ae 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,114 +1,114 @@
 
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@@ -3024,16 +3024,16 @@
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@@ -3042,7 +3042,7 @@
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@@ -3051,13 +3051,13 @@
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@@ -3065,43 +3065,43 @@
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@@ -3124,31 +3124,31 @@
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((-501 . -842) T) ((-501 . -950) T) ((-372 . -1253) T) ((-367 . -1253) T) ((-359 . -1253) T) ((-331 . -1143) T) ((-326 . -1082) 193545) ((-325 . -1082) 193474) ((-108 . -1253) T) ((-645 . -635) 193455) ((-372 . -571) T) ((-221 . -950) T) ((-221 . -842) T) ((-326 . -662) 193365) ((-325 . -662) 193294) ((-367 . -571) T) ((-359 . -571) T) ((-659 . -111) 193273) ((-497 . -635) 193254) ((-108 . -571) T) ((-1199 . -1051) NIL) ((-676 . -739) 193224) ((-496 . -874) 193175) ((-222 . -635) 193156) ((-331 . -23) T) ((-67 . -1248) T) ((-1031 . -632) 193088) ((-1328 . -1183) T) ((-716 . -274) 193070) ((-716 . -234) 193052) ((-1323 . -21) T) ((-736 . -111) 193017) ((-1323 . -25) T) ((-663 . -34) T) ((-252 . -503) 193001) ((-1320 . -133) T) ((-1319 . -133) T) ((-1312 . -102) T) ((-1295 . -632) 192967) ((-1128 . -1130) 192951) ((-174 . -1132) T) ((-1288 . -1248) T) ((-1279 . -1248) T) ((-1279 . -1069) 192886) ((-1258 . -1248) T) ((-1258 . -911) NIL) ((-975 . -939) 192865) ((-1258 . -909) 192817) ((-1258 . -1069) 192783) ((-1241 . -528) 192750) ((-529 . -635) 192734) ((-1220 . -633) NIL) ((-1220 . -632) 192716) ((-1173 . -1154) 192661) ((-495 . -939) 192640) ((-1118 . -739) 192489) ((-1093 . -670) 192461) ((-975 . -670) 192350) ((-840 . -874) T) ((-803 . -739) 192179) ((-611 . -504) 192160) ((-600 . -504) 192141) ((-611 . -632) 192107) ((-600 . -632) 192073) ((-549 . -632) 192055) ((-593 . -1248) T) ((-549 . -633) 192036) ((-802 . -739) 191885) ((-1108 . -102) T) ((-642 . -668) 191857) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191746) ((-475 . -739) 191717) ((-468 . -739) 191566) ((-1017 . -102) T) ((-1077 . -1243) 191495) ((-930 . -321) 191433) ((-758 . -102) T) ((-659 . -635) 191410) ((-119 . -668) 191340) ((-900 . -93) T) ((-736 . -635) 191294) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191276) ((-667 . -504) 191257) ((-667 . -632) 191210) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1248) T) ((-609 . -1248) T) ((-357 . -1088) T) ((-301 . -1143) T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-935 . -632) 190487) ((-935 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1274) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -819) T) ((-170 . -1248) T) ((-227 . -1132) T) ((-391 . -814) T) ((-58 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1110 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1248) T) ((-895 . -939) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1248) T) ((-661 . -1132) T) ((-1258 . -351) 189637) ((-895 . -670) 189582) ((-1258 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1257 . -684) T) ((-1118 . -175) 189155) ((-987 . -385) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-975 . -748) T) ((-1312 . -321) 188723) ((-1288 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1284 . -1087) 188334) ((-1279 . -927) 188240) ((-1263 . -1087) 188048) ((-495 . -748) T) ((-1258 . -927) 187881) ((-1241 . -302) 187860) ((-1218 . -1248) T) ((-1215 . -381) T) ((-1214 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1146 . -1132) T) ((-1110 . -23) T) ((-1110 . -1143) T) ((-1107 . -102) T) ((-1089 . -632) 187811) ((-1034 . -424) 187783) ((-954 . -984) T) ((-758 . -321) 187721) ((-76 . -1248) T) ((-686 . -397) 187693) ((-171 . -939) 187646) ((-30 . -984) T) ((-114 . -866) T) ((-1 . -632) 187628) ((-1027 . -921) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-896 . -1080) T) ((-854 . -871) 187324) ((-81 . -1248) T) ((-733 . -302) T) ((-40 . -1088) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1143) T) ((-367 . -1143) T) ((-359 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1284 . -111) 186944) ((-1263 . -111) 186733) ((-252 . -1287) 186717) ((-560 . -870) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1035 . -1051) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1132) T) ((-678 . -662) 186541) ((-1285 . -38) 186433) ((-1267 . -939) 186412) ((-114 . -1132) T) ((-838 . -1248) T) ((-427 . -1248) T) ((-1066 . -102) T) ((-1267 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1284 . -635) 185618) ((-1263 . -635) 185366) ((-60 . -1248) T) ((-638 . -871) 185345) ((-514 . -684) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-525 . -814) T) ((-488 . -1087) 185086) ((-514 . -113) T) ((-357 . -1132) T) ((-325 . -1183) NIL) ((-301 . -133) T) ((-407 . -1132) T) ((-893 . -1088) T) ((-716 . -383) 185053) ((-353 . -668) 184983) ((-227 . -640) 184960) ((-339 . -298) 184912) ((-488 . -111) 184733) ((-1284 . -1080) T) ((-1263 . -1080) T) ((-838 . -390) 184717) ((-848 . -1248) T) ((-171 . -748) T) ((-1314 . -1248) T) ((-678 . -102) T) ((-1284 . -250) 184696) ((-1284 . -240) 184648) ((-1263 . -240) 184553) ((-1263 . -250) 184532) ((-1034 . -416) NIL) ((-692 . -660) 184480) ((-326 . -38) 184390) ((-325 . -38) 184319) ((-69 . -632) 184301) ((-331 . -507) 184267) ((-48 . -668) 184217) ((-1220 . -300) 184196) ((-1257 . -871) T) ((-1144 . -1143) 184174) ((-84 . -1248) T) ((-62 . -632) 184156) ((-888 . -874) T) ((-493 . -300) 184135) ((-1314 . -1069) 184112) ((-1196 . -1132) T) ((-1144 . -23) 183964) ((-838 . -927) 183900) ((-1267 . -748) T) ((-1128 . -1248) T) ((-488 . -635) 183726) ((-365 . -239) T) ((-1118 . -302) 183657) ((-995 . -1132) T) ((-918 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1179 . -34) T) ((-972 . -1248) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1208 . -635) 182524) ((-343 . -1248) T) ((-488 . -1080) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1151 . -1183) T) ((-1279 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1258 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1248) T) ((-734 . -662) 181995) ((-1258 . -1051) NIL) ((-1110 . -133) T) ((-896 . -819) 181974) ((-146 . -102) T) ((-40 . -1132) T) ((-896 . -814) 181953) ((-663 . -1041) 181937) ((-594 . -1088) T) ((-560 . -1088) T) ((-509 . -1088) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1213 . -1132) T) ((-1151 . -38) 181869) ((-1120 . -632) 181836) ((-108 . -133) T) ((-983 . -1132) T) ((-948 . -1132) T) ((-793 . -1132) T) ((-694 . -1132) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-377 . -1248) T) ((-368 . -1087) 181772) ((-366 . -1087) 181724) ((-358 . -1087) 181676) ((-260 . -1248) T) ((-259 . -1248) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1253) 181320) ((-562 . -866) T) ((-326 . -929) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-931 . -874) 180693) ((-130 . -684) T) ((-837 . -660) 180599) ((-839 . -571) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-935 . -1087) 180181) ((-734 . -102) T) ((-721 . -1088) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-935 . -111) 179984) ((-40 . -739) 179929) ((-893 . -1132) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1132) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1248) T) ((-1263 . -814) 179062) ((-1263 . -819) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-564 . -874) T) ((-678 . -38) 178923) ((-627 . -34) T) ((-496 . -1143) 178901) ((-489 . -34) T) ((-1144 . -133) 178772) ((-993 . -25) 178583) ((-935 . -635) 178533) ((-898 . -632) 178515) ((-218 . -866) T) ((-993 . -21) 178470) ((-837 . -25) 178303) ((-837 . -21) 178214) ((-1255 . -381) T) ((-642 . -1088) T) ((-1210 . -571) 178193) ((-1202 . -47) 178170) ((-368 . -1080) T) ((-366 . -1080) T) ((-496 . -23) 178022) ((-358 . -1080) T) ((-275 . -1080) T) ((-255 . -1080) T) ((-1156 . -47) 177994) ((-119 . -1088) T) ((-1065 . -670) 177968) ((-987 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-366 . -240) 177926) ((-366 . -250) T) ((-358 . -240) 177905) ((-358 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1186 . -153) 177797) ((-260 . -927) 177729) ((-259 . -927) 177661) ((-1173 . -921) 177582) ((-1113 . -871) T) ((-1265 . -1248) 177560) ((-429 . -1143) T) ((-1241 . -1033) 177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-935 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1205 . -950) 177432) ((-1199 . -950) 177411) ((-1199 . -842) NIL) ((-1027 . -1082) 177307) ((-996 . -1248) T) ((-935 . -250) T) ((-839 . -376) 177286) ((-218 . -1132) T) ((-394 . -23) T) ((-129 . -1132) 177264) ((-123 . -1132) 177242) ((-935 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1027 . -662) 177155) ((-893 . -739) 177142) ((-1328 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1248) T) ((-887 . -1248) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-856 . -670) 177008) ((-850 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1132) T) ((-560 . -1132) T) ((-509 . -1132) T) ((-1202 . -1248) T) ((-252 . -300) 176938) ((-1156 . -1248) T) ((-878 . -1248) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1254 . -874) T) ((-1202 . -911) NIL) ((-55 . -1132) T) ((-1156 . -911) 176719) ((-130 . -871) T) ((-1202 . -1069) 176599) ((-1156 . -1069) 176482) ((-187 . -632) 176464) ((-878 . -1069) 176360) ((-803 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1027 . -102) T) ((-839 . -23) T) ((-734 . -1183) 176085) ((-716 . -1088) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1301 . -1132) T) ((-256 . -1132) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1132) T) ((-721 . -1132) T) ((-374 . -487) T) ((-1241 . -632) 176051) ((-1202 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -426) 175981) ((-143 . -233) 175963) ((-391 . -816) T) ((-391 . -813) T) ((-893 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1298 . -1297) 175758) ((-365 . -416) T) ((-1298 . -1132) 175708) ((-1222 . -1132) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1285 . -668) 175537) ((-326 . -649) 175516) ((-856 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1253) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1253) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1093 . -1248) T) ((-975 . -1248) T) ((-735 . -1248) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1248) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1128 . -107) 173800) ((-1093 . -911) 173782) ((-975 . -911) 173707) ((-677 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1120 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-975 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-677 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-820 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -939) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1317) 172342) ((-366 . -1317) 172326) ((-358 . -1317) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -814) T) ((-526 . -819) T) ((-525 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1132) T) ((-896 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-975 . -390) 171946) ((-893 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) ((-1027 . -38) 171848) ((-626 . -1132) T) ((-621 . -1132) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-935 . -1317) 171765) ((-895 . -1248) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1310 . -1248) T) ((-1309 . -1248) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1322 . -1313) 171652) ((-895 . -909) 171629) ((-895 . -911) NIL) ((-993 . -871) 171528) ((-837 . -871) 171479) ((-1256 . -102) T) ((-678 . -680) 171463) ((-1235 . -34) T) ((-174 . -632) 171445) ((-1144 . -25) 171278) ((-1144 . -21) 171189) ((-895 . -1069) 171166) ((-975 . -927) 171147) ((-1267 . -47) 171124) ((-935 . -381) T) ((-607 . -874) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -927) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1248) T) ((-850 . -730) 170989) ((-1202 . -319) 170968) ((-1210 . -133) T) ((-1173 . -1082) 170952) ((-119 . -175) T) ((-1173 . -662) 170884) ((-1177 . -321) 170822) ((-171 . -1248) T) ((-1311 . -133) T) ((-1279 . -950) 170801) ((-1263 . -939) 170754) ((-1258 . -950) 170733) ((-890 . -1082) 170703) ((-652 . -766) 170687) ((-620 . -766) 170671) ((-1258 . -842) NIL) ((-1055 . -1132) T) ((-931 . -1143) T) ((-890 . -662) 170641) ((-716 . -739) 170591) ((-925 . -1248) T) ((-895 . -390) 170568) ((-895 . -351) 170545) ((-863 . -1248) T) ((-830 . -1248) T) ((-171 . -909) 170529) ((-171 . -911) 170454) ((-791 . -1248) T) ((-699 . -1248) T) ((-1298 . -528) 170387) ((-1284 . -670) 170284) ((-1110 . -236) 170157) ((-501 . -1143) T) ((-353 . -1132) T) ((-221 . -1143) T) ((-77 . -455) T) ((-77 . -410) T) ((-171 . -1069) 170053) ((-305 . -921) 170010) ((-331 . -871) T) ((-1263 . -670) 169818) ((-896 . -816) 169797) ((-896 . -813) 169776) ((-896 . -748) T) ((-501 . -23) T) ((-372 . -236) 169749) ((-367 . -236) 169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1323 . -1318) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1267 . -1248) T) ((-137 . -484) 169520) ((-879 . -1248) T) ((-678 . -668) 169479) ((-48 . -1132) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1248) T) ((-1267 . -911) NIL) ((-913 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1132) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1267 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1027 . -929) 169096) ((-677 . -133) T) ((-674 . -814) 169075) ((-674 . -819) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-305 . -1306) 168914) ((-1199 . -874) NIL) ((-890 . -102) T) ((-985 . -571) 168893) ((-1241 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-934 . -1132) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1179 . -1248) T) ((-1241 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1328 . -1088) T) ((-1267 . -390) 168084) ((-419 . -1253) 168062) ((-1146 . -632) 168044) ((-325 . -870) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1263 . -813) 167997) ((-1263 . -816) 167950) ((-1284 . -748) T) ((-1263 . -748) T) ((-48 . -739) 167915) ((-229 . -1051) T) ((-1285 . -426) 167881) ((-1267 . -927) 167824) ((-365 . -1306) 167801) ((-1241 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1322 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1322 . -662) 167115) ((-642 . -302) T) ((-597 . -1087) 167090) ((-450 . -1132) T) ((-1093 . -319) T) ((-119 . -302) T) ((-1134 . -102) T) ((-1034 . -102) T) ((-597 . -111) 167058) ((-1241 . -1080) T) ((-1173 . -321) 166996) ((-1093 . -1051) T) ((-1085 . -25) T) ((-66 . -1248) T) ((-915 . -1248) T) ((-1085 . -21) T) ((-733 . -1080) T) ((-394 . -21) T) ((-394 . -25) T) ((-716 . -528) NIL) ((-1055 . -175) T) ((-733 . -250) T) ((-1093 . -559) T) ((-734 . -668) 166906) ((-520 . -102) T) ((-516 . -102) T) ((-357 . -632) 166888) ((-353 . -175) T) ((-421 . -1082) 166840) ((-407 . -632) 166822) ((-1151 . -870) T) ((-488 . -748) T) ((-915 . -1069) 166790) ((-421 . -662) 166742) ((-108 . -871) T) ((-676 . -1087) 166726) ((-501 . -133) T) ((-1285 . -1088) T) ((-221 . -133) T) ((-1186 . -102) 166676) ((-99 . -1132) T) ((-246 . -874) 166627) ((-252 . -688) 166611) ((-252 . -673) 166595) ((-676 . -111) 166574) ((-597 . -635) 166558) ((-326 . -426) 166542) ((-252 . -385) 166526) ((-1191 . -242) 166473) ((-1027 . -274) 166457) ((-1027 . -234) 166441) ((-74 . -1248) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1322 . -102) T) ((-1230 . -1248) T) ((-1228 . -635) 166423) ((-1119 . -1248) T) ((-1118 . -1087) 166266) ((-1106 . -1248) T) ((-275 . -939) 166245) ((-255 . -939) 166224) ((-803 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1248) T) ((-1196 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1248) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1190 . -871) T) ((-1119 . -1069) 164755) ((-1106 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-987 . -1248) T) ((-985 . -1143) T) ((-128 . -1041) 164488) ((-872 . -1248) T) ((-895 . -1051) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-676 . -635) 164406) ((-1298 . -503) 164390) ((-1216 . -1248) T) ((-1215 . -1248) T) ((-1173 . -38) 164350) ((-985 . -23) T) ((-935 . -670) 164315) ((-889 . -1132) T) ((-864 . -102) T) ((-839 . -21) T) ((-652 . -1082) 164299) ((-620 . -1082) 164283) ((-839 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1087) 164216) ((-532 . -1087) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1214 . -1248) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-890 . -38) 164089) ((-1118 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1143) T) ((-326 . -1088) 163600) ((-325 . -1088) T) ((-132 . -1248) T) ((-131 . -1248) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1080) T) ((-1328 . -1132) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1022) 162778) ((-118 . -894) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) ((-1235 . -1041) 162696) ((-1213 . -632) 162663) ((-1220 . -34) T) ((-983 . -632) 162629) ((-948 . -632) 162611) ((-1144 . -871) 162562) ((-793 . -632) 162544) ((-694 . -632) 162526) ((-531 . -1248) T) ((-1267 . -319) 162505) ((-1186 . -321) 162443) ((-1172 . -34) T) ((-493 . -34) T) ((-1123 . -1248) T) ((-491 . -466) T) ((-1065 . -1248) T) ((-1118 . -1080) T) ((-50 . -635) 162412) ((-803 . -1080) T) ((-802 . -1080) T) ((-669 . -242) 162396) ((-651 . -242) 162342) ((-1210 . -21) T) ((-595 . -635) 162292) ((-532 . -635) 162222) ((-496 . -236) 162113) ((-1210 . -25) T) ((-1118 . -338) 162074) ((-468 . -1080) T) ((-1118 . -240) 162053) ((-803 . -338) 162030) ((-803 . -240) T) ((-802 . -338) 162002) ((-753 . -1253) 161981) ((-533 . -34) T) ((-339 . -673) 161965) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161944) ((-339 . -385) 161928) ((-374 . -1248) T) ((-334 . -1248) T) ((-1034 . -1183) NIL) ((-753 . -571) 161859) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1248) T) ((-1311 . -21) T) ((-1077 . -321) 161767) ((-1311 . -25) T) ((-930 . -1132) 161745) ((-840 . -236) 161732) ((-50 . -1080) T) ((-1206 . -571) 161711) ((-1205 . -1253) 161690) ((-1205 . -571) 161641) ((-1199 . -1253) 161620) ((-1199 . -571) 161571) ((-1055 . -302) T) ((-595 . -1080) T) ((-532 . -1080) T) ((-1034 . -38) 161516) ((-374 . -1069) 161500) ((-334 . -1069) 161484) ((-1027 . -668) 161407) ((-391 . -911) 161389) ((-856 . -1248) T) ((-850 . -1248) T) ((-847 . -1248) T) ((-820 . -1143) T) ((-935 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1157 . -571) 161368) ((-353 . -302) T) ((-669 . -717) 161352) ((-391 . -1069) 161312) ((-305 . -1082) 161233) ((-352 . -921) 161212) ((-1151 . -1088) T) ((-103 . -127) 161196) ((-305 . -662) 161138) ((-820 . -23) T) ((-1320 . -1318) 161114) ((-1319 . -1318) 161093) ((-1298 . -298) 161045) ((-1285 . -1132) T) ((-421 . -321) 161010) ((-1173 . -929) 160933) ((-893 . -632) 160915) ((-856 . -1069) 160884) ((-661 . -1087) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1033) T) ((-285 . -861) T) ((-284 . -861) T) ((-283 . -861) T) ((-282 . -861) T) ((-48 . -302) T) ((-281 . -861) T) ((-280 . -861) T) ((-279 . -861) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -871) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -871) T) ((-677 . -21) T) ((-677 . -25) T) ((-1322 . -38) 160696) ((-119 . -298) 160647) ((-1298 . -19) 160631) ((-1258 . -874) NIL) ((-1298 . -618) 160608) ((-1312 . -1132) T) ((-365 . -1082) 160553) ((-1108 . -1132) T) ((-1017 . -1132) T) ((-985 . -133) T) ((-839 . -236) 160540) ((-758 . -1132) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -815) T) ((-526 . -816) T) ((-467 . -133) T) ((-421 . -1183) 160463) ((-227 . -1080) T) ((-305 . -102) 160245) ((-143 . -1132) T) ((-721 . -1033) T) ((-1136 . -298) 160201) ((-91 . -1248) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1328 . -175) T) ((-1205 . -376) 160026) ((-1199 . -376) 160005) ((-326 . -1132) T) ((-419 . -133) T) ((-325 . -1132) T) ((-421 . -38) 159957) ((-1164 . -102) T) ((-1285 . -739) 159849) ((-1166 . -1294) T) ((-1127 . -1248) T) ((-1122 . -1248) T) ((-678 . -1088) T) ((-1104 . -1248) T) ((-1097 . -1248) T) ((-1067 . -1248) T) ((-1050 . -1248) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1132) T) ((-137 . -1132) T) ((-115 . -1132) T) ((-882 . -102) T) ((-645 . -1248) T) ((-497 . -1248) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1248) T) ((-496 . -871) 159548) ((-501 . -660) 159530) ((-994 . -632) 159512) ((-1034 . -929) 159421) ((-221 . -660) 159403) ((-229 . -418) T) ((-674 . -670) 159387) ((-55 . -632) 159369) ((-1202 . -950) 159348) ((-753 . -1143) T) ((-657 . -102) T) ((-529 . -1248) T) ((-525 . -1248) T) ((-522 . -1248) T) ((-365 . -102) T) ((-1249 . -1114) T) ((-1151 . -866) T) ((-840 . -871) T) ((-753 . -23) T) ((-357 . -1087) 159293) ((-1179 . -107) 159277) ((-1301 . -632) 159259) ((-1206 . -23) T) ((-1206 . -1143) T) ((-1205 . -1143) T) ((-659 . -1248) T) ((-1205 . -23) T) ((-1199 . -1143) T) ((-1199 . -23) T) ((-1173 . -274) 159243) ((-529 . -1069) 159227) ((-1173 . -234) 159211) ((-1157 . -1143) T) ((-357 . -111) 159140) ((-1035 . -1253) T) ((-128 . -1248) T) ((-943 . -1253) T) ((-1157 . -23) T) ((-1107 . -1132) T) ((-716 . -298) NIL) ((-736 . -1248) T) ((-1035 . -571) T) ((-943 . -571) T) ((-837 . -239) 159037) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1248) T) ((-186 . -1248) T) ((-163 . -1248) T) ((-159 . -1248) T) ((-256 . -632) 159019) ((-622 . -684) T) ((-820 . -133) T) ((-732 . -632) 159001) ((-326 . -739) 158911) ((-325 . -739) 158840) ((-721 . -632) 158822) ((-721 . -633) 158767) ((-421 . -414) 158751) ((-452 . -1132) T) ((-501 . -25) T) ((-501 . -21) T) ((-1151 . -1132) T) ((-221 . -25) T) ((-221 . -21) T) ((-734 . -426) 158735) ((-736 . -1069) 158704) ((-1298 . -632) 158616) ((-1298 . -633) 158577) ((-1285 . -175) T) ((-1222 . -632) 158559) ((-252 . -34) T) ((-357 . -635) 158489) ((-407 . -635) 158471) ((-956 . -1005) T) ((-1235 . -1248) T) ((-674 . -813) 158450) ((-674 . -816) 158429) ((-412 . -410) T) ((-537 . -102) 158379) ((-1255 . -1248) T) ((-1066 . -1132) T) ((-421 . -929) 158302) ((-226 . -1026) 158286) ((-860 . -1248) T) ((-518 . -102) T) ((-642 . -632) 158268) ((-45 . -871) NIL) ((-642 . -633) 158245) ((-1066 . -629) 158220) ((-930 . -528) 158153) ((-331 . -239) 158105) ((-357 . -1080) T) ((-119 . -633) NIL) ((-119 . -632) 158087) ((-896 . -1248) T) ((-692 . -432) 158071) ((-692 . -1154) 158016) ((-514 . -153) 157998) ((-357 . -240) T) ((-357 . -250) T) ((-40 . -1087) 157943) ((-896 . -909) 157927) ((-896 . -911) 157852) ((-734 . -1088) T) ((-716 . -1033) NIL) ((-1284 . -47) 157822) ((-1263 . -47) 157799) ((-1172 . -1041) 157770) ((-1151 . -739) 157757) ((-3 . |UnionCategory|) T) ((-1136 . -632) 157739) ((-1110 . -149) 157718) ((-1110 . -147) 157669) ((-1035 . -376) T) ((-995 . -635) 157653) ((-229 . -950) T) ((-40 . -111) 157582) ((-896 . -1069) 157446) ((-1034 . -234) 157423) ((-1034 . -274) 157400) ((-723 . -1082) 157387) ((-943 . -376) T) ((-723 . -662) 157374) ((-331 . -1237) 157340) ((-391 . -319) T) ((-331 . -1234) 157306) ((-326 . -175) 157285) ((-325 . -175) T) ((-627 . -1225) 157261) ((-595 . -1317) 157248) ((-532 . -1317) 157225) ((-118 . -1082) 157212) ((-372 . -149) 157191) ((-372 . -147) 157142) ((-367 . -149) 157121) ((-367 . -147) 157072) ((-359 . -149) 157051) ((-118 . -662) 157038) ((-359 . -147) 156989) ((-331 . -35) 156955) ((-489 . -1225) 156934) ((0 . |EnumerationCategory|) T) ((-331 . -95) 156900) ((-391 . -1051) T) ((-108 . -149) T) ((-108 . -147) NIL) ((-45 . -242) 156850) ((-678 . -1132) T) ((-627 . -107) 156797) ((-499 . -133) T) ((-489 . -107) 156747) ((-246 . -1143) 156725) ((-31 . -1248) T) ((-896 . -390) 156709) ((-896 . -351) 156693) ((-246 . -23) 156545) ((-40 . -635) 156475) ((-1312 . -528) 156408) ((-1093 . -950) T) ((-1093 . -842) T) ((-595 . -381) T) ((-532 . -381) T) ((-1288 . -571) 156387) ((-1284 . -1248) T) ((-1279 . -1253) 156366) ((-1279 . -571) 156317) ((-1263 . -1248) T) ((-365 . -1183) T) ((-339 . -34) T) ((-44 . -432) 156301) ((-1213 . -635) 156237) ((-897 . -1248) T) ((-404 . -766) 156221) ((-1263 . -911) 156094) ((-1263 . -909) 156064) ((-1173 . -668) 156023) ((-753 . -133) T) ((-694 . -635) 156007) ((-1258 . -1253) 155986) ((-1258 . -571) 155937) ((-1206 . -133) T) ((-1205 . -133) T) ((-1199 . -133) T) ((-1157 . -133) T) ((-324 . -1114) T) ((-1055 . -1033) T) ((-758 . -528) 155870) ((-1035 . -23) T) ((-1035 . -1143) T) ((-918 . -1132) T) ((-146 . -866) T) ((-1034 . -363) NIL) ((-713 . -632) 155852) ((-972 . -874) 155831) ((-537 . -321) 155769) ((-1002 . -23) T) ((-143 . -528) NIL) ((-890 . -668) 155714) ((-943 . -1143) T) ((-943 . -23) T) ((-896 . -927) 155673) ((-365 . -38) 155638) ((-893 . -1087) 155625) ((-343 . -874) T) ((-83 . -632) 155607) ((-40 . -1080) T) ((-893 . -111) 155592) ((-740 . -1248) T) ((-723 . -102) T) ((-716 . -632) 155574) ((-616 . -1248) T) ((-610 . -571) 155553) ((-443 . -1143) T) ((-352 . -1082) 155537) ((-216 . -1132) T) ((-177 . -1082) 155469) ((-488 . -47) 155439) ((-40 . -240) 155411) ((-40 . -250) T) ((-136 . -102) T) ((-118 . -102) T) ((-609 . -571) 155390) ((-352 . -662) 155374) ((-716 . -633) 155282) ((-326 . -528) 155248) ((-177 . -662) 155180) ((-325 . -528) 155072) ((-501 . -236) 155059) ((-1284 . -1069) 155043) ((-1263 . -1069) 154829) ((-1027 . -426) 154813) ((-221 . -236) 154800) ((-443 . -23) T) ((-1151 . -175) T) ((-626 . -504) 154767) ((-621 . -504) 154749) ((-626 . -632) 154701) 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143042) ((-1220 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1225) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1151 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1151 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1258 . -660) 142704) ((-493 . -107) 142654) ((-1024 . -23) T) ((-1323 . -38) 142624) ((-1202 . -1143) T) ((-1156 . -1143) T) ((-1093 . -1253) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-878 . -1143) T) ((-975 . -1253) 142494) ((-495 . -1253) 142473) ((-1093 . -571) T) ((-975 . -571) 142404) ((-1202 . -23) T) ((-1184 . -1114) T) ((-1156 . -23) T) ((-878 . -23) T) ((-495 . -571) 142335) ((-1173 . -739) 142267) ((-692 . -1082) 142251) ((-1177 . -528) 142184) ((-692 . -662) 142168) ((-1066 . -633) NIL) ((-1066 . -632) 142150) ((-96 . -1114) T) ((-1328 . -1087) 142137) ((-890 . -739) 142107) ((-1328 . -111) 142092) ((-1241 . -47) 142061) ((-1199 . -871) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1134 . -1132) T) ((-1034 . -1132) T) ((-63 . -632) 142043) ((-1110 . -921) 141912) ((-1055 . -814) T) ((-1055 . -819) T) ((-1288 . -25) T) ((-1288 . -21) T) ((-1279 . -21) T) ((-1279 . -25) T) ((-893 . -670) 141899) ((-1258 . -21) T) ((-1258 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -950) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1248) T) ((-948 . -816) T) ((-948 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1132) T) ((-516 . -1132) T) ((-793 . -748) T) ((-229 . -376) T) ((-1320 . -1082) 141537) ((-1319 . -1082) 141521) ((-1320 . -662) 141491) ((-1186 . -1132) 141469) ((-895 . -1253) T) ((-1319 . -662) 141439) ((-1119 . -874) T) ((-678 . -632) 141421) ((-895 . -571) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1328 . -635) 141387) ((-1322 . -1132) T) ((-692 . -102) T) ((-372 . -1306) 141371) ((-367 . -1306) 141355) ((-44 . -662) 141339) ((-359 . -1306) 141323) ((-563 . -102) T) ((-1241 . -1248) T) ((-534 . -871) 141302) ((-733 . -1248) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1132) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1215 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1214 . -874) T) ((-1110 . -746) 140934) ((-1328 . -1080) T) ((-838 . -660) 140882) ((-305 . -1088) 140824) ((-171 . -1253) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1199 . -1022) 140681) ((-1285 . -1087) 140586) ((-864 . -1132) T) ((-131 . -874) T) ((-1157 . -762) 140565) ((-1284 . -950) 140544) ((-1263 . -950) 140523) ((-893 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1132) T) ((-270 . -1132) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1263 . -842) 140278) ((-1320 . -102) T) ((-505 . -1248) T) ((-353 . -1317) 140255) ((-1319 . -102) T) ((-1285 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-246 . -871) 139770) ((-597 . -1248) T) ((-1267 . -1253) 139749) ((-103 . -503) 139733) ((-1322 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-975 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1267 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1228 . -1248) T) ((-1202 . -133) T) ((-353 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-975 . -23) T) ((-585 . -571) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1248) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-560 . -816) T) ((-171 . -376) 137289) ((-560 . -813) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1248) T) ((-802 . -1248) T) ((-1177 . -503) 137273) ((-475 . -1248) T) ((-468 . -1248) T) ((-1320 . -1321) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -939) NIL) ((-1319 . -1321) 137228) ((-671 . -1248) T) ((-803 . -911) NIL) ((-802 . -911) 137087) ((-1314 . -25) T) ((-1314 . -21) T) ((-1246 . -102) 137065) ((-1137 . -410) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-803 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1248) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1248) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1248) T) ((-532 . -1248) T) ((-226 . -503) 135750) ((-1298 . -34) T) ((-638 . -668) 135709) ((-301 . -1082) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-86 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1248) T) ((-336 . -133) T) ((-326 . -1080) 135332) ((-325 . -1080) T) ((-171 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1022) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1132) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-171 . -23) T) ((-820 . -149) 134957) ((-820 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1186 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1132) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-803 . -927) 134280) ((-802 . -927) 134264) ((-1320 . -38) 134234) ((-1319 . -38) 134204) ((-1267 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1132) T) ((-1267 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-525 . -874) T) ((-368 . -950) T) ((-366 . -950) T) ((-301 . -102) T) ((-358 . -950) T) ((-1001 . -1114) T) ((-975 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -939) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1248) T) ((-657 . -1132) T) ((-652 . -783) T) ((-620 . -783) T) ((-1258 . -871) NIL) ((-1110 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1132) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-935 . -950) T) ((-1110 . -662) 133600) ((-496 . -1306) 133570) ((-1151 . -1080) 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-871) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1069) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1132) T) ((-177 . -1132) T) ((-343 . -871) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-856 . -1143) T) ((-108 . -38) 126992) ((-850 . -1143) T) ((-795 . -1132) T) ((-118 . -739) 126979) ((-694 . -1069) 126963) ((-630 . -102) T) ((-856 . -23) T) ((-850 . -23) T) ((-1186 . -298) 126915) ((-1144 . -321) 126853) ((-496 . -1082) 126754) ((-1128 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1184 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -876) 126621) ((-1202 . -236) 126608) ((-1166 . -1114) T) ((-1093 . -21) T) ((-1093 . -25) T) ((-1085 . -1082) 126592) ((-837 . -274) 126561) ((-837 . -234) 126530) ((-975 . -25) T) ((-975 . -21) T) ((-1151 . -381) T) ((-1085 . 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. -47) 98886) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-365 . -1317) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-359 . -175) T) ((-177 . -250) T) ((-1263 . -871) 98637) ((-108 . -175) T) ((-896 . -1022) 98621) ((-676 . -1143) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-326 . -319) 98564) ((-325 . -319) T) ((-616 . -871) 98543) ((-1144 . -739) 98485) ((-623 . -1248) T) ((-534 . -294) 98469) ((-676 . -23) T) ((-419 . -234) 98453) ((-419 . -274) 98437) ((-325 . -1051) NIL) ((-346 . -23) T) ((-103 . -1041) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-630 . -1132) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98338) ((-1118 . -1143) T) ((-1322 . -670) 98312) ((-803 . -1143) T) ((-802 . -1143) T) ((-1210 . -426) 98296) ((-468 . -1143) T) ((-1093 . -466) T) ((-1184 . -1132) T) ((-975 . -466) 98247) ((-1147 . -1114) T) ((-110 . -1132) T) ((-1118 . -23) T) ((-1191 . -528) 98030) 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-979) 94641) ((-44 . -298) 94618) ((-130 . -632) 94585) ((-51 . -632) 94567) ((-218 . -874) T) ((-677 . -426) 94551) ((-1258 . -102) T) ((-1190 . -528) NIL) ((-674 . -25) T) ((-638 . -1087) 94535) ((-674 . -21) T) ((-985 . -668) 94445) ((-757 . -668) 94390) ((-737 . -668) 94362) ((-404 . -111) 94341) ((-226 . -263) 94325) ((-1085 . -1084) 94265) ((-1085 . -1132) T) ((-1035 . -1183) T) ((-840 . -1132) T) ((-467 . -668) 94180) ((-652 . -670) 94164) ((-638 . -111) 94143) ((-620 . -670) 94127) ((-610 . -102) T) ((-357 . -1253) T) ((-324 . -504) 94108) ((-597 . -133) T) ((-609 . -102) T) ((-429 . -1132) T) ((-394 . -1132) T) ((-324 . -632) 94074) ((-231 . -1132) 94052) ((-669 . -528) 93985) ((-651 . -528) 93829) ((-854 . -1080) 93808) ((-663 . -153) 93792) ((-357 . -571) T) ((-734 . -927) 93735) ((-565 . -233) 93685) ((-1288 . -296) 93651) ((-1279 . -296) 93617) ((-1110 . -302) 93568) ((-560 . -874) T) ((-501 . -870) T) ((-227 . -1143) T) ((-1258 . -296) 93534) ((-1241 . -507) 93500) 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90854) ((-1191 . -503) 90788) ((-1314 . -1082) 90772) ((-395 . -1087) 90756) ((-1314 . -662) 90726) ((-838 . -102) T) ((-491 . -250) T) ((-736 . -149) 90705) ((-736 . -147) 90684) ((-119 . -874) NIL) ((-498 . -503) 90668) ((-499 . -349) 90637) ((-524 . -1132) 90588) ((-1323 . -111) 90567) ((-1027 . -390) 90551) ((-427 . -102) T) ((-395 . -111) 90530) ((-1027 . -351) 90514) ((-290 . -1014) 90498) ((-289 . -1014) 90482) ((-1035 . -929) NIL) ((-1320 . -632) 90464) ((-1319 . -632) 90446) ((-110 . -528) NIL) ((-1202 . -1274) 90430) ((-878 . -876) 90414) ((-1210 . -1132) T) ((-103 . -1248) T) ((-975 . -979) 90375) ((-839 . -739) 90317) ((-1258 . -1183) NIL) ((-495 . -979) 90262) ((-1093 . -145) T) ((-60 . -102) 90212) ((-44 . -632) 90194) ((-75 . -632) 90176) ((-365 . -670) 90121) ((-625 . -1132) T) ((-624 . -1132) T) ((-622 . -1132) T) ((-1311 . -1132) T) ((-526 . -871) T) ((-301 . -298) 90100) ((-357 . -1143) T) ((-307 . -1132) T) ((-1027 . -927) 90059) ((-307 . -629) 90038) ((-1323 . -635) 89987) ((-1288 . -38) 89884) ((-1279 . -38) 89725) ((-1258 . -38) 89521) ((-501 . -1088) T) ((-395 . -635) 89505) ((-221 . -1088) T) ((-357 . -23) T) ((-154 . -632) 89487) ((-854 . -819) 89466) ((-854 . -814) 89445) ((-1249 . -635) 89426) ((-610 . -38) 89399) ((-609 . -38) 89296) ((-893 . -571) T) ((-227 . -133) T) ((-331 . -1033) 89262) ((-79 . -632) 89244) ((-734 . -319) 89223) ((-305 . -748) 89125) ((-848 . -102) T) ((-888 . -866) T) ((-305 . -487) 89104) ((-1314 . -102) T) ((-40 . -376) T) ((-896 . -149) 89083) ((-499 . -668) 89065) ((-896 . -147) 89044) ((-1190 . -503) 89026) ((-1323 . -1080) T) ((-496 . -528) 88959) ((-661 . -133) T) ((-1177 . -1248) T) ((-993 . -632) 88941) ((-669 . -503) 88925) ((-651 . -503) 88856) ((-837 . -632) 88549) ((-48 . -27) T) ((-1210 . -739) 88446) ((-975 . -921) 88425) ((-677 . -1132) T) ((-886 . -885) T) ((-451 . -378) 88399) ((-753 . -668) 88309) ((-495 . -921) 88284) ((-1128 . -102) T) ((-1001 . -1132) T) ((-888 . -1132) T) ((-838 . -321) 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T) ((-560 . -1253) T) ((-509 . -1253) T) ((-1035 . -274) 86649) ((-331 . -632) 86631) ((-1035 . -234) 86613) ((-171 . -168) 86597) ((-594 . -571) T) ((-560 . -571) T) ((-509 . -571) T) ((-793 . -23) T) ((-1284 . -149) 86576) ((-1284 . -147) 86555) ((-1191 . -618) 86531) ((-1263 . -147) 86456) ((-1058 . -503) 86440) ((-1256 . -1248) T) ((-1263 . -149) 86365) ((-1314 . -1321) 86344) ((-895 . -921) NIL) ((-490 . -503) 86328) ((-477 . -503) 86312) ((-537 . -34) T) ((-677 . -739) 86282) ((-1288 . -929) 86195) ((-1279 . -929) 86101) ((-1258 . -929) 85862) ((-114 . -998) T) ((-1210 . -175) 85813) ((-674 . -871) 85792) ((-377 . -102) T) ((-609 . -929) 85705) ((-246 . -245) 85684) ((-260 . -102) T) ((-259 . -102) T) ((-1267 . -979) 85653) ((-252 . -871) 85632) ((-1055 . -874) T) ((-838 . -38) 85481) ((-45 . -528) 85273) ((-1190 . -298) 85223) ((-217 . -1132) T) ((-1182 . -1132) T) ((-896 . -239) 85174) ((-1182 . -629) 85153) ((-597 . -25) T) ((-597 . -21) T) ((-1128 . -321) 85091) ((-985 . -426) 85075) ((-721 . -1253) T) ((-651 . -298) 85028) ((-1118 . -660) 84976) ((-931 . -1132) T) ((-803 . -660) 84924) ((-802 . -660) 84872) ((-357 . -133) T) ((-301 . -632) 84854) ((-893 . -1143) T) ((-721 . -571) T) ((-130 . -635) 84836) ((-468 . -660) 84784) ((-171 . -921) 84705) ((-931 . -933) 84689) ((-391 . -466) T) ((-501 . -1132) T) ((-972 . -321) 84627) ((-723 . -670) 84599) ((-564 . -866) T) ((-221 . -1132) T) ((-326 . -950) 84578) ((-325 . -950) T) ((-325 . -842) NIL) ((-404 . -742) T) ((-893 . -23) T) ((-118 . -670) 84565) ((-488 . -147) 84544) ((-419 . -426) 84528) ((-488 . -149) 84507) ((-110 . -503) 84489) ((-324 . -635) 84470) ((-2 . -632) 84452) ((-190 . -102) T) ((-1190 . -19) 84434) ((-1190 . -618) 84409) ((-676 . -21) T) ((-676 . -25) T) ((-607 . -1175) T) ((-1144 . -298) 84386) ((-346 . -25) T) ((-346 . -21) T) ((-913 . -1248) T) ((-910 . -1248) T) ((-1320 . -1087) 84370) ((-246 . -668) 84149) ((-509 . -376) T) ((-1319 . -1087) 84133) ((-1314 . -38) 84103) ((-1284 . -1234) 84069) ((-1284 . -1237) 84035) ((-1267 . -921) 83938) ((-1202 . -1082) 83761) ((-1173 . -1248) T) ((-1156 . -1082) 83604) ((-878 . -1082) 83588) ((-651 . -618) 83563) ((-1284 . -95) 83529) ((-1284 . -239) 83481) ((-1265 . -102) 83459) ((-1202 . -662) 83288) ((-1156 . -662) 83137) ((-878 . -662) 83107) ((-1263 . -1234) 83073) ((-1118 . -25) T) ((-564 . -1132) T) ((-1118 . -21) T) ((-985 . -1088) T) ((-545 . -814) T) ((-545 . -819) T) ((-119 . -1253) T) ((-890 . -1248) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1088) T) ((-737 . -1088) T) ((-692 . -1087) 83057) ((-531 . -1114) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1263 . -1237) 83023) ((-1184 . -93) T) ((-1173 . -1069) 82919) ((-839 . -302) 82898) ((-1263 . -239) 82757) ((-846 . -1132) T) ((-995 . -998) T) ((-692 . -111) 82736) ((-636 . -1248) T) ((-307 . -528) 82528) ((-1258 . -234) 82480) ((-1258 . -274) 82432) ((-1257 . -381) T) ((-260 . -321) 82370) ((-259 . -321) 82308) ((-1254 . -866) T) ((-1191 . -633) NIL) ((-1191 . -632) 82290) ((-1173 . -390) 82274) ((-1151 . -842) T) ((-1151 . -950) T) ((-96 . -93) T) ((-1144 . -618) 82251) ((-1110 . -633) 82235) ((-1110 . -632) 82217) ((-1035 . -668) 82167) ((-943 . -668) 82104) ((-837 . -300) 82081) ((-498 . -632) 82013) ((-627 . -153) 81960) ((-501 . -739) 81910) ((-419 . -1088) T) ((-496 . -503) 81894) ((-443 . -668) 81853) ((-339 . -871) 81832) ((-352 . -670) 81806) ((-50 . -21) T) ((-50 . -25) T) ((-221 . -739) 81756) ((-171 . -746) 81727) ((-177 . -670) 81659) ((-595 . -21) T) ((-595 . -25) T) ((-532 . -25) T) ((-532 . -21) T) ((-489 . -153) 81609) ((-1092 . -632) 81591) ((-1024 . -102) T) ((-887 . -102) T) ((-838 . -929) 81491) ((-820 . -426) 81454) ((-40 . -133) T) ((-721 . -376) T) ((-723 . -748) T) ((-723 . -816) T) ((-723 . -813) T) ((-215 . -922) T) ((-594 . -1143) T) ((-560 . -1143) T) ((-509 . -1143) T) ((-372 . -632) 81436) ((-367 . -632) 81418) ((-359 . -632) 81400) ((-66 . -411) T) ((-66 . -410) T) ((-108 . -633) 81330) ((-108 . -632) 81272) ((-214 . -922) T) ((-987 . -153) 81256) ((-793 . -133) T) ((-692 . -635) 81174) ((-136 . -748) T) ((-118 . -748) T) ((-1284 . -35) 81140) ((-1085 . -503) 81124) ((-594 . -23) T) ((-560 . -23) T) ((-509 . -23) T) ((-1263 . -95) 81090) ((-1263 . -35) 81056) ((-1202 . -102) T) ((-1156 . -102) T) ((-878 . -102) T) ((-231 . -503) 81040) ((-1320 . -111) 81019) ((-1319 . -111) 80998) ((-44 . -1087) 80982) ((-1322 . -1248) T) ((-1320 . -635) 80928) ((-1320 . -1080) T) ((-1319 . -635) 80857) ((-1319 . -1080) T) ((-1267 . -1274) 80841) ((-879 . -876) 80825) ((-1210 . -302) 80804) ((-1134 . -1248) T) ((-110 . -298) 80754) ((-1034 . -1248) T) ((-131 . -153) 80736) ((-1173 . -927) 80695) ((-44 . -111) 80674) ((-1254 . -1132) T) ((-1213 . -1294) T) ((-1199 . -870) NIL) ((-1198 . -504) 80655) ((-692 . -1080) T) ((-1198 . -632) 80621) ((-1190 . -632) 80603) ((-488 . -239) 80555) ((-1094 . -629) 80530) ((-1025 . -504) 80511) ((-74 . -455) T) ((-74 . -410) T) ((-1094 . -1132) T) ((-154 . -1087) 80495) ((-1025 . -632) 80461) ((-692 . -240) 80440) ((-585 . -569) 80424) ((-368 . -149) 80403) ((-368 . -147) 80354) ((-366 . -149) 80333) ((-366 . -147) 80284) ((-358 . -149) 80263) ((-358 . -147) 80214) ((-275 . -147) 80193) ((-275 . -149) 80172) ((-255 . -149) 80151) ((-119 . -376) T) ((-255 . -147) 80130) ((-1190 . -633) NIL) ((-154 . -111) 80109) ((-1034 . -1069) 79997) ((-1186 . -1248) T) ((-716 . -1253) T) ((-820 . -1088) T) ((-721 . -1143) T) ((-1034 . -390) 79974) ((-520 . -1248) T) ((-516 . -1248) T) ((-935 . -147) T) ((-935 . -149) 79956) ((-893 . -133) T) ((-837 . -1087) 79877) ((-721 . -23) T) ((-716 . -571) T) ((-229 . -1082) 79842) ((-669 . -632) 79774) ((-669 . -633) 79735) ((-651 . -633) NIL) ((-651 . -632) 79717) ((-501 . -175) T) ((-229 . -662) 79682) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1237) 79648) ((-488 . -1234) 79614) ((-285 . -632) 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. -1088) T) ((-1241 . -149) 63676) ((-334 . -1082) 63658) ((-1241 . -147) 63637) ((-1216 . -102) T) ((-1215 . -102) T) ((-1214 . -102) T) ((-1206 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1248) T) ((-1205 . -175) 63501) ((-1199 . -175) 63432) ((-1184 . -635) 63413) ((-1157 . -175) 63364) ((-610 . -1088) T) ((-609 . -1088) T) ((-1035 . -1132) T) ((-1002 . -1132) T) ((-391 . -1082) 63329) ((-136 . -1248) T) ((-118 . -1248) T) ((-943 . -1132) T) ((-895 . -929) NIL) ((-391 . -662) 63294) ((-146 . -874) T) ((-820 . -818) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -911) 63237) ((-443 . -1132) T) ((-326 . -1253) 63216) ((-325 . -1253) T) ((-171 . -414) 63200) ((-856 . -1082) 63170) ((-488 . -1004) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-850 . -1082) 63098) ((-108 . -819) T) ((-108 . -814) T) ((-723 . -1069) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-856 . -662) 63029) ((-850 . -662) 62999) ((-1328 . -23) T) ((-136 . -1069) 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. -921) 60880) ((-987 . -321) 60818) ((-856 . -102) T) ((-443 . -739) 60802) ((-229 . -843) T) ((-850 . -102) T) ((-847 . -102) T) ((-1320 . -670) 60776) ((-1284 . -1283) 60755) ((-493 . -153) 60705) ((-1284 . -1277) 60675) ((-1151 . -1253) T) ((-352 . -1069) 60642) ((-1284 . -1281) 60626) ((-1267 . -929) 60533) ((-1263 . -1262) 60512) ((-80 . -632) 60494) ((-931 . -632) 60476) ((-1263 . -1277) 60453) ((-1151 . -571) T) ((-948 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1263 . -1260) 60308) ((-1285 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1317) 60048) ((-367 . -1317) 60032) ((-359 . -1317) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1319 . -670) 59929) ((-131 . -321) NIL) ((-1285 . -23) T) 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. -950) T) ((-723 . -842) T) ((-443 . -632) 39859) ((-1151 . -21) T) ((-1151 . -25) T) ((-692 . -390) 39843) ((-118 . -950) T) ((-896 . -274) 39827) ((-896 . -234) 39811) ((-44 . -1248) T) ((-75 . -1248) T) ((-128 . -127) 39795) ((-1085 . -34) T) ((-1320 . -1069) 39769) ((-1319 . -1069) 39726) ((-1267 . -1088) T) ((-879 . -1088) T) ((-368 . -1183) 39705) ((-366 . -1183) 39684) ((-358 . -1183) 39663) ((-496 . -816) 39642) ((-496 . -815) 39621) ((-231 . -34) T) ((-496 . -748) 39599) ((-820 . -635) 39445) ((-674 . -1082) 39429) ((-60 . -503) 39413) ((-585 . -1088) T) ((-1202 . -175) 39304) ((-674 . -662) 39288) ((-488 . -929) 39194) ((-154 . -1248) T) ((-1156 . -175) 39105) ((-1093 . -1132) T) ((-1118 . -979) 39050) ((-975 . -1132) T) ((-839 . -670) 39001) ((-803 . -979) 38970) ((-735 . -1132) T) ((-802 . -979) 38937) ((-530 . -294) 38921) ((-692 . -927) 38880) ((-495 . -1132) T) ((-468 . -979) 38847) ((-79 . -1248) T) ((-368 . -38) 38812) ((-366 . -38) 38777) ((-358 . -38) 38742) ((-275 . -38) 38591) ((-255 . -38) 38440) ((-935 . -1183) T) ((-538 . -504) 38421) ((-642 . -149) 38400) ((-642 . -147) 38379) ((-612 . -1248) T) ((-538 . -632) 38345) ((-119 . -149) T) ((-119 . -147) NIL) ((-429 . -748) T) ((-820 . -1080) T) ((-560 . -239) T) ((-509 . -239) T) ((-357 . -466) T) ((-1288 . -1033) 38311) ((-1279 . -1033) 38277) ((-1258 . -1033) 38243) ((-935 . -38) 38208) ((-229 . -739) 38173) ((-1027 . -133) T) ((-659 . -668) 38142) ((-331 . -47) 38112) ((-40 . -424) 38084) ((-142 . -632) 38066) ((-993 . -1248) T) ((-837 . -1248) T) ((-177 . -950) T) ((-564 . -381) T) ((-736 . -668) 38011) ((-619 . -635) 37992) ((-357 . -416) T) ((-693 . -635) 37973) ((-325 . -236) NIL) ((-183 . -635) 37954) ((-164 . -635) 37935) ((-158 . -635) 37916) ((-156 . -635) 37897) ((-534 . -300) 37874) ((-1263 . -234) 37844) ((-1263 . -274) 37814) ((-1246 . -1248) 37792) ((-1210 . -670) 37717) ((-900 . -102) T) ((-837 . -1069) 37544) ((-45 . -34) T) ((-703 . -102) T) ((-698 . -102) T) ((-678 . -21) T) 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30630) ((-943 . -111) 30568) ((-758 . -717) 30552) ((-733 . -662) 30517) ((-275 . -274) 30501) ((-275 . -234) 30485) ((-443 . -1087) 30469) ((-391 . -1088) T) ((-246 . -635) 30267) ((-716 . -1237) NIL) ((-501 . -670) 30217) ((-488 . -668) 30099) ((-108 . -909) 30081) ((-108 . -911) 30063) ((-716 . -1234) NIL) ((-221 . -670) 30013) ((-372 . -1069) 29997) ((-367 . -1069) 29981) ((-339 . -321) 29919) ((-359 . -1069) 29903) ((-229 . -302) T) ((-443 . -111) 29882) ((-60 . -632) 29814) ((-171 . -175) T) ((-1151 . -871) T) ((-108 . -1069) 29774) ((-915 . -1132) T) ((-856 . -1088) T) ((-850 . -1088) T) ((-716 . -35) NIL) ((-716 . -95) NIL) ((-325 . -1022) 29735) ((-187 . -102) T) ((-1322 . -1143) T) ((-1322 . -23) T) ((-594 . -466) T) ((-560 . -466) T) ((-509 . -466) T) ((-1314 . -632) 29717) ((-1267 . -175) 29608) ((-1241 . -102) T) ((-421 . -376) T) ((-1230 . -1132) T) ((-1220 . -233) 29558) ((-1215 . -866) T) ((-1214 . -866) T) ((-1198 . -1248) T) ((-246 . -1080) 29536) ((-1025 . -1248) T) 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21091) ((-91 . -1132) 21069) ((-108 . -1051) T) ((-560 . -145) T) ((-1298 . -153) 21053) ((-496 . -1069) 20880) ((-1285 . -147) 20841) ((-1285 . -149) 20802) ((-1085 . -1248) T) ((-1310 . -93) T) ((-1024 . -632) 20784) ((-840 . -1248) T) ((-887 . -632) 20766) ((-838 . -1087) 20609) ((-1309 . -93) T) ((-1202 . -633) NIL) ((-1127 . -1132) T) ((-1122 . -1132) T) ((-1118 . -321) 20596) ((-429 . -1248) T) ((-394 . -1248) T) ((-1104 . -1132) T) ((-231 . -1248) T) ((-1097 . -1132) T) ((-1067 . -1132) T) ((-1050 . -1132) T) ((-803 . -321) 20583) ((-802 . -321) 20570) ((-1202 . -632) 20552) ((-838 . -111) 20381) ((-1156 . -632) 20363) ((-645 . -1132) T) ((-591 . -176) T) ((-543 . -176) T) ((-468 . -321) 20350) ((-497 . -1132) T) ((-1156 . -633) 20098) ((-1065 . -175) T) ((-972 . -300) 20075) ((-222 . -1132) T) ((-878 . -632) 20057) ((-627 . -528) 19840) ((-81 . -635) 19781) ((-840 . -1069) 19765) ((-489 . -528) 19557) ((-854 . -874) 19536) ((-985 . -748) T) ((-757 . -748) T) ((-737 . -748) T) 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\ No newline at end of file
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-23) T) ((-530 . -298) 195899) ((-339 . -528) 195832) ((-510 . -298) 195784) ((-391 . -250) T) ((-391 . -240) T) ((-858 . -1081) T) ((-852 . -1081) T) ((-734 . -980) 195753) ((-723 . -872) T) ((-630 . -875) T) ((-488 . -632) 195735) ((-1286 . -1083) 195640) ((-594 . -668) 195612) ((-560 . -668) 195584) ((-509 . -668) 195534) ((-852 . -240) 195513) ((-136 . -872) T) ((-1286 . -662) 195405) ((-676 . -1133) T) ((-1221 . -618) 195384) ((-565 . -1226) 195363) ((-346 . -1133) T) ((-331 . -376) 195342) ((-421 . -149) 195321) ((-421 . -147) 195300) ((-994 . -1144) 195199) ((-839 . -1144) 195177) ((-246 . -928) 195109) ((-678 . -877) 195093) ((-493 . -618) 195072) ((-110 . -875) T) ((-538 . -1249) T) ((-565 . -107) 195022) ((-1036 . -390) 195004) ((-1036 . -351) 194986) ((-1209 . -632) 194968) ((-97 . -1133) T) ((-994 . -23) 194779) ((-491 . -21) T) ((-491 . -25) T) ((-839 . -23) 194631) ((-1209 . -633) 194553) ((-58 . -19) 194537) ((-1203 . -748) T) ((-1157 . -748) T) ((-1119 . -1133) T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1035 . -239) 194419) ((-931 . -102) 194369) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1133) T) ((-802 . -1097) 194290) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194265) ((-671 . -1133) T) ((-1289 . -47) 194242) ((-1286 . -102) T) ((-1280 . -47) 194212) ((-1259 . -47) 194189) ((-1242 . -175) 194140) ((-1206 . -319) 194119) ((-1200 . -319) 194098) ((-1128 . -635) 194079) ((-1123 . -635) 194060) ((-1111 . -571) 194011) ((-1111 . -1254) 193962) ((-1105 . -635) 193943) ((-1036 . -928) NIL) ((-1098 . -635) 193924) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193905) ((-1051 . -635) 193886) ((-736 . -1088) 193856) ((-734 . -922) 193759) ((-721 . -668) 193709) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193693) ((-50 . -1133) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1133) T) ((-532 . -1133) T) ((-501 . -844) T) ((-501 . -951) T) ((-372 . -1254) T) ((-367 . -1254) T) ((-359 . -1254) T) ((-331 . -1144) T) ((-326 . -1083) 193545) ((-325 . -1083) 193474) ((-108 . -1254) T) ((-645 . -635) 193455) ((-372 . -571) T) ((-221 . -951) T) ((-221 . -844) T) ((-326 . -662) 193365) ((-325 . -662) 193294) ((-367 . -571) T) ((-359 . -571) T) ((-659 . -111) 193273) ((-497 . -635) 193254) ((-108 . -571) T) ((-1200 . -1052) NIL) ((-676 . -739) 193224) ((-496 . -875) 193175) ((-222 . -635) 193156) ((-331 . -23) T) ((-67 . -1249) T) ((-1032 . -632) 193088) ((-1329 . -1184) T) ((-716 . -274) 193070) ((-716 . -234) 193052) ((-1324 . -21) T) ((-736 . -111) 193017) ((-1324 . -25) T) ((-663 . -34) T) ((-252 . -503) 193001) ((-1321 . -133) T) ((-1320 . -133) T) ((-1313 . -102) T) ((-1296 . -632) 192967) ((-1129 . -1131) 192951) ((-174 . -1133) T) ((-1289 . -1249) T) ((-1280 . -1249) T) ((-1280 . -1070) 192886) ((-1259 . -1249) T) ((-1259 . -912) NIL) ((-976 . -940) 192865) ((-1259 . -910) 192817) ((-1259 . -1070) 192783) ((-1242 . -528) 192750) ((-529 . -635) 192734) ((-1221 . -633) NIL) ((-1221 . -632) 192716) ((-1174 . -1155) 192661) ((-495 . -940) 192640) ((-1119 . -739) 192489) ((-1094 . -670) 192461) ((-976 . -670) 192350) ((-842 . -875) T) ((-803 . -739) 192179) ((-611 . -504) 192160) ((-600 . -504) 192141) ((-611 . -632) 192107) ((-600 . -632) 192073) ((-549 . -632) 192055) ((-593 . -1249) T) ((-549 . -633) 192036) ((-802 . -739) 191885) ((-1109 . -102) T) ((-642 . -668) 191857) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191746) ((-475 . -739) 191717) ((-468 . -739) 191566) ((-1018 . -102) T) ((-1078 . -1244) 191495) ((-931 . -321) 191433) ((-758 . -102) T) ((-659 . -635) 191410) ((-119 . -668) 191340) ((-901 . -93) T) ((-736 . -635) 191294) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191276) ((-667 . -504) 191257) ((-667 . -632) 191210) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1249) T) ((-609 . -1249) T) ((-357 . -1089) T) ((-301 . -1144) T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190662) ((-1152 . -662) 190649) ((-1152 . -1083) 190636) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190487) ((-936 . -633) 190469) ((-400 . -748) T) ((-897 . -1088) 190421) ((-897 . -111) 190359) ((-736 . -1081) T) ((-734 . -1275) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190236) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1111 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189637) ((-896 . -670) 189582) ((-1259 . -390) 189534) ((-994 . -133) 189389) ((-839 . -133) 189260) ((-45 . -875) NIL) ((-988 . -673) 189244) ((-1258 . -684) T) ((-1119 . -175) 189155) ((-988 . -385) 189139) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-840 . -47) 188801) ((-1094 . -748) T) ((-339 . -503) 188785) ((-976 . -748) T) ((-1313 . -321) 188723) ((-1289 . -928) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1285 . -1088) 188334) ((-1280 . -928) 188240) ((-1264 . -1088) 188048) ((-495 . -748) T) ((-1259 . -928) 187881) ((-1242 . -302) 187860) ((-1219 . -1249) T) ((-1216 . -381) T) ((-1215 . -381) T) ((-1178 . -153) 187844) ((-1152 . -102) T) ((-1147 . -1133) T) ((-1111 . -23) T) ((-1111 . -1144) T) ((-1108 . -102) T) ((-1090 . -632) 187811) ((-1035 . -424) 187783) ((-955 . -985) T) ((-758 . -321) 187721) ((-76 . -1249) T) ((-686 . -397) 187693) ((-171 . -940) 187646) ((-30 . -985) T) ((-114 . -868) T) ((-1 . -632) 187628) ((-1028 . -922) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -928) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-897 . -1081) T) ((-856 . -872) 187324) ((-81 . -1249) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1144) T) ((-367 . -1144) T) ((-359 . -1144) T) ((-1036 . -319) T) ((-944 . -319) T) ((-897 . -250) T) ((-108 . -1144) T) ((-897 . -240) 187123) ((-1285 . -111) 186944) ((-1264 . -111) 186733) ((-252 . -1288) 186717) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1083) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1133) T) ((-678 . -662) 186541) ((-1286 . -38) 186433) ((-1268 . -940) 186412) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186301) ((-896 . -818) NIL) ((-880 . -670) 186275) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-840 . -1070) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1285 . -635) 185618) ((-1264 . -635) 185366) ((-60 . -1249) T) ((-638 . -872) 185345) ((-514 . -684) T) ((-1178 . -1008) 185314) ((-1056 . -668) 185251) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) ((-488 . -1088) 185086) ((-514 . -113) T) ((-357 . -1133) T) ((-325 . -1184) NIL) ((-301 . -133) T) ((-407 . -1133) T) ((-894 . -1089) T) ((-716 . -383) 185053) ((-353 . -668) 184983) ((-227 . -640) 184960) ((-339 . -298) 184912) ((-488 . -111) 184733) ((-1285 . -1081) T) ((-1264 . -1081) T) ((-840 . -390) 184717) ((-850 . -1249) T) ((-171 . -748) T) ((-1315 . -1249) T) ((-678 . -102) T) ((-1285 . -250) 184696) ((-1285 . -240) 184648) ((-1264 . -240) 184553) ((-1264 . -250) 184532) ((-1035 . -416) NIL) ((-692 . -660) 184480) ((-326 . -38) 184390) ((-325 . -38) 184319) ((-69 . -632) 184301) ((-331 . -507) 184267) ((-48 . -668) 184217) ((-1221 . -300) 184196) ((-1258 . -872) T) ((-1145 . -1144) 184174) ((-84 . -1249) T) ((-62 . -632) 184156) ((-889 . -875) T) ((-493 . -300) 184135) ((-1315 . -1070) 184112) ((-1197 . -1133) T) ((-1145 . -23) 183964) ((-840 . -928) 183900) ((-1268 . -748) T) ((-1129 . -1249) T) ((-488 . -635) 183726) ((-365 . -239) T) ((-1119 . -302) 183657) ((-996 . -1133) T) ((-919 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1067 . -321) 183173) ((-901 . -504) 183154) ((-901 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182524) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1152 . -1184) T) ((-1280 . -319) 182433) ((-734 . -1083) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1249) T) ((-734 . -662) 181995) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181974) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181953) ((-663 . -1042) 181937) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181869) ((-1121 . -632) 181836) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181820) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181772) ((-366 . -1088) 181724) ((-358 . -1088) 181676) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181519) ((-255 . -1088) 181362) ((-686 . -111) 181341) ((-841 . -1254) 181320) ((-562 . -868) T) ((-326 . -930) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -930) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180693) ((-130 . -684) T) ((-839 . -660) 180599) ((-841 . -571) 180578) ((-501 . -875) T) ((-260 . -1070) 180405) ((-259 . -1070) 180232) ((-128 . -121) 180216) ((-221 . -875) T) ((-936 . -1088) 180181) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-936 . -111) 179984) ((-40 . -739) 179929) ((-894 . -1133) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1133) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1249) T) ((-1264 . -816) 179062) ((-1264 . -821) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-564 . -875) T) ((-678 . -38) 178923) ((-627 . -34) T) ((-496 . -1144) 178901) ((-489 . -34) T) ((-1145 . -133) 178772) ((-994 . -25) 178583) ((-936 . -635) 178533) ((-899 . -632) 178515) ((-218 . -868) T) ((-994 . -21) 178470) ((-839 . -25) 178303) ((-839 . -21) 178214) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178193) ((-1203 . -47) 178170) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 178022) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177994) ((-119 . -1089) T) ((-1066 . -670) 177968) ((-988 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-366 . -240) 177926) ((-366 . -250) T) ((-358 . -240) 177905) ((-358 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1187 . -153) 177797) ((-260 . -928) 177729) ((-259 . -928) 177661) ((-1174 . -922) 177582) ((-1114 . -872) T) ((-1266 . -1249) 177560) ((-429 . -1144) T) ((-1242 . -1034) 177526) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1206 . -951) 177432) ((-1200 . -951) 177411) ((-1200 . -844) NIL) ((-1028 . -1083) 177307) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177286) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177264) ((-123 . -1133) 177242) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1028 . -662) 177155) ((-894 . -739) 177142) ((-1329 . -668) 177114) ((-1078 . -153) 177079) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-858 . -670) 177008) ((-852 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176938) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176719) ((-130 . -872) T) ((-1203 . -1070) 176599) ((-1157 . -1070) 176482) ((-187 . -632) 176464) ((-879 . -1070) 176360) ((-803 . -298) 176287) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176216) ((-616 . -673) 176200) ((-1035 . -922) 176107) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176085) ((-716 . -1089) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176051) ((-1203 . -390) 176035) ((-1157 . -390) 176019) ((-1056 . -426) 175981) ((-143 . -233) 175963) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1299 . -1298) 175758) ((-365 . -416) T) ((-1299 . -1133) 175708) ((-1223 . -1133) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1286 . -668) 175537) ((-326 . -649) 175516) ((-858 . -748) T) 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T) ((-901 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1254) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1254) T) ((-421 . -922) 174525) ((-229 . -1070) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1249) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173800) ((-1094 . -912) 173782) ((-976 . -912) 173707) ((-677 . -1144) T) ((-642 . -739) 173694) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173678) ((-1094 . -1070) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-976 . -1070) 173522) ((-119 . -739) 173467) ((-734 . -930) 173374) ((-677 . -23) T) ((-495 . -1070) 173250) ((-1119 . -633) NIL) ((-1119 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1145 . -660) 172647) ((-822 . -875) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1067 . -233) 172397) ((-897 . -940) 172376) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1318) 172342) ((-366 . -1318) 172326) ((-358 . -1318) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-976 . -390) 171946) ((-894 . -302) T) ((-50 . -632) 171928) ((-1152 . -668) 171900) ((-1028 . -38) 171848) ((-626 . -1133) T) ((-621 . -1133) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-936 . -1318) 171765) ((-896 . -1249) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1311 . -1249) T) ((-1310 . -1249) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1323 . -1314) 171652) ((-896 . -910) 171629) ((-896 . -912) NIL) ((-994 . -872) 171528) ((-839 . -872) 171479) ((-1257 . -102) T) ((-678 . -680) 171463) ((-1236 . -34) T) ((-174 . -632) 171445) ((-1145 . -25) 171278) ((-1145 . -21) 171189) ((-896 . -1070) 171166) ((-976 . -928) 171147) ((-1268 . -47) 171124) ((-936 . -381) T) ((-607 . -875) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -928) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1249) T) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1324 . -1319) 169581) ((-699 . -1070) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169520) ((-880 . -1249) T) ((-678 . -668) 169479) ((-48 . -1133) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169429) ((-402 . -1133) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1268 . -1070) 169277) ((-880 . -1070) 169173) ((-1174 . -102) T) ((-1028 . -930) 169096) ((-677 . -133) T) ((-674 . -816) 169075) ((-674 . -821) 169054) ((-119 . -528) 168962) ((-585 . -1070) 168944) ((-305 . -1307) 168914) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168893) ((-1242 . -1088) 168776) ((-1035 . -1083) 168721) ((-496 . -660) 168627) ((-935 . -1133) T) ((-1056 . -739) 168564) ((-733 . -1088) 168529) ((-1035 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -928) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1329 . -1089) T) ((-1268 . -390) 168084) ((-419 . -1254) 168062) ((-1147 . -632) 168044) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167997) ((-1264 . -818) 167950) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167915) ((-229 . -1052) T) ((-1286 . -426) 167881) ((-1268 . -928) 167824) ((-365 . -1307) 167801) ((-1242 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -875) 167644) ((-1145 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1323 . -1083) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1323 . -662) 167115) ((-642 . -302) T) ((-597 . -1088) 167090) ((-450 . -1133) T) ((-1094 . -319) T) ((-119 . -302) T) ((-1135 . -102) T) ((-1035 . -102) T) ((-597 . -111) 167058) ((-1242 . -1081) T) ((-1174 . -321) 166996) ((-1094 . -1052) T) ((-1086 . -25) T) ((-66 . -1249) T) ((-916 . -1249) T) ((-1086 . -21) T) ((-733 . -1081) T) ((-394 . -21) T) ((-394 . -25) T) ((-716 . -528) NIL) ((-1056 . -175) T) ((-733 . -250) T) ((-1094 . -559) T) ((-734 . -668) 166906) ((-520 . -102) T) ((-516 . -102) T) ((-357 . -632) 166888) ((-353 . -175) T) ((-421 . -1083) 166840) ((-407 . -632) 166822) ((-1152 . -871) T) ((-488 . -748) T) ((-916 . -1070) 166790) ((-421 . -662) 166742) ((-108 . -872) T) ((-676 . -1088) 166726) ((-501 . -133) T) ((-1286 . -1089) T) ((-221 . -133) T) ((-1187 . -102) 166676) ((-99 . -1133) T) ((-246 . -875) 166627) ((-252 . -688) 166611) ((-252 . -673) 166595) ((-676 . -111) 166574) ((-597 . -635) 166558) ((-326 . -426) 166542) ((-252 . -385) 166526) ((-1192 . -242) 166473) ((-1028 . -274) 166457) ((-1028 . -234) 166441) ((-74 . -1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166423) ((-1120 . -1249) T) ((-1119 . -1088) 166266) ((-1107 . -1249) T) ((-275 . -940) 166245) ((-255 . -940) 166224) ((-803 . -1088) 166047) ((-802 . -1088) 165890) ((-627 . -1249) T) ((-1197 . -632) 165872) ((-1119 . -111) 165701) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165672) ((-468 . -1088) 165515) ((-686 . -670) 165499) ((-896 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1191 . -872) T) ((-1120 . -1070) 164755) ((-1107 . -1070) 164732) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1003 . -875) T) ((-996 . -632) 164504) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164488) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164406) ((-1299 . -503) 164390) ((-1217 . -1249) T) ((-1216 . -1249) T) ((-1174 . -38) 164350) ((-986 . -23) T) ((-936 . -670) 164315) ((-890 . -1133) T) ((-866 . -102) T) ((-841 . -21) T) ((-652 . -1083) 164299) ((-620 . -1083) 164283) ((-841 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1088) 164216) ((-532 . -1088) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1215 . -1249) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-891 . -38) 164089) ((-1119 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1144) T) ((-326 . -1089) 163600) ((-325 . -1089) T) ((-132 . -1249) T) ((-131 . -1249) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1081) T) ((-1329 . -1133) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1023) 162778) ((-118 . -895) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) ((-1236 . -1042) 162696) ((-1214 . -632) 162663) ((-1221 . -34) T) ((-984 . -632) 162629) ((-949 . -632) 162611) ((-1145 . -872) 162562) ((-793 . -632) 162544) ((-694 . -632) 162526) ((-531 . -1249) T) ((-1268 . -319) 162505) ((-1187 . -321) 162443) ((-1173 . -34) T) ((-493 . -34) T) ((-1124 . -1249) T) ((-491 . -466) T) ((-1066 . -1249) T) ((-1119 . -1081) T) ((-50 . -635) 162412) ((-803 . -1081) T) ((-802 . -1081) T) ((-669 . -242) 162396) ((-651 . -242) 162342) ((-1211 . -21) T) ((-595 . -635) 162292) ((-532 . -635) 162222) ((-496 . -236) 162113) ((-1211 . -25) T) ((-1119 . -338) 162074) ((-468 . -1081) T) ((-1119 . -240) 162053) ((-803 . -338) 162030) ((-803 . -240) T) ((-802 . -338) 162002) ((-753 . -1254) 161981) ((-533 . -34) T) ((-339 . -673) 161965) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161944) ((-339 . -385) 161928) ((-374 . -1249) T) ((-334 . -1249) T) ((-1035 . -1184) NIL) ((-753 . -571) 161859) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1249) T) ((-1312 . -21) T) ((-1078 . -321) 161767) ((-1312 . -25) T) ((-931 . -1133) 161745) ((-842 . -236) 161732) ((-50 . -1081) T) ((-1207 . -571) 161711) ((-1206 . -1254) 161690) ((-1206 . -571) 161641) ((-1200 . -1254) 161620) ((-1200 . -571) 161571) ((-1056 . -302) T) ((-595 . -1081) T) ((-532 . -1081) T) ((-1035 . -38) 161516) ((-374 . -1070) 161500) ((-334 . -1070) 161484) ((-1028 . -668) 161407) ((-391 . -912) 161389) ((-858 . -1249) T) ((-852 . -1249) T) ((-849 . -1249) T) ((-822 . -1144) T) ((-936 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1158 . -571) 161368) ((-353 . -302) T) ((-669 . -717) 161352) ((-391 . -1070) 161312) ((-305 . -1083) 161233) ((-352 . -922) 161212) ((-1152 . -1089) T) ((-103 . -127) 161196) ((-305 . -662) 161138) ((-822 . -23) T) ((-1321 . -1319) 161114) ((-1320 . -1319) 161093) ((-1299 . -298) 161045) ((-1286 . -1133) T) ((-421 . -321) 161010) ((-1174 . -930) 160933) ((-894 . -632) 160915) ((-858 . -1070) 160884) ((-661 . -1088) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -872) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160696) ((-119 . -298) 160647) ((-1299 . -19) 160631) ((-1259 . -875) NIL) ((-1299 . -618) 160608) ((-1313 . -1133) T) ((-365 . -1083) 160553) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160540) ((-758 . -1133) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -817) T) ((-526 . -818) T) ((-467 . -133) T) ((-421 . -1184) 160463) ((-227 . -1081) T) ((-305 . -102) 160245) ((-143 . -1133) T) ((-721 . -1034) T) ((-1137 . -298) 160201) ((-91 . -1249) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1329 . -175) T) ((-1206 . -376) 160026) ((-1200 . -376) 160005) ((-326 . -1133) T) ((-419 . -133) T) ((-325 . -1133) T) ((-421 . -38) 159957) ((-1165 . -102) T) ((-1286 . -739) 159849) ((-1167 . -1295) T) ((-1128 . -1249) T) ((-1123 . -1249) T) ((-678 . -1089) T) ((-1105 . -1249) T) ((-1098 . -1249) T) ((-1068 . -1249) T) ((-1051 . -1249) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1133) T) ((-137 . -1133) T) ((-115 . -1133) T) ((-883 . -102) T) ((-645 . -1249) T) ((-497 . -1249) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1249) T) ((-496 . -872) 159548) ((-501 . -660) 159530) ((-995 . -632) 159512) ((-1035 . -930) 159421) ((-221 . -660) 159403) ((-229 . -418) T) ((-674 . -670) 159387) ((-55 . -632) 159369) ((-1203 . -951) 159348) ((-753 . -1144) T) ((-657 . -102) T) ((-529 . -1249) T) ((-525 . -1249) T) ((-522 . -1249) T) ((-365 . -102) T) ((-1250 . -1115) T) ((-1152 . -868) T) ((-842 . -872) T) ((-753 . -23) T) ((-357 . -1088) 159293) ((-1180 . -107) 159277) ((-1302 . -632) 159259) ((-1207 . -23) T) ((-1207 . -1144) T) ((-1206 . -1144) T) ((-659 . -1249) T) ((-1206 . -23) T) ((-1200 . -1144) T) ((-1200 . -23) T) ((-1174 . -274) 159243) ((-529 . -1070) 159227) ((-1174 . -234) 159211) ((-1158 . -1144) T) ((-357 . -111) 159140) ((-1036 . -1254) T) ((-128 . -1249) T) ((-944 . -1254) T) ((-1158 . -23) T) ((-1108 . -1133) T) ((-716 . -298) NIL) ((-736 . -1249) T) ((-1036 . -571) T) ((-944 . -571) T) ((-839 . -239) 159037) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1249) T) ((-186 . -1249) T) ((-163 . -1249) T) ((-159 . -1249) T) ((-256 . -632) 159019) ((-622 . -684) T) ((-822 . -133) T) 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-1133) 146013) ((-1257 . -868) T) ((-331 . -1005) 145975) ((-105 . -102) T) ((-48 . -1088) 145940) ((-896 . -875) NIL) ((-1324 . -102) T) ((-395 . -102) T) ((-1286 . -632) 145922) ((-1165 . -1166) 145906) ((-1036 . -660) 145888) ((-901 . -1249) T) ((-48 . -111) 145844) ((-703 . -1249) T) ((-698 . -1249) T) ((-674 . -1249) T) ((-839 . -922) 145711) ((-492 . -1249) T) ((-252 . -1249) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1307) 145695) ((-140 . -1249) T) ((-139 . -1249) T) ((-135 . -1249) T) ((-1250 . -102) T) ((-1056 . -635) 145632) ((-841 . -239) T) ((-1203 . -1254) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1157 . -1254) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1203 . -571) 145127) ((-1157 . -571) 145058) ((-1257 . -1133) T) ((-561 . -875) T) ((-1067 . -298) 145033) ((-1199 . -1115) T) ((-1026 . -1115) T) ((-840 . -133) T) ((-119 . -821) NIL) ((-119 . -816) NIL) ((-368 . -319) T) 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143042) ((-1221 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1226) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1152 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1152 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1259 . -660) 142704) ((-493 . -107) 142654) ((-1025 . -23) T) ((-1324 . -38) 142624) ((-1203 . -1144) T) ((-1157 . -1144) T) ((-1094 . -1254) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-879 . -1144) T) ((-976 . -1254) 142494) ((-495 . -1254) 142473) ((-1094 . -571) T) ((-976 . -571) 142404) ((-1203 . -23) T) ((-1185 . -1115) T) ((-1157 . -23) T) ((-879 . -23) T) ((-495 . -571) 142335) ((-1174 . -739) 142267) ((-692 . -1083) 142251) ((-1178 . -528) 142184) ((-692 . -662) 142168) ((-1067 . -633) NIL) ((-1067 . -632) 142150) ((-96 . -1115) T) ((-1329 . -1088) 142137) ((-891 . -739) 142107) ((-1329 . -111) 142092) ((-1242 . -47) 142061) ((-1200 . -872) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142043) ((-1111 . -922) 141912) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141899) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141883) ((-1036 . -236) 141870) ((-897 . -844) 141849) ((-897 . -951) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141537) ((-1320 . -1083) 141521) ((-1321 . -662) 141491) ((-1187 . -1133) 141469) ((-896 . -1254) T) ((-1320 . -662) 141439) ((-1120 . -875) T) ((-678 . -632) 141421) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141405) ((-1329 . -635) 141387) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141371) ((-367 . -1307) 141355) ((-44 . -662) 141339) ((-359 . -1307) 141323) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141302) ((-733 . -1249) T) ((-988 . -875) 141281) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141260) ((-154 . -1083) 141244) ((-1078 . -1103) 141173) ((-1059 . -1008) 141142) ((-843 . -1144) T) ((-1035 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1144) T) ((-490 . -1008) 141040) ((-477 . -1008) 141009) ((-1216 . -875) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-919 . -632) 140955) ((-1215 . -875) T) ((-1111 . -746) 140934) ((-1329 . -1081) T) ((-840 . -660) 140882) ((-305 . -1089) 140824) ((-171 . -1254) 140729) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140681) ((-1286 . -1088) 140586) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140565) ((-1285 . -951) 140544) ((-1264 . -951) 140523) ((-894 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1133) T) ((-270 . -1133) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1264 . -844) 140278) ((-1321 . -102) T) ((-505 . -1249) T) ((-353 . -1318) 140255) ((-1320 . -102) T) ((-1286 . -111) 140147) ((-1145 . -922) 140014) ((-839 . -1083) 139915) ((-839 . -662) 139837) ((-146 . -632) 139819) ((-1025 . -133) T) ((-44 . -102) T) ((-246 . -872) 139770) ((-597 . -1249) T) ((-1268 . -1254) 139749) ((-103 . -503) 139733) ((-1323 . -739) 139703) ((-1119 . -47) 139664) ((-1094 . -1144) T) ((-976 . -1144) T) ((-129 . -34) T) ((-123 . -34) T) ((-1268 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1229 . -1249) T) ((-1203 . -133) T) ((-353 . -381) T) ((-495 . -1144) T) ((-1157 . -133) T) ((-896 . -376) T) ((-468 . -47) 139503) ((-879 . -133) T) ((-334 . -875) 139482) ((-154 . -102) T) ((-1094 . -23) T) ((-976 . -23) T) ((-585 . -571) T) ((-840 . -25) T) ((-840 . -21) T) 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137363) ((-1119 . -1249) T) ((-1067 . -300) 137338) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137289) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137273) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137249) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137228) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137087) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137065) ((-1138 . -410) T) ((-642 . -670) 137052) ((-468 . -912) NIL) ((-697 . -102) 137002) ((-1119 . -1070) 136829) ((-896 . -23) T) ((-803 . -1070) 136688) ((-802 . -1070) 136545) ((-119 . -670) 136490) ((-468 . -1070) 136366) ((-286 . -1249) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1249) T) ((-404 . -668) 135782) ((-671 . -1070) 135766) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135750) ((-1299 . -34) T) ((-638 . -668) 135709) ((-301 . -1083) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1152 . -1088) 135582) ((-86 . -632) 135564) ((-50 . -1070) 135548) ((-1119 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135478) ((-595 . -1070) 135465) ((-532 . -1070) 135442) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135332) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1036 . -1023) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134993) ((-229 . -133) T) ((-1152 . -111) 134978) ((-171 . -23) T) ((-822 . -149) 134957) ((-822 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1187 . -528) 134647) ((-491 . -668) 134597) ((-657 . -868) T) ((-496 . -922) 134464) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134402) ((-1119 . -928) 134337) ((-803 . -928) 134280) ((-802 . -928) 134264) ((-1321 . -38) 134234) ((-1320 . -38) 134204) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134181) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134153) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134098) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133999) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133798) ((-1035 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133600) ((-496 . -1307) 133570) ((-1152 . -1081) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1083) 133522) ((-367 . -1083) 133474) ((-359 . -1083) 133426) ((-372 . -662) 133378) ((-227 . -1070) 133355) ((-367 . -662) 133307) ((-108 . -1083) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1249) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1152 . -240) T) ((-307 . -153) 132963) ((-1028 . -633) 132924) ((-1028 . -632) 132906) ((-1021 . -632) 132888) ((-118 . -1089) T) ((-678 . -1088) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1086 . -1307) 132801) ((-678 . -111) 132780) ((-692 . -930) 132703) ((-1174 . -503) 132687) ((-1324 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1192 . -102) T) ((-896 . -133) T) ((-498 . -102) 132565) ((-1147 . -1249) T) ((-1256 . -875) T) ((-1329 . -381) T) ((-1111 . -102) T) ((-1093 . -102) T) ((-365 . -739) 132510) ((-897 . -875) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1191 . -102) T) ((-1268 . -133) T) ((-1264 . -875) 131065) ((-1203 . -25) T) ((-1203 . -21) T) ((-1192 . -321) 130860) ((-357 . -1249) T) ((-1157 . -25) T) ((-880 . -133) T) ((-407 . -1249) T) ((-1157 . -21) T) ((-879 . -25) T) ((-879 . -21) T) ((-803 . -319) 130839) ((-1187 . -503) 130823) ((-1183 . -153) 130773) ((-1178 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1178 . -633) 130646) ((-585 . -133) T) ((-638 . -871) 130625) ((-1056 . -814) T) ((-1056 . -818) T) ((-1056 . -748) T) ((-839 . -930) 130494) ((-734 . -1088) 130317) ((-616 . -875) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1070) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -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) ((-734 . -111) 129759) ((-353 . -748) T) ((-692 . -274) 129743) ((-692 . -234) 129727) ((-595 . -319) T) ((-532 . -319) T) ((-305 . -528) 129676) ((-1197 . -1249) T) ((-108 . -321) NIL) ((-72 . -410) T) ((-1145 . -102) 129408) ((-856 . -426) 129392) ((-1152 . -821) T) ((-1152 . -816) T) ((-723 . -1133) T) ((-592 . -632) 129374) ((-391 . -376) T) ((-171 . -507) 129352) ((-226 . -632) 129284) ((-136 . -1133) T) ((-118 . -1133) T) ((-996 . -1249) T) ((-48 . -748) T) ((-1078 . -503) 129249) ((-143 . -440) 129231) ((-143 . -381) T) ((-1059 . -102) T) ((-524 . -523) 129210) ((-734 . -635) 128966) ((-1257 . -632) 128948) ((-1214 . -1249) T) ((-1214 . -1070) 128884) ((-1207 . -239) 128843) ((-490 . -102) T) ((-477 . -102) T) ((-1206 . -239) 128795) ((-1200 . -239) 128618) ((-1066 . -1144) T) ((-331 . -930) 128524) ((-1209 . -875) T) ((-1207 . -35) 128490) ((-1207 . -95) 128456) ((-1207 . -1238) 128422) ((-1207 . -1235) 128388) ((-1206 . -1235) 128354) ((-1206 . -1238) 128320) ((-1206 . -95) 128286) ((-1206 . -35) 128252) ((-1200 . -1235) 128218) ((-1200 . -1238) 128184) ((-1191 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1111 . -1184) 128163) ((-40 . -1249) T) ((-1200 . -95) 128129) ((-1066 . -23) T) ((-1200 . -35) 128095) ((-585 . -507) T) ((-1158 . -35) 128061) ((-1158 . -95) 128027) ((-1158 . -1238) 127993) ((-1158 . -1235) 127959) ((-374 . -1144) T) ((-372 . -1184) 127938) ((-367 . -1184) 127917) ((-359 . -1184) 127896) ((-1135 . -298) 127852) ((-984 . -1249) T) ((-949 . -1249) T) ((-108 . -1184) T) ((-856 . -1089) 127831) ((-793 . -1249) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1249) T) ((-734 . -1081) T) ((-1094 . -660) 127602) ((-1111 . -38) 127470) ((-976 . -660) 127418) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-391 . -1144) T) ((-336 . -25) T) ((-334 . -23) T) ((-973 . -872) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1070) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1133) T) ((-177 . -1133) T) ((-343 . -872) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-858 . -1144) T) ((-108 . -38) 126992) ((-852 . -1144) T) ((-795 . -1133) T) ((-118 . -739) 126979) ((-694 . -1070) 126963) ((-630 . -102) T) ((-858 . -23) T) ((-852 . -23) T) ((-1187 . -298) 126915) ((-1145 . -321) 126853) ((-496 . -1083) 126754) ((-1129 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1185 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -877) 126621) ((-1203 . -236) 126608) ((-1167 . -1115) T) ((-1094 . -21) T) ((-1094 . -25) T) ((-1086 . -1083) 126592) ((-839 . -274) 126561) ((-839 . -234) 126530) ((-976 . -25) T) ((-976 . -21) T) ((-1152 . -381) T) ((-1086 . -662) 126472) ((-638 . -1089) T) ((-1059 . -321) 126410) ((-914 . -632) 126392) ((-692 . -668) 126351) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1083) 126335) ((-911 . -632) 126317) ((-894 . -1249) T) ((-537 . -528) 126250) ((-260 . -872) 126201) ((-259 . -872) 126152) ((-394 . -662) 126122) ((-896 . -660) 126099) ((-490 . -321) 126037) ((-562 . -1249) T) ((-477 . -321) 125975) ((-365 . -302) T) ((-1187 . -1288) 125959) ((-1174 . -632) 125921) ((-1174 . -633) 125882) ((-1172 . -102) T) ((-1028 . -1088) 125778) ((-40 . -928) 125730) ((-1187 . -618) 125707) ((-1329 . -670) 125694) ((-1095 . -153) 125640) ((-501 . -922) NIL) ((-891 . -504) 125617) ((-1028 . -111) 125499) ((-897 . -1254) T) ((-221 . -922) NIL) ((-352 . -739) 125483) ((-891 . -632) 125445) ((-177 . -739) 125377) ((-897 . -571) T) ((-421 . -298) 125335) ((-246 . -239) 125232) ((-108 . -414) 125214) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125196) ((-99 . -748) T) ((-496 . -102) 124928) ((-99 . 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123970) ((-1028 . -240) 123949) ((-1289 . -149) 123928) ((-1285 . -1254) 123907) ((-856 . -1133) T) ((-1280 . -149) 123886) ((-1280 . -147) 123865) ((-1264 . -1254) 123844) ((-1259 . -147) 123751) ((-1259 . -149) 123658) ((-391 . -133) T) ((-229 . -236) 123645) ((-177 . -175) T) ((-560 . -912) 123627) ((0 . -1133) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1249) T) ((-49 . -1133) T) ((-1286 . -670) 123532) ((-1285 . -571) 123483) ((-1264 . -571) 123434) ((-736 . -1144) T) ((-659 . -23) T) ((-560 . -1070) 123416) ((-609 . -149) 123395) ((-609 . -147) 123374) ((-509 . -1070) 123317) ((-1167 . -1169) T) ((-88 . -398) T) ((-88 . -410) T) ((-897 . -376) T) ((-858 . -133) T) ((-852 . -133) T) ((-994 . -668) 123261) ((-736 . -23) T) ((-520 . -632) 123211) ((-516 . -632) 123193) ((-839 . -668) 122972) ((-1324 . -1089) T) ((-391 . -1092) T) ((-1058 . -1133) 122950) ((-55 . -1070) 122932) ((-931 . -34) T) ((-496 . -321) 122870) ((-606 . -102) T) ((-1187 . -633) 122831) ((-1187 . -632) 122763) 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-321) 78364) ((-1094 . -1083) 78351) ((-1167 . -1133) T) ((-976 . -1083) 78194) ((-1157 . -321) 78181) ((-1128 . -1115) T) ((-642 . -1144) T) ((-1094 . -662) 78168) ((-1123 . -1115) T) ((-976 . -662) 78017) ((-1119 . -236) 77962) ((-495 . -1083) 77805) ((-1105 . -1115) T) ((-1098 . -1115) T) ((-1068 . -1115) T) ((-1051 . -1115) T) ((-119 . -1144) T) ((-495 . -662) 77654) ((-803 . -236) 77641) ((-843 . -102) T) ((-645 . -1115) T) ((-642 . -23) T) ((-1183 . -528) 77433) ((-497 . -1115) T) ((-986 . -1133) T) ((-400 . -102) T) ((-336 . -102) T) ((-222 . -1115) T) ((-866 . -1249) T) ((-154 . -1081) T) ((-753 . -426) 77417) ((-119 . -23) T) ((-1035 . -928) 77369) ((-757 . -1133) T) ((-737 . -1133) T) ((-1289 . -668) 77279) ((-1280 . -668) 77161) ((-467 . -1133) T) ((-421 . -1249) T) ((-326 . -435) 77145) ((-606 . -93) T) ((-1059 . -633) 77106) ((-270 . -1249) T) ((-1056 . -1254) T) ((-229 . -102) T) ((-1059 . -632) 77068) ((-840 . -274) 77052) ((-840 . -234) 77036) ((-839 . -635) 76834) 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T) ((-896 . -321) 69641) ((-677 . -298) 69620) ((-657 . -1249) T) ((-114 . -684) T) ((-365 . -1249) T) ((-372 . -635) 69557) ((-367 . -635) 69494) ((-359 . -635) 69431) ((-77 . -1249) T) ((-108 . -635) 69381) ((-114 . -113) T) ((-1094 . -38) 69368) ((-686 . -387) 69347) ((-976 . -38) 69196) ((-753 . -1133) T) ((-495 . -38) 69045) ((-82 . -1249) T) ((-606 . -504) 69026) ((-1259 . -871) NIL) ((-1207 . -1133) T) ((-585 . -296) T) ((-1206 . -1133) T) ((-606 . -632) 68992) ((-1200 . -1133) T) ((-1152 . -875) T) ((-1111 . -1081) T) ((-365 . -1070) 68969) ((-841 . -504) 68953) ((-1036 . -1089) T) ((-45 . -632) 68935) ((-45 . -633) NIL) ((-944 . -1089) T) ((-841 . -632) 68904) ((-1180 . -102) 68854) ((-1111 . -250) 68805) ((-443 . -1089) T) ((-372 . -1081) T) ((-367 . -1081) T) ((-377 . -378) 68782) ((-359 . -1081) T) ((-357 . -236) 68769) ((-260 . -245) 68748) ((-259 . -245) 68727) ((-1111 . -240) 68652) ((-1158 . -1133) T) ((-305 . -928) 68611) ((-108 . -1081) T) ((-716 . -133) T) ((-419 . -528) 68453) ((-372 . -240) 68432) ((-372 . -250) T) ((-44 . -742) T) ((-367 . -240) 68411) ((-367 . -250) T) ((-359 . -240) 68390) ((-359 . -250) T) ((-1199 . -635) 68371) ((-171 . -321) 68336) ((-108 . -250) T) ((-108 . -240) T) ((-1026 . -635) 68317) ((-331 . -816) T) ((-894 . -21) T) ((-894 . -25) T) ((-421 . -319) T) ((-514 . -34) T) ((-110 . -300) 68292) ((-1145 . -1088) 68213) ((-896 . -1184) NIL) ((-342 . -632) 68195) ((-421 . -1052) 68173) ((-1145 . -111) 68089) ((-713 . -1295) T) ((-451 . -1133) T) ((-258 . -1133) T) ((-1324 . -748) T) ((-64 . -632) 68071) ((-896 . -38) 68016) ((-616 . -153) 68000) ((-537 . -1249) T) ((-524 . -632) 67940) ((-1268 . -321) 67927) ((-753 . -739) 67776) ((-545 . -817) T) ((-545 . -818) T) ((-560 . -660) 67758) ((-509 . -660) 67718) ((-518 . -1249) T) ((-659 . -1307) 67702) ((-368 . -466) T) ((-366 . -466) T) ((-358 . -466) T) ((-275 . -466) 67653) ((-539 . -1133) T) ((-534 . -1133) 67603) ((-255 . -466) 67554) ((-1183 . -298) 67533) ((-1211 . 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. -922) 60880) ((-988 . -321) 60818) ((-858 . -102) T) ((-443 . -739) 60802) ((-229 . -845) T) ((-852 . -102) T) ((-849 . -102) T) ((-1321 . -670) 60776) ((-1285 . -1284) 60755) ((-493 . -153) 60705) ((-1285 . -1278) 60675) ((-1152 . -1254) T) ((-352 . -1070) 60642) ((-1285 . -1282) 60626) ((-1268 . -930) 60533) ((-1264 . -1263) 60512) ((-80 . -632) 60494) ((-932 . -632) 60476) ((-1264 . -1278) 60453) ((-1152 . -571) T) ((-949 . -872) T) ((-793 . -872) T) ((-694 . -872) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1264 . -1261) 60308) ((-1286 . -1144) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1095 . -618) 60154) ((-842 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1318) 60048) ((-367 . -1318) 60032) ((-359 . -1318) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1081) 59973) ((-716 . -660) 59955) ((-1320 . -670) 59929) ((-131 . -321) NIL) ((-1286 . -23) T) 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-34) T) ((-606 . -1249) T) ((-565 . -34) T) ((-498 . -107) 18640) ((-260 . -300) 18617) ((-259 . -300) 18594) ((-1256 . -868) T) ((-896 . -298) 18545) ((-45 . -1249) T) ((-1242 . -930) 18526) ((-841 . -1249) T) ((-840 . -1081) T) ((-638 . -875) 18505) ((-674 . -668) 18474) ((-1211 . -47) 18450) ((-840 . -338) 18412) ((-1119 . -38) 18261) ((-840 . -240) 18240) ((-803 . -38) 18069) ((-802 . -38) 17918) ((-1148 . -504) 17899) ((-468 . -38) 17748) ((-1148 . -632) 17714) ((-1147 . -102) T) ((-663 . -633) 17675) ((-663 . -632) 17587) ((-595 . -1184) T) ((-532 . -1184) T) ((-1180 . -503) 17571) ((-357 . -1083) 17516) ((-1236 . -1133) 17494) ((-1174 . -25) T) ((-1174 . -21) T) ((-357 . -662) 17439) ((-1315 . -635) 17388) ((-342 . -1249) T) ((-488 . -1089) T) ((-1256 . -1133) T) ((-1259 . -816) NIL) ((-1259 . -821) NIL) ((-1028 . -872) 17367) ((-891 . -21) T) ((-862 . -1133) T) ((-843 . -632) 17349) ((-891 . -25) T) ((-822 . -748) T) ((-659 . -739) 17333) ((-177 . -1254) T) ((-595 . -38) 17298) ((-532 . -38) 17263) ((-400 . -632) 17245) ((-345 . -102) T) ((-336 . -632) 17227) ((-171 . -298) 17185) ((-1258 . -875) T) ((-64 . -1249) T) ((-114 . -102) T) ((-897 . -1133) T) ((-524 . -1249) T) ((-177 . -571) T) ((-736 . -739) 17155) ((-305 . -133) 17038) ((-229 . -632) 17020) ((-229 . -633) 16950) ((-1035 . -660) 16889) ((-1315 . -1081) T) ((-1211 . -1249) T) ((-1152 . -149) T) ((-651 . -1226) 16864) ((-753 . -940) 16843) ((-607 . -34) T) ((-669 . -107) 16827) ((-651 . -107) 16773) ((-625 . -1249) T) ((-624 . -1249) T) ((-622 . -1249) T) ((-1312 . -1249) T) ((-642 . -922) 16694) ((-1268 . -298) 16621) ((-753 . -670) 16510) ((-307 . -1249) T) ((-1211 . -1070) 16406) ((-973 . -637) 16383) ((-591 . -590) T) ((-591 . -541) T) ((-543 . -541) T) ((-119 . -922) NIL) ((-1200 . -940) NIL) ((-1094 . -633) 16298) ((-1094 . -632) 16280) ((-976 . -632) 16262) ((-735 . -504) 16212) ((-357 . -102) T) ((-260 . -1088) 16133) ((-259 . -1088) 16054) ((-407 . -102) T) ((-31 . -1133) T) ((-976 . -633) 15915) ((-735 . -632) 15850) ((-1313 . -1244) 15819) ((-495 . -632) 15801) ((-495 . -633) 15662) ((-275 . -426) 15646) ((-255 . -426) 15630) ((-325 . -239) NIL) ((-260 . -111) 15546) ((-259 . -111) 15462) ((-1257 . -684) T) ((-1207 . -670) 15387) ((-1206 . -670) 15284) ((-1200 . -670) 15136) ((-1158 . -670) 15061) ((-365 . -133) T) ((-83 . -455) T) ((-83 . -410) T) ((-1035 . -25) T) ((-1035 . -21) T) ((-898 . -1133) 15012) ((-40 . -1083) 14957) ((-897 . -739) 14909) ((-40 . -662) 14854) ((-391 . -302) T) ((-171 . -1034) 14805) ((-1119 . -930) 14704) ((-716 . -401) T) ((-1028 . -1030) 14688) ((-723 . -1144) T) ((-716 . -168) 14670) ((-803 . -930) 14577) ((-802 . -930) 14561) ((-1285 . -1133) T) ((-1264 . -1133) T) ((-1197 . -102) T) ((-326 . -1235) 14540) ((-326 . -1238) 14519) ((-468 . -930) 14496) ((-326 . -990) 14475) ((-136 . -1144) T) ((-118 . -1144) T) ((-1002 . -1249) T) ((-889 . -1249) T) ((-723 . -23) T) ((-677 . -1249) T) ((-616 . -1298) 14459) ((-616 . -1133) 14409) ((-545 . -875) T) ((-514 . -875) T) ((-326 . -95) 14388) ((-91 . -528) 14321) ((-177 . -376) T) ((-260 . -635) 14119) ((-259 . -635) 13917) ((-326 . -35) 13896) ((-627 . -503) 13830) ((-136 . -23) T) ((-118 . -23) T) ((-996 . -102) T) ((-740 . -1133) T) ((-489 . -503) 13767) ((-421 . -660) 13715) ((-677 . -1070) 13611) ((-988 . -503) 13595) ((-368 . -1089) T) ((-366 . -1089) T) ((-358 . -1089) T) ((-275 . -1089) T) ((-255 . -1089) T) ((-896 . -633) NIL) ((-896 . -632) 13577) ((-1311 . -504) 13558) ((-1310 . -504) 13539) ((-1323 . -21) T) ((-1311 . -632) 13505) ((-1310 . -632) 13471) ((-585 . -1034) T) ((-753 . -748) T) ((-1323 . -25) T) ((-260 . -1081) 13449) ((-259 . -1081) 13427) ((-72 . -1249) T) ((-1174 . -236) 13372) ((-260 . -240) 13324) ((-259 . -240) 13276) ((-1152 . -239) T) ((-40 . -102) T) ((-936 . -1089) T) ((-716 . -922) NIL) ((-1214 . -102) T) ((-131 . -503) 13258) ((-1207 . -748) T) ((-1206 . -748) T) ((-1200 . -748) T) ((-1200 . -814) NIL) ((-1200 . -818) NIL) ((-984 . -102) T) ((-949 . -102) T) ((-894 . -1083) 13245) ((-1158 . -748) T) ((-793 . -102) T) ((-694 . -102) T) ((-894 . -662) 13232) ((-561 . -632) 13214) ((-488 . -1133) T) ((-352 . -1144) T) ((-177 . -1144) T) ((-331 . -951) 13193) ((-1285 . -739) 13034) ((-897 . -175) T) ((-1264 . -739) 12848) ((-866 . -21) 12800) ((-866 . -25) 12752) ((-252 . -1182) 12736) ((-128 . -528) 12669) ((-421 . -25) T) ((-421 . -21) T) ((-352 . -23) T) ((-171 . -633) 12435) ((-171 . -632) 12417) ((-177 . -23) T) ((-663 . -300) 12394) ((-534 . -34) T) ((-636 . -684) T) ((-926 . -632) 12376) ((-89 . -1249) T) ((-865 . -632) 12358) ((-832 . -632) 12340) ((-791 . -632) 12322) ((-699 . -632) 12304) ((-246 . -670) 12137) ((-636 . -113) T) ((-1209 . -1133) T) ((-1203 . -1088) 11960) ((-217 . -1249) T) ((-1183 . -1249) T) ((-1157 . -1088) 11803) ((-879 . -1088) 11787) ((-1114 . -875) T) ((-1266 . -637) 11771) ((-1203 . -111) 11580) ((-1157 . -111) 11409) ((-879 . -111) 11388) ((-1257 . -872) T) ((-1268 . -633) NIL) ((-1268 . -632) 11370) ((-357 . -1184) T) ((-880 . -632) 11352) ((-1107 . -298) 11331) ((-1242 . -668) 11241) ((-80 . -1249) T) ((-932 . -1249) T) ((-1236 . -528) 11174) ((-1036 . -940) NIL) ((-1119 . -274) 11158) ((-627 . -298) 11134) ((-1119 . -234) 11118) ((-501 . -1249) T) ((-585 . -632) 11100) ((-489 . -298) 11079) ((-1036 . -670) 11029) ((-531 . -93) T) ((-1035 . -236) 10960) ((-221 . -1249) T) ((-988 . -298) 10912) ((-894 . -102) T) ((-301 . -951) T) ((-841 . -319) 10891) ((-803 . -274) 10875) ((-803 . -234) 10859) ((-944 . -670) 10811) ((-733 . -668) 10761) ((-716 . -746) 10728) ((-652 . -21) T) ((-652 . -25) T) ((-620 . -21) T) ((-562 . -102) T) ((-357 . -38) 10693) ((-501 . -910) 10675) ((-501 . -912) 10657) ((-488 . -739) 10498) ((-61 . -1249) T) ((-221 . -910) 10480) ((-221 . -912) 10462) ((-620 . -25) T) ((-443 . -670) 10436) ((-1203 . -635) 10205) ((-501 . -1070) 10165) ((-897 . -528) 10077) ((-1157 . -635) 9869) ((-879 . -635) 9787) ((-221 . -1070) 9747) ((-246 . -34) T) ((-1032 . -1133) 9725) ((-594 . -1083) 9712) ((-560 . -1083) 9699) ((-509 . -1083) 9664) ((-1285 . -175) 9595) ((-1264 . -175) 9526) ((-594 . -662) 9513) ((-560 . -662) 9500) ((-509 . -662) 9465) ((-734 . -147) 9444) ((-734 . -149) 9423) ((-130 . -875) T) ((-723 . -133) T) ((-564 . -1249) T) ((-137 . -479) 9400) ((-1180 . -632) 9332) ((-676 . -680) 9316) ((-131 . -298) 9266) ((-118 . -133) T) ((-491 . -1254) T) ((-627 . -618) 9242) ((-489 . -618) 9221) ((-611 . -1133) T) ((-346 . -349) 9190) ((-600 . -1133) T) ((-549 . -1133) T) ((-491 . -571) T) ((-1203 . -1081) T) ((-1157 . -1081) T) ((-879 . -1081) T) ((-848 . -1249) T) ((-246 . -818) 9169) ((-246 . -817) 9148) ((-1203 . -338) 9125) ((-246 . -748) 9103) ((-988 . -19) 9087) ((-501 . -390) 9069) ((-501 . -351) 9051) ((-1157 . -338) 9023) ((-353 . -1307) 9000) ((-221 . -390) 8982) ((-221 . -351) 8964) ((-988 . -618) 8941) ((-1203 . -240) T) ((-1296 . -1133) T) ((-1221 . -1133) T) ((-686 . -1133) T) ((-667 . -1133) T) ((-1119 . -262) 8878) ((-597 . -668) 8838) ((-368 . -1133) T) ((-366 . -1133) T) ((-358 . -1133) T) ((-275 . -1133) T) ((-255 . -1133) T) ((-85 . -1249) T) ((-218 . -102) T) ((-129 . -102) 8788) ((-123 . -102) 8738) ((-1264 . -528) 8598) ((-1221 . -629) 8577) ((-1173 . -1133) T) ((-1148 . -635) 8558) ((-1111 . -951) 8509) ((-493 . -1133) T) ((-1036 . -818) T) ((-1036 . -814) T) ((-493 . -629) 8488) ((-260 . -821) 8467) ((-260 . -816) 8446) ((-259 . -821) 8425) ((-40 . -1184) NIL) ((-259 . -816) 8404) ((-1036 . -748) T) ((-131 . -19) 8386) ((-1003 . -818) T) ((-721 . -1083) 8351) ((-944 . -748) T) ((-936 . -1133) T) ((-916 . -632) 8333) ((-131 . -618) 8308) ((-721 . -662) 8273) ((-91 . -503) 8257) ((-501 . -928) NIL) ((-897 . -302) T) ((-229 . -1088) 8222) ((-858 . -298) 8201) ((-221 . -928) NIL) ((-856 . -1144) 8180) ((-58 . -1133) 8130) ((-533 . -1133) 8108) ((-530 . -1133) 8058) ((-511 . -1133) 8036) ((-510 . -1133) 7986) ((-594 . -102) T) ((-560 . -102) T) ((-509 . -102) T) ((-488 . -175) 7917) ((-372 . -951) T) ((-367 . -951) T) ((-359 . -951) T) ((-229 . -111) 7873) ((-856 . -23) 7825) ((-443 . -748) T) ((-108 . -951) T) ((-40 . -38) 7770) ((-108 . -844) T) ((-595 . -363) T) ((-532 . -363) T) ((-676 . -668) 7729) ((-326 . -466) 7708) ((-325 . -466) T) ((-616 . -528) 7641) ((-421 . -236) 7586) ((-352 . -133) T) ((-177 . -133) T) ((-305 . -25) 7450) ((-305 . -21) 7333) ((-45 . -1226) 7312) ((-66 . -632) 7294) ((-55 . -102) T) ((-346 . -668) 7276) ((-1302 . -102) T) ((-1299 . -102) 7206) ((-1289 . -670) 7131) ((-1280 . -670) 7028) ((-45 . -107) 6978) ((-843 . -635) 6962) ((-1259 . -670) 6814) ((-1259 . -940) NIL) ((-1255 . -1249) T) ((-1231 . -632) 6796) ((-1223 . -102) T) ((-1129 . -440) 6780) ((-1129 . -381) 6759) ((-400 . -635) 6743) ((-336 . -635) 6727) ((-1128 . -93) T) ((-1119 . -668) 6637) ((-1095 . -1249) T) ((-1094 . -1088) 6624) ((-1094 . -111) 6609) ((-976 . -111) 6438) ((-976 . -1088) 6281) ((-803 . -668) 6191) ((-802 . -668) 6101) ((-686 . -739) 6085) ((-642 . -1083) 6072) ((-642 . -662) 6059) ((-563 . -875) T) ((-495 . -1088) 5902) ((-491 . -376) T) ((-475 . -668) 5858) ((-468 . -668) 5768) ((-229 . -635) 5718) ((-368 . -739) 5670) ((-366 . -739) 5622) ((-119 . -1083) 5567) ((-358 . -739) 5519) ((-275 . -739) 5368) ((-255 . -739) 5217) ((-1123 . -93) T) ((-1105 . -93) T) ((-119 . -662) 5162) ((-1098 . -93) T) ((-973 . -673) 5146) ((-1090 . -1133) 5124) ((-495 . -111) 4953) ((-1068 . -93) T) ((-1051 . -93) T) ((-973 . -385) 4937) ((-256 . -102) T) ((-986 . -47) 4916) ((-74 . -632) 4898) ((-734 . -239) T) ((-732 . -102) T) ((-721 . -102) T) ((-1 . -1133) T) ((-638 . -1144) T) ((-1120 . -632) 4880) ((-645 . -93) T) ((-1107 . -632) 4862) ((-936 . -739) 4827) ((-128 . -503) 4811) ((-497 . -93) T) ((-638 . -23) T) ((-404 . -23) T) ((-88 . -1249) T) ((-222 . -93) T) ((-627 . -632) 4793) ((-627 . -633) NIL) ((-489 . -633) NIL) ((-489 . -632) 4775) ((-365 . -25) T) ((-365 . -21) T) ((-50 . -668) 4734) ((-526 . -1133) T) ((-521 . -1133) T) ((-123 . -321) 4672) ((-129 . -321) 4610) ((-610 . -670) 4584) ((-609 . -670) 4509) ((-595 . -668) 4459) ((-229 . -1081) T) ((-532 . -668) 4389) ((-1094 . -635) 4361) ((-391 . -1034) T) ((-229 . -250) T) ((-229 . -240) T) ((-873 . -504) 4345) ((-1094 . -637) 4326) ((-988 . -633) 4287) ((-988 . -632) 4199) ((-976 . -635) 3988) ((-873 . -632) 3936) ((-894 . -38) 3923) ((-735 . -635) 3873) ((-1285 . -302) 3824) ((-1264 . -302) 3775) ((-495 . -635) 3560) ((-1152 . -466) T) ((-516 . -872) T) ((-326 . -1171) 3539) ((-1134 . -1249) T) ((-1028 . -149) 3518) ((-1028 . -147) 3497) ((-509 . -321) 3484) ((-1217 . -632) 3466) ((-307 . -1226) 3445) ((-1216 . -632) 3427) ((-1167 . -1249) T) ((-1215 . -632) 3409) ((-896 . -1088) 3354) ((-491 . -1144) T) ((-141 . -860) 3336) ((-115 . -860) 3317) ((-1236 . -503) 3301) ((-1094 . -1081) T) ((-642 . -102) T) ((-986 . -1249) T) ((-976 . -1081) T) ((-260 . -381) 3280) ((-259 . -381) 3259) ((-896 . -111) 3188) ((-307 . -107) 3138) ((-132 . -632) 3120) ((-131 . -633) NIL) ((-131 . -632) 3064) ((-119 . -102) T) ((-757 . -1249) T) ((-737 . -1249) T) ((-491 . -23) T) ((-467 . -1249) T) ((-495 . -1081) T) ((-1094 . -240) T) ((-976 . -338) 3033) ((-40 . -930) 2942) ((-495 . -338) 2899) ((-368 . -175) T) ((-366 . -175) T) ((-358 . -175) T) ((-275 . -175) 2810) ((-255 . -175) 2721) ((-986 . -1070) 2617) ((-531 . -504) 2598) ((-757 . -1070) 2569) ((-531 . -632) 2535) ((-419 . -1249) T) ((-1137 . -102) T) ((-1124 . -632) 2494) ((-1066 . -632) 2476) ((-716 . -1083) 2426) ((-1313 . -153) 2410) ((-1311 . -635) 2391) ((-1310 . -635) 2372) ((-1305 . -632) 2354) ((-1289 . -748) T) ((-716 . -662) 2304) ((-1280 . -748) T) ((-1259 . -814) NIL) ((-1259 . -818) NIL) ((-171 . -1088) 2214) ((-936 . -175) T) ((-896 . -635) 2144) ((-1259 . -748) T) ((-1035 . -355) 2118) ((-227 . -668) 2070) ((-1032 . -528) 2003) ((-866 . -872) 1982) ((-560 . -1184) T) ((-488 . -302) 1933) ((-610 . -748) T) ((-374 . -632) 1915) ((-334 . -632) 1897) ((-419 . -1070) 1793) ((-609 . -748) T) ((-421 . -872) 1744) ((-171 . -111) 1640) ((-856 . -133) 1592) ((-1299 . -321) 1530) ((-758 . -153) 1514) ((-994 . -875) 1413) ((-839 . -875) 1364) ((-501 . -319) T) ((-391 . -632) 1331) ((-534 . -1042) 1315) ((-391 . -633) 1229) ((-221 . -319) T) ((-143 . -153) 1211) ((-736 . -298) 1190) ((-501 . -1052) T) ((-594 . -38) 1177) ((-560 . -38) 1164) ((-509 . -38) 1129) ((-661 . -668) 1098) ((-221 . -1052) T) ((-896 . -1081) T) ((-858 . -632) 1080) ((-852 . -632) 1062) ((-849 . -632) 1044) ((-840 . -940) 1023) ((-1324 . -1144) T) ((-323 . -1249) T) ((-1268 . -1088) 846) ((-880 . -1088) 830) ((-896 . -250) T) ((-896 . -240) NIL) ((-711 . -1249) T) ((-1324 . -23) T) ((-840 . -670) 719) ((-565 . -1249) T) ((-419 . -351) 703) ((-585 . -1088) 690) ((-1268 . -111) 499) ((-723 . -660) 481) ((-880 . -111) 460) ((-395 . -23) T) ((-171 . -635) 238) ((-1221 . -528) 30) ((-901 . -1133) T) ((-703 . -1133) T) ((-698 . -1133) T) ((-674 . -1133) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 55712c75..d5d46f0c 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3508766235)            
-(4512 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3508838143)            
+(4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -290,7 +290,8 @@
  |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory|
  |Numeric| |NumberFormats| |NumericalIntegrationCategory|
  |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature|
- |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid|
+ |NumericTubePlot| |OrderedAbelianGroup&| |OrderedAbelianGroup|
+ |OrderedAbelianMonoid&| |OrderedAbelianMonoid|
  |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup|
  |OctonionCategory&| |OctonionCategory|
  |OrderedCancellationAbelianMonoid| |Octonion|
@@ -313,8 +314,8 @@
  |OperatorSignature| |NumericalOptimizationCategory|
  |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem|
  |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite|
- |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing|
- |OrderedSet| |OrderedStructure| |OrderedType&| |OrderedType|
+ |OrderingFunctions| |OrderedMonoid| |OrderedRing| |OrderedSet|
+ |OrderedStructure| |OrderedType&| |OrderedType|
  |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory|
  |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial|
  |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions|
@@ -488,676 +489,676 @@
  |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial|
  |YoungDiagram| |ParadoxicalCombinatorsForStreams|
  |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod|
- |Enumeration| |Mapping| |Record| |Union| |constantLeft| |mathieu22|
- |list| |parametersOf| |setchildren!| |revert| |tubePointsDefault|
- |swap| |whileLoop| |draw| |atanIfCan| |jacobi| |cyclicEqual?|
- |monomRDE| |leviCivitaSymbol| |horizontalTab| |flexible?| |rightTrace|
- |bright| |buildSyntax| |lazyIntegrate| |ocf2ocdf| |chebyshevU|
- |mapDown!| |tracePowMod| |irVar| |rightMinimalPolynomial| |f07adf|
- |iisin| |null| |laplace| |ptFunc| |iFTable| |euler| |Ci| |insert!|
- |startPolynomial| |stronglyReduce| |cAtan| |not| |iicoth| |cache|
- |acotIfCan| |untab| |interpretString| |taylorRep| |resize| |sinIfCan|
- |SturmHabichtCoefficients| |atrapezoidal| |and| |makeObject|
- |listOfLists| |host| |ddFact| |OMgetEndAttr| |cAtanh| |ParCond|
- |functorData| |cAsinh| |or| |primPartElseUnitCanonical!|
- |exprToGenUPS| |showTheRoutinesTable| |printHeader| |coef|
- |controlPanel| |wreath| |lfunc| |symmetricSquare| |distance| |xor|
- |decompose| |quasiComponent| |finiteBound| |write!| |nthr|
- |taylorQuoByVar| |legendre| |makeSketch| |laguerreL| |iterationVar|
- |case| |list?| |extension| |squareFreeLexTriangular| |categoryMode|
- |isAbsolutelyIrreducible?| |outlineRender| |supRittWu?| |empty|
- |e02akf| |mesh?| |expintfldpoly| |Zero| |homogeneous?| |testModulus|
- |rur| |monicModulo| |left| |lintgcd| |in?| |c05adf| |torsion?|
- |splitLinear| |over| |One| |isEquiv| |shift| |retractIfCan|
- |bernoulli| |mainDefiningPolynomial| |scripted?| |bag| |infinite?|
- |right| |coshIfCan| |size| |primes| |curve?| |reindex|
- |measure2Result| |splitSquarefree| |more?| |OMputEndError|
- |setEpilogue!| |selectfirst| |cardinality| |sumOfDivisors| |exprToUPS|
- |OMwrite| |concat!| |viewWriteAvailable| |insertBottom!| |aLinear|
- |lyndonIfCan| |mat| |aspFilename| |OMgetEndBind| |leadingBasisTerm|
- |listexp| |f01mcf| |mathieu11| |normalForm| |cdr| |distdfact| |f02ajf|
- |s17ajf| |tanhIfCan| |resetBadValues| |isTimes| |monomRDEsys|
- |underscore| |OMputAttr| |recoverAfterFail| |headReduce|
- |mapUnivariate| |OMputInteger| |LiePolyIfCan| |sayLength| |frobenius|
- |makeCos| |elt| |OMconnOutDevice| |primeFrobenius| |setlast!| |prem|
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- |signature| |someBasis| |makeSin| |gcdprim| |prime?| |scopes|
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- |intcompBasis| |ratPoly| |rarrow| |inverseIntegralMatrix| |curryRight|
- |conjugate| |basisOfRightNucleus| |po| |pomopo!| |f01maf| |matrixGcd|
- |sinhcosh| |complexRoots| |isAtom| |viewPhiDefault| |musserTrials|
- |dual| |jvmVolatile| |OMgetBind| |iiacot| |composite| |d02ejf| |node|
- |minset| |root?| |double?| |pushup| |Hausdorff| |jvmPublic| |zeroDim?|
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- |stirling2| |retractable?| |lex| |denominator| |singular?| |leftMult|
- |printStats!| |symbol| |eof?| |parts| |decomposeFunc| |eigenvalues|
- |mergeFactors| |viewDefaults| |d02raf| SEGMENT |algint| |returnTypeOf|
- |meshFun2Var| |expression| |minGbasis| |schema| |d01amf|
- |viewZoomDefault| |sncndn| |unknown| |badValues| |bandedHessian|
- |radicalSimplify| |exponents| |integer| |integral?| |implies| |f2df|
- |exprex| |s21bcf| |magnitude| |c06ebf| |internalInfRittWu?|
- |linearElement| |dn| |parametric?| |genericPosition|
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- |linearAssociatedOrder| |irreducibleFactor| |linearForm|
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- |iicsch| |setClosed| |addPointLast| |interReduce| |symbolTable|
- |dimensions| |cscIfCan| |stripCommentsAndBlanks| |midpoint|
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- |fractRagits| |physicalLength!| |mainKernel| |integer?| |elementary|
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- |deepExpand| |mainValue| |typeList| |closed?|
- |reducedContinuedFraction| |innerSolve| |s19abf| |insert| |nlde|
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- |mainCoefficients| |rootProduct| |elliptic| |jacobian| |totalLex|
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- |expressIdealMember| |algebraic?| |bit?| |besselI| |assert|
- |clearTheSymbolTable| |iilog| |continuedFraction| |iprint|
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- |solveLinearPolynomialEquationByFractions| |mainVariable|
- |numberOfHues| |f04asf| |isOp| |generalizedContinuumHypothesisAssumed|
- |tab| |thenBranch| |uniform01| |findConstructor| |countRealRoots|
- |explogs2trigs| |systemCommand| |readBytes!| |OMParseError?|
- |property| |e01saf| |gcdcofactprim| |OMsend| |mdeg| |cCos|
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- |tanh2trigh| |head| |argumentListOf| |iiacosh| |normal| |open|
- |OMgetAtp| |redmat| |imagi| |endSubProgram| |iidprod| |deleteRoutine!|
- |singleFactorBound| |clipWithRanges| |internalSubPolSet?| |nullity|
- |adjoint| |superHeight| |makeVariable| |oddlambert|
- |replaceKthElement| |tanAn| |zCoord| |integerBound| |generic|
- |atanhIfCan| |lazyPremWithDefault| |trace2PowMod| |epilogue|
- |shellSort| |arity| |listConjugateBases| |showTheFTable| |move|
- |graphStates| |invertIfCan| |setImagSteps| |hasSolution?|
- |totalDifferential| |partitions| |listYoungTableaus| |edf2fi|
- |solveid| |preprocess| |frst| |operations| |cRationalPower| |updatF|
- |iExquo| |createNormalElement| |karatsubaDivide| |eq| |compBound|
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- |dequeue!| |iter| |f02aef| |removeSinSq| |pastel| |cap| |fortranReal|
- |alphabetic?| |close| |getBadValues| |subPolSet?| |quatern| |refine|
- |noValueMode| |inR?| |collect| |tanIfCan| |pol| |asimpson|
- |numericalIntegration| |randnum| |possiblyInfinite?| |iitanh| |basis|
- |setScreenResolution3D| |radicalRoots| |one?| |roman| |traceMatrix|
- |positiveSolve| |iifact| |display| |var2Steps| |karatsuba| |e02bcf|
- |child| |belong?| |normalizedAssociate| |lexGroebner| |extractBottom!|
- |sequence| |matrixDimensions| |toseInvertible?| |parseString|
- |coth2tanh| |ignore?| |capacity| |leader| |divisors|
- |localIntegralBasis| |coHeight| |critT| |getGoodPrime| |lhs| |unary?|
- |jordanAdmissible?| |unaryFunction| |leftExtendedGcd| |iiacsc|
- |linear| |reduceBasisAtInfinity| |integralBasis| |asecIfCan|
- |rightUnits| |toseLastSubResultant| |rhs| |s17dhf| |quasiRegular?|
- |recur| |connectTo| |constantOpIfCan| |prime| |fortranComplex|
- |normalElement| |multiEuclideanTree| |exp| |point| |consnewpol|
- |OMgetString| |pleskenSplit| |palgRDE0| |subscriptedVariables| |arg1|
- |polynomial| LODO2FUN |iiacos| |rk4f| |lambda| |screenResolution|
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- |generalizedEigenvector| |arg2| |cyclotomic| |jvmLongConstantTag|
- |f02xef| |minimumExponent| |output| |extract!| |psolve|
- |zeroDimPrimary?| |charpol| |transcendent?| |OMconnInDevice|
- |fractionPart| |positive?| |test| |leadingCoefficientRicDE| |series|
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- |indiceSubResultantEuclidean| |factorial| |adaptive?|
- |semiIndiceSubResultantEuclidean| |ScanArabic| |superscript| |Beta|
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- |edf2efi| |linGenPos| |loadNativeModule| |asinhIfCan| |invertibleSet|
- |nonSingularModel| |characteristicSerie| |definingEquations|
- |LowTriBddDenomInv| |message| |closedCurve| |min| |s17dcf| |optional|
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- |cyclotomicFactorization| |pointColorPalette| |getOrder|
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- |setProperties| |genericLeftDiscriminant| |moduloP| |nextItem|
- |remove| |vspace| |newSubProgram| |setTex!| |powerAssociative?|
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- |complexElementary| |startTableInvSet!| |att2Result|
- |subQuasiComponent?| |e02bbf| |addPoint2| |fi2df| |elaborate|
- |exptMod| |categoryFrame| |last| |linearAssociatedLog|
- |topFortranOutputStack| |enterPointData| |brillhartIrreducible?|
- |leastPower| |readUInt16!| |assoc| |representationType| |mkPrim|
- |extractProperty| |halfExtendedSubResultantGcd2| |logical?| |exists?|
- |factorPolynomial| |invmod| |cAcot| |choosemon| |OMputEndAtp|
- |ip4Address| |initials| |makeSeries| |map| |reflect| |scale|
- |realEigenvectors| |semicolonSeparate| |e01baf| |iiasin| |coefChoose|
- |primitivePart| |resultant| |expr| |reducedQPowers| UTS2UP
- |tubeRadiusDefault| |stoseLastSubResultant| |squareFreePart| |diag|
- |symmetricProduct| |iisinh| |coordinates| |deepCopy| |e02zaf|
- |shufflein| |equiv| |OMputFloat| |chebyshevT| |leftOne| |lift| |label|
- |dec| |bubbleSort!| |imagJ| |readIfCan!| |parabolic|
- |binaryTournament| |iisech| |semiResultantEuclideannaif|
- |monicLeftDivide| |getOperator| |cAsin| BY |reduce| |condition|
- |createNormalPrimitivePoly| |numeric| |lp| |position!|
- |transcendentalDecompose| |d01apf| |sylvesterMatrix| |depth| |d01gaf|
- |argscript| |rules| |showRegion| |bernoulliB| |prefix| |radical|
- |cSin| |pmComplexintegrate| |mightHaveRoots| |hasPredicate?|
- |variable| |prindINFO| |imagk| |range| |curveColor| |poisson|
- |cotIfCan| |primitive?| |rightScalarTimes!| |bumprow| |iterators|
- |nextsousResultant2| |prefixRagits| |fglmIfCan| |cycleLength|
- |setOfMinN| |realEigenvalues| |meatAxe| |open?| |e02agf|
- |bipolarCylindrical| |simpleBounds?| |functionIsOscillatory|
- |rightOne| |optAttributes| |OMsupportsSymbol?|
- |exprHasWeightCosWXorSinWX| |d03faf| |setPosition|
- |genericRightMinimalPolynomial| |numerator| |f04atf| |janko2| |repSq|
- |screenResolution3D| |outputFixed| |paraboloidal| |shuffle|
- |setMaxPoints| |next| |selectIntegrationRoutines| |tab1|
- |leftExactQuotient| |moreAlgebraic?| |ode| |option| |rightExtendedGcd|
- |tanQ| |triangulate| |acosIfCan| NOT |sup| |OMencodingBinary| |tube|
- |radicalEigenvector| |exponential1| |lprop| |read!| |OMgetFloat|
- |center| |low| |edf2ef| OR |printCode| |setColumn!| |lifting1|
- |moduleSum| |listLoops| |multiEuclidean| |primlimitedint| |orbit|
- |update| |reverseLex| |sub| AND |components| |radPoly| |removeZero|
- |leftReducedSystem| |explicitlyEmpty?| |pushuconst| |leftDivide|
- |d03eef| |setEmpty!| |hconcat| |basisOfCenter| |writeBytes!|
- |acoshIfCan| |e01daf| |f01rcf| |predicates|
- |zeroSetSplitIntoTriangularSystems| |rational?| |viewPosDefault|
- |cCot| |oddInfiniteProduct| |diagonals| |infieldIntegrate|
- |createGenericMatrix| |invmultisect| |delete!| |byteBuffer|
- |ramified?| |shade| |factorSFBRlcUnit| |returnType!| |setright!|
- |subNode?| |yellow| |interpolate| |getConstant| |prevPrime|
- |roughBase?| |rem| |iipow| |roughUnitIdeal?| |knownInfBasis|
- |conditionsForIdempotents| |byte| |finiteBasis| |headAst| |mantissa|
- |lazyPquo| |order| |quasiAlgebraicSet| |quo| |zeroDimensional?|
- |conjunction| |simplifyPower| |genericRightNorm| |overbar|
- |linearPart| |iiacsch| RF2UTS |ridHack1| |totalfract| |zoom|
- |elaborateFile| |diagonal?| |subTriSet?| |generators| |hyperelliptic|
- |resultantEuclidean| |countable?| |div| |substitute| |abelianGroup|
- |rroot| |coefficients| |createZechTable| |orthonormalBasis| |sorted?|
- |addBadValue| |partialNumerators| |exquo| |bringDown|
- |lazyIrreducibleFactors| |inrootof| |crest| |SturmHabichtMultiple|
- |qqq| |sdf2lst| |nthCoef| |raisePolynomial| * ~= |doublyTransitive?|
- |rk4qc| |operators| |FormatRoman| |qroot| |polygon| |integralMatrix|
- |lineColorDefault| |chainSubResultants| |sin2csc| |#| |makeEq|
- |sts2stst| |mapGen| |cschIfCan| |ode2| |binomThmExpt| |e01bef|
- |function| |stFunc2| |qPot| |primlimintfrac| ~ |iidsum| |e01sbf|
- |rotatey| |fullDisplay| |airyAi| |int| |sizePascalTriangle|
- |outputAsScript| |squareFree| |certainlySubVariety?| |dimension| =
- |leadingSupport| |leftRemainder| |rationalPoints| |OMencodingXML|
- |linearDependence| FG2F |reducedSystem| |isAnd| |meshPar2Var| |f04adf|
- |phiCoord| |lieAdmissible?| |jvmDoubleConstantTag| |iiabs|
- |constantKernel| |deleteProperty!| |showIntensityFunctions| |s15aef|
- |/\\| < |problemPoints| |symmetricDifference| |eulerPhi| |integral|
- |OMputEndApp| |times!| |OMputBVar| |laguerre| |queue| |\\/| >
- |hexDigit| |orbits| |perfectNthRoot| |typeLists| |linearAssociatedExp|
- |generalInfiniteProduct| |useNagFunctions| |super| |flagFactor|
- |monicRightFactorIfCan| |initTable!| <= |unitVector|
- |commonDenominator| |basisOfLeftAnnihilator|
- |inverseIntegralMatrixAtInfinity| |algSplitSimple| |infix| |number?|
- |deepestTail| |setStatus!| |OMunhandledSymbol| >= |groebnerFactorize|
- |f04mcf| |genericRightTrace| |pop!| |perfectSquare?| |content|
- |combineFeatureCompatibility| |badNum| |prinb| |resetAttributeButtons|
- |alternating| |normalized?| |particularSolution| |tablePow|
- |readInt8!| |s18aef| |weakBiRank| |cons| |inv|
- |primPartElseUnitCanonical| |mapSolve| |subresultantVector| |vark|
- |abs| |declare| |setDifference| |nsqfree| |OMUnknownCD?| |ground?| +
- |fortranInteger| |numberOfVariables| |minus!| |lazyPseudoRemainder|
- |cyclicSubmodule| |s18aff| |ravel| |goto| |upperCase| |lowerCase?|
- |discreteLog| |ground| - |flatten| |s13aaf| |isExpt| |bounds|
- |generic?| |rombergo| |lcm| |cLog| |reshape| /
- |getSyntaxFormsFromFile| |hdmpToP| |leadingMonomial| |cAcosh|
- |mainForm| |s17dlf| |alphabetic| |totalGroebner| |vector| |viewpoint|
- |drawCurves| |iiexp| |leftTrace| |leadingCoefficient| |cup|
- |viewport3D| |coefficient| |rightTraceMatrix|
- |factorSquareFreePolynomial| |nextSubsetGray| |differentiate| |append|
- |mix| |maximumExponent| |source| |primitiveMonomials| |cyclicParents|
- |isobaric?| |numberOfComponents| |create3Space| |sqfrFactor|
- |wordInGenerators| |check| |gcd| |var1StepsDefault| |front|
- |pointColorDefault| |reductum| |ffactor| |getButtonValue|
- |quadraticNorm| |augment| |false| |ran| |set| |commaSeparate|
- |quoByVar| |checkForZero| |rewriteIdealWithRemainder| |eigenvectors|
- |factorsOfDegree| |maxrank| |subResultantGcd| |OMencodingUnknown|
- |target| |partialQuotients| |safeCeiling| |subtractIfCan|
- |nextLatticePermutation| |exponentialOrder| |space| |bigEndian|
- |ListOfTerms| |basisOfCommutingElements| |select!| |reduced?|
- |permutation| |ReduceOrder| |linear?| |explicitEntries?| |mkcomm|
- |f01qdf| |eigenvector| |areEquivalent?| |drawComplexVectorField|
- |stFunc1| |Frobenius| |isOpen?| |innerSolve1| |fixedPoints| |ideal|
- |intermediateResultsIF| |component| |table| |approxSqrt|
- |outerProduct| |square?| |printInfo| |OMputObject| |UP2ifCan|
- |resultantnaif| |setIntersection| |predicate| |rational| |new|
- |addMatchRestricted| |position| |clearTable!| |digit| |gramschmidt|
- |has?| |domainTemplate| |coerce| |inputOutputBinaryFile|
- |numberOfMonomials| |dimensionsOf| |pdf2ef| |branchPoint?| |solid|
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- |redpps| |dominantTerm| |internal?| |void| |appendPoint| |An| |zag|
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- |makingStats?| |subSet| |duplicates?| |stopTableGcd!| |meshPar1Var|
- |third| |jvmMethodrefConstantTag| |jacobiIdentity?| |sturmSequence|
- |listRepresentation| |symmetricGroup| |readLineIfCan!| |makeMulti|
- |computePowers| |firstUncouplingMatrix| |goodnessOfFit| |zero|
- |singRicDE| |removeRedundantFactorsInPols| |removeSquaresIfCan|
- |solveRetract| |userOrdered?| |OMsetEncoding| |rootOfIrreduciblePoly|
- |pushNewContour| |inHallBasis?| |unitNormalize| |node?| |localReal?|
- |nextPartition| |pseudoRemainder| |currentSubProgram| |outputSpacing|
- |lookup| |atoms| |And| |comment| |bitLength| |OMcloseConn|
- |fortranLogical| |prinshINFO|
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- |selectsecond| |contours| |shape| |coth2trigh| |bezoutDiscriminant|
- |BasicMethod| |palglimint0| |complexEigenvectors| |unitsColorDefault|
- |Not| |equality| |lieAlgebra?| |d02kef| |infRittWu?| |cycleElt|
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- |tryFunctionalDecomposition| |nthRoot| |prod| |failed| |match?|
- |every?| |nextSublist| |nand| |infiniteProduct| |subResultantsChain|
- |cAcsc| |OMputApp| |extend| |limitPlus| |minimize| |exQuo| |pointData|
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- |usingTable?| |setelt| |leftRankPolynomial| |yCoord| |negative?| |sin|
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- |ScanFloatIgnoreSpacesIfCan| |nonLinearPart| |error|
- |rightDiscriminant| |fortranDouble| |s18adf| |outputArgs| |cos|
- |rootSimp| |coerceP| |hostPlatform| |errorKind| |real?| |max| |c06gqf|
- |numberOfOperations| |copy| |cSech| |rowEchelon| |cyclePartition|
- |tan| |rootKerSimp| |physicalLength| |complexEigenvalues| |palgint|
- |complexLimit| |definingPolynomial| |numerators| |block| |pointColor|
- |wrregime| |numberOfPrimitivePoly| |cot| |Nul| |primintegrate|
- |cyclicEntries| |ratDsolve| |permanent| |binomial| |showTheIFTable|
- |autoCoerce| |FormatArabic| |sinhIfCan| |comparison| |sec|
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- |expPot| |build| |genericLeftTraceForm| |indicialEquationAtInfinity|
- |generalPosition| |csc| |leftUnits| |univcase| |iiatan| |c06gbf|
- |leftQuotient| |top| |companionBlocks| |minimalPolynomial| |polCase|
- |f02akf| |asin| |normDeriv2| |pushdown| |coerceListOfPairs| |se2rfi|
- |firstDenom| |continue| |graphState| |getMultiplicationTable|
- |OMputBind| |createRandomElement| |acos| |boundOfCauchy| |upperCase!|
- |mkIntegral| |trapezoidalo| |seed| |basisOfCentroid|
- |splitDenominator| |quasiRegular| |t| |member?| |atan|
- |jvmStringConstantTag| |makeResult| |rootDirectory| |algDsolve|
- |getMatch| |mapExpon| |eval| |verticalTab| |rootSplit| |module|
- |PollardSmallFactor| |acot| |ranges| |expt| |pointSizeDefault|
- |writeByte!| |green| |rightFactorCandidate| |multMonom| |denomLODE|
- |removeDuplicates!| |init| |jvmProtected| |asec| |polyRDE| |sin?|
- |imagj| |hspace| |tan2cot| |printingInfo?| |f07aef|
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- |permutationRepresentation| |associatorDependence| |interpret| |plus!|
- |presuper| |functionIsFracPolynomial?| |xn| |df2fi| |push!| |split!|
- |colorDef| |removeRoughlyRedundantFactorsInContents|
- |initiallyReduced?| |Lazard2| |symbolTableOf| |seriesToOutputForm|
- |semiResultantEuclidean1| |copyInto!| |numFunEvals| |binarySearchTree|
- |diophantineSystem| |dimensionOfIrreducibleRepresentation|
- |roughSubIdeal?| |bivariatePolynomials| |separant| |removeDuplicates|
- |viewport2D| |extractClosed| |nthFactor| |macroExpand| |d01asf|
- |polygon?| |ldf2lst| |support| |skewSFunction| |outputFloating|
- |drawToScale| |exactQuotient!| |trigs| |lepol| |children|
- |separateDegrees| |regularRepresentation| |duplicates| |tValues|
- |subResultantChain| |rewriteSetWithReduction| |OMgetSymbol| |nil|
- |iitan| |e01bff| |newReduc| |halfExtendedSubResultantGcd1|
- |categories| |string?| |jvmFieldrefConstantTag| |OMopenString| |cCsc|
- |lighting| |Vectorise| |fortranTypeOf|
- |functionIsContinuousAtEndPoints| |genericRightDiscriminant|
- |rightUnit| |stoseInvertibleSetreg| |scanOneDimSubspaces|
- |expenseOfEvaluationIF| |antiCommutator| |errorInfo| |s18acf|
- |alphanumeric?| |level| |minIndex| |s14aaf| |lifting|
- |normInvertible?| |cycleTail| |setScreenResolution| |rightRemainder|
- |lastSubResultant| |enumerate| |approximate| |nary?| |subst| |closed|
- |normFactors| |modularGcd| |numericIfCan| |OMgetError|
- |linearDependenceOverZ| |e01bhf| |structuralConstants| |d02cjf|
- |complex| |seriesSolve| |leadingTerm| |internalZeroSetSplit| |f01rdf|
- |OMputAtp| |traverse| |fixedPointExquo| |high| |removeCosSq| |f04jgf|
- |dom| |basisOfRightAnnihilator| |reopen!|
- |rewriteIdealWithHeadRemainder| |outputAsTex| |ScanFloatIgnoreSpaces|
- |rangePascalTriangle| |lllip| |OMputEndBVar| |obj| |putProperties|
- |trailingCoefficient| |gbasis| |dmpToP| |powers| |acsch| |drawStyle|
- |OMgetType| |divideExponents| |palginfieldint| |objects|
- |insertionSort!| |expandTrigProducts| |multiple?| |blue|
- |splitConstant| |localUnquote| |cn| |addiag| |d01aqf| |op| |base|
- |mathieu24| |parent| |limitedint| |s17ahf| |chiSquare1|
- |bezoutResultant| |tubePoints| |leftUnit| |uniform| |findCycle|
- |computeBasis| |polynomialZeros| |tan2trig| |hasHi|
- |indicialEquations| |mainCharacterization| |powerSum| |represents|
- |leastMonomial| |f02wef| |iomode| |OMconnectTCP| |nextPrime| |moebius|
- |scalarMatrix| |complexSolve| |withPredicates| |autoReduced?|
- |semiSubResultantGcdEuclidean2| |linearMatrix| |separate| |setleft!|
- |trigs2explogs| |viewThetaDefault| |algebraicOf| |cosh2sech|
- |ellipticCylindrical| |carriageReturn| |palgintegrate| |digits|
- |doubleComplex?| |symmetricRemainder| |algebraicCoefficients?|
- |monomialIntegrate| |f02fjf| |createPrimitivePoly| |optimize|
- |modularGcdPrimitive| |plotPolar| |indicialEquation| |subNodeOf?|
- |reciprocalPolynomial| |exprHasLogarithmicWeights| |latex|
- |rewriteIdealWithQuasiMonicGenerators| |nthFractionalTerm|
- |subResultantGcdEuclidean| |hMonic| |conjugates| |henselFact|
- |retract| |odd?| |unvectorise| |var2StepsDefault| |bindings|
- |genericRightTraceForm| |closedCurve?| |nthExpon| |getMeasure| |scan|
- |child?| |size?| |lazyPseudoQuotient| |prolateSpheroidal| |polyRicDE|
- |integrate| |encodingDirectory| |stoseInternalLastSubResultant|
- |mindegTerm| |iflist2Result| |countRealRootsMultiple| |constDsolve|
- |coercePreimagesImages| |halfExtendedResultant1| |LyndonWordsList|
- |jvmInterface| |partialFraction| |OMgetObject| |previous|
- |patternMatch| |axes| |rightZero| |selectMultiDimensionalRoutines|
- |signatureAst| |elRow2!| |reorder| |asinIfCan| |sn|
- |nextPrimitiveNormalPoly| |divide| |removeRedundantFactors| |maxrow|
- |crushedSet| |cosIfCan| |modulus| |generalSqFr| |factorList|
- |asechIfCan| |merge!| |simplifyLog| |copies|
- |setLegalFortranSourceExtensions| |prinpolINFO| |innerEigenvectors|
- |anfactor| |e02def| |lowerCase| |forLoop| |leadingIdeal|
- |integralAtInfinity?| |isImplies| |setLabelValue| |assign| |sort!|
- |expextendedint| |e02adf| |cSinh| |leftFactor| |c06gsf| |solveInField|
- |beauzamyBound| |geometric| |OMgetVariable| |reducedDiscriminant|
- |showAll?| |lfintegrate| |var1Steps| |reseed| |nextColeman| |points|
- |palgextint| |normalize| |norm| |hash| |reify| |complementaryBasis|
- |leastAffineMultiple| |basisOfMiddleNucleus| |medialSet| |variable?|
- |connect| |tubeRadius| |pToHdmp| |oblateSpheroidal| |count| |corrPoly|
- |randomR| |resultantReduitEuclidean| |stoseIntegralLastSubResultant|
- |entries| |category| |irCtor| |OMbindTCP| |resetVariableOrder|
- |factorAndSplit| |mappingAst| |rightNorm| |factorset| |currentScope|
- |rootPoly| |float?| |realElementary| |cylindrical| |domain| |mindeg|
- |writeUInt8!| |besselY| |mvar| |lambert| |element?| |setVariableOrder|
- |rotate| |generator| |lowerCase!| |readUInt8!| |package| |minrank|
- |firstSubsetGray| |fixPredicate| |systemSizeIF| |validExponential|
- |charthRoot| |fortranCharacter| |palgextint0| |s17dgf| |headReduced?|
- |coord| |char| |algintegrate| |quickSort| |even?| |maxint| |bsolve|
- |prefix?| |besselK| |rightTrim| |writeLine!| |localAbs| |getCurve|
- |properties| |accuracyIF| |outputBinaryFile| |cAcoth| |rischDE|
- |central?| |getDatabase| |purelyAlgebraic?| |maxIndex|
- |identification| |leftTrim| |f02agf| |f02bjf| |trapezoidal|
- |translate| |imports| |aromberg| |stoseSquareFreePart| |deriv|
- |subCase?| |mpsode| |zerosOf| |tower| |fortranCarriageReturn|
- |leftGcd| |s14abf| |clearDenominator| |debug3D| |acothIfCan| |cyclic|
- |pushucoef| |overlabel| |bivariateSLPEBR| |multiplyCoefficients|
- |rightPower| |c06fpf| |setStatus| |f07fdf|
- |factorSquareFreeByRecursion| |perfectSqrt| |setPoly|
- |integralDerivationMatrix| |simpson| |addmod| |part?| |rst| |float|
- |degreeSubResultant| |mainVariable?| |mathieu12| |generalLambert|
- |imagK| |closeComponent| |qualifier| |showScalarValues|
- |createThreeSpace| |signAround| |pile| |commutativeEquality|
- |numberOfImproperPartitions| |OMgetApp| |baseRDE| |makeFloatFunction|
- |rowEchelonLocal| |createPrimitiveNormalPoly| |numberOfChildren|
- |basisOfLeftNucloid| |d01gbf| |infix?| |directSum| |hexDigit?| |cycle|
- |colorFunction| |f04mbf| |patternVariable| |infLex?| |readByte!|
- |topPredicate| |OMsupportsCD?| |expIfCan| |mask| |units| |matrix|
- |divisorCascade| |logpart| |s20acf| |minordet| |numericalOptimization|
- |decrease| |weights| |ef2edf| |gcdPolynomial| |idealSimplify| |radix|
- |biRank| |lookupFunction| |complexNumeric| |totalDegree| |swap!|
- |incr| |pointLists| |numFunEvals3D| |summation| |lazy?|
- |primextintfrac| |f01ref| |returns| |hessian| |sturmVariationsOf| |hi|
- |overset?| |lexico| |startTable!| |iteratedInitials| |fmecg|
- |euclideanSize| |vectorise| |kernels| |gcdcofact| |infieldint|
- |vconcat| |subset?| |find| |useEisensteinCriterion|
- |invertibleElseSplit?| |changeWeightLevel| |rightAlternative?|
- |viewDeltaXDefault| |evaluateInverse| |sort| |smith| |operator|
- |regime| |csc2sin| |identity| |derivative| |iiasec| |keys|
- |trivialIdeal?| |birth| |OMlistCDs| GE |code| |associative?|
- |univariate| |airyBi| |OMgetEndError| |null?| |extendedEuclidean|
- |options| |clip| |voidMode| |rationalFunction| |modifyPointData|
- |trunc| GT |constructor| |random| |pmintegrate| |cAsech| |subHeight|
- |sample| |associatedSystem| |lSpaceBasis| |setFieldInfo| |fixedPoint|
- |s20adf| |coordinate| LE |kovacic| |cyclicGroup| |tubePlot| |unexpand|
- |monic?| |string| |exprHasAlgebraicWeight| |c06ecf| |ldf2vmf|
- |stoseInvertible?| |c06fuf| LT |squareFreePolynomial| |torsionIfCan|
- |factor| |divergence| |linearlyDependentOverZ?| |slash|
- |rootNormalize| |qelt| |OMputString| |stoseInvertible?reg|
- |collectQuasiMonic| |gethi| |definingInequation| |changeNameToObjf|
- |removeRoughlyRedundantFactorsInPols| |sqrt| |antiAssociative?|
- |stoseInvertibleSetsqfreg| |operation| |region| |qsetelt|
- |euclideanNormalForm| |randomLC| |rotate!| |cfirst|
- |fortranDoubleComplex| |HenselLift| |environment|
- |unrankImproperPartitions1| |real| |linkToFortran|
- |algebraicDecompose| |characteristic| |xRange| |perspective| |polar|
- |outputMeasure| |monicRightDivide| |tableau| |unparse| |nonQsign|
- |mapMatrixIfCan| |pToDmp| |imag| |expintegrate| |wholePart|
- |denominators| |approxNthRoot| |yRange| |delete| |back| |univariate?|
- |exactQuotient| |halfExtendedResultant2| |cyclicCopy| |directProduct|
- |identityMatrix| |pow| |packageCall| |e04jaf| |bitTruth| |zRange|
- |rightMult| |identitySquareMatrix| |sizeMultiplication|
- |numberOfNormalPoly| |purelyTranscendental?| |cubic| |d01anf| |d01bbf|
- |polyred| |secIfCan| |c02aff| |map!| |insertTop!| |tree| |nthFlag|
- |whitePoint| |makeViewport2D| |showClipRegion| |rename| |brace|
- |removeSinhSq| |realZeros| |readLine!| |littleEndian| |qsetelt!|
- |jvmUTF8ConstantTag| |isMult| |midpoints| |backspace|
- |monomialIntPoly| |vertConcat| |ParCondList| |destruct| |rspace|
- |normal01| |maxPoints3D| |isQuotient| |changeVar| |algebraicVariables|
- |jvmFinal| |semiLastSubResultantEuclidean| |sum| |lowerBound| |dot|
- |zeroSquareMatrix| |squareMatrix| |conditionP| |jvmIntegerConstantTag|
- |e01sff| |symbol?| |variationOfParameters| |stopMusserTrials|
- |firstNumer| |printStatement| |LazardQuotient2| |jvmStatic|
- |squareFreePrim| |top!| |setButtonValue| |leftAlternative?| |overlap|
- |zeroSetSplit| |polarCoordinates| |complexNumericIfCan| |call|
- |calcRanges| |normalise| |backOldPos| |defineProperty| |realRoots|
- |nullary?| |edf2df| |internalAugment| |setPrologue!| |leftTraceMatrix|
- |generate| |froot| |branchIfCan| |kmax|
- |initializeGroupForWordProblem| |monomial| |fprindINFO|
- |setTopPredicate| |pascalTriangle| |linears| |surface| |swapColumns!|
- |d01akf| |createMultiplicationTable| |alternatingGroup| |quadratic?|
- |jvmClassConstantTag| |triangular?| |multivariate| |leftFactorIfCan|
- |rquo| |mainPrimitivePart| |incrementBy| |intChoose| |height|
- |monomials| |standardBasisOfCyclicSubmodule| |stoseInvertibleSet|
- |completeHensel| |principalIdeal| |writable?| |factor1| |id|
- |sequences| |variables| |lfextlimint| |factorSquareFree| |trim|
- |useSingleFactorBound| |bothWays| |expand| |processTemplate|
- |mappingMode| |nothing| |elseBranch| |lo| |light| |lazyResidueClass|
- |makeprod| |lagrange| |atom?| |integralMatrixAtInfinity| |interval|
- |filterWhile| |externalList| |cot2trig| |compile| |compactFraction|
- |step| |trueEqual| |fibonacci| |balancedFactorisation|
- |supDimElseRittWu?| |rowEchLocal| |sumOfSquares| |f02abf|
- |diagonalMatrix| |filterUntil| |transcendenceDegree| |tRange|
- |nthRootIfCan| |tanh| |critpOrder| |mainMonomials| |double|
- |symmetricTensors| |stack| |bat1| |stoseInvertible?sqfreg| |log10|
- |mulmod| |rightRecip| |acschIfCan| |select| |viewSizeDefault| |copy!|
- |c02agf| |coth| |fractRadix| |LagrangeInterpolation|
- |resultantEuclideannaif| |f04faf| |aCubic| |probablyZeroDim?|
- |normal?| |compdegd| |finite?| |bitand| |inverseColeman|
- |discriminant| |sech| |createMultiplicationMatrix|
- |tableForDiscreteLogarithm| |zero?| |taylor| |schwerpunkt|
- |OMreadFile| |showSummary| |sincos| |s01eaf| |fortranCompilerName|
- |bitior| |rootsOf| |singularAtInfinity?| |csch| |parabolicCylindrical|
- |minPoints3D| |selectSumOfSquaresRoutines| |laurent| |coerceImages|
- |showAllElements| |separateFactors| |generalTwoFactor| |putGraph|
- |groebgen| |setMinPoints| |asinh| |innerint| |setprevious!| |puiseux|
- |newLine| |getCode| |showAttributes| |numberOfFractionalTerms|
- |binding| |viewDeltaYDefault| |optional?| |deref| |acosh| |tanNa|
- |stronglyReduced?| |integerIfCan| |headRemainder| |linearPolynomials|
- |groebner?| |quasiMonic?| |updatD| |delay| |atanh| |gradient|
- |RittWuCompare| |jvmAbstract| |makeRecord| |d02gbf|
- |semiDegreeSubResultantEuclidean| |eisensteinIrreducible?|
- |inRadical?| |Aleph| |acoth| |OMclose| |omError| |declare!| |escape|
- |compiledFunction| |Lazard| |e02aef| |changeMeasure| |readInt16!|
- |pair?| |s13acf| |asech| |pureLex| |UpTriBddDenomInv| |typeForm|
- |bits| |incrementKthElement| |extensionDegree| |dihedralGroup|
- |selectODEIVPRoutines| |addPoint| |slex| |setRealSteps| |figureUnits|
- |rk4a| |OMputEndAttr| |delta| |lllp| |internalIntegrate0| |coleman|
- |formula| |unknownEndian| |degreePartition| |multiple| |contract|
- |constantCoefficientRicDE| |contains?| |padicallyExpand| |diagonal|
- |constant| |setCondition!| |leftLcm| |getOperands|
- |branchPointAtInfinity?| |minColIndex| |applyQuote| |heapSort|
- |submod| |tail| |Ei| |expandLog| |toseInvertibleSet| |tanSum|
- |ratpart| |llprop| |distribute| |Si| |associatedEquations|
- |relativeApprox| |credPol| |invertible?| |option?| |fixedDivisor|
- |makeTerm| |setfirst!| |initial| |npcoef| |OMencodingSGML| |style|
- |e02bdf| |lazyGintegrate| |droot| |extendedint| |f01bsf| |pquo|
- |normalDenom| |nrows| |OMserve| |substring?| |f02axf| |ruleset|
- |unmakeSUP| |fortran| |solveLinearPolynomialEquation| |segment|
- |clearTheIFTable| |conjug| |selectOrPolynomials| |digamma| |ncols|
- |coerceS| |primitivePart!| |neglist| |d02bbf| |getProperties|
- |ricDsolve| |interactiveEnv| |clearTheFTable| |apply| |clipBoolean|
- |e02ahf| |polyPart| |s17akf| |suffix?| |readable?| |whatInfinity|
- |optpair| |Is| Y |digit?| |irDef| |point?| |first| |rank|
- |maxRowIndex| |varList| |noncommutativeJordanAlgebra?| |suchThat|
- |e02bef| |split| |elColumn2!| |reduceLODE| |sPol| |mesh| |rest|
- |leftRank| |flexibleArray| |brillhartTrials| |shallowExpand| |ipow|
- |palgLODE| |lyndon| |complex?| |unprotectedRemoveRedundantFactors|
- |LyndonCoordinates| |rangeIsFinite| |key| |f02aff| |minPoints|
- |multiset| |tensorProduct| |increment| |solve| |ode1| |leftRecip|
- |setOrder| |wordsForStrongGenerators| |attributeData| |df2ef|
- |primaryDecomp| |LiePoly| |middle| |normalDeriv| |normalizedDivide|
- |increase| |f02adf| |filename| |monicCompleteDecompose| |associates?|
- |OMreadStr| |commutative?| |constantIfCan| |binaryTree| |f02aaf|
- |bipolar| |pack!| |complement| |binary| |csch2sinh| |e04ucf|
- |OMReadError?| |ksec| |addMatch| |dequeue| |lazyPseudoDivide|
- |useSingleFactorBound?| |postfix| |OMgetInteger| |before?|
- |computeCycleEntry| |parse| |iicos| |B1solve| |quoted?| |pade|
- |relationsIdeal| |empty?| |minPoly| |leftRegularRepresentation|
- |ScanRoman| |logGamma| |unit?| |dark| |lists|
- |internalLastSubResultant| |fullPartialFraction| |fTable| |legendreP|
- |is?| |exponent| |selectPDERoutines| |monicDivide| |rischNormalize|
- |rewriteSetByReducingWithParticularGenerators| |KrullNumber| |makeFR|
- |compose| |OMgetEndApp| |getZechTable| |htrigs| |decimal|
- |radicalSolve| |ord| |input| |transpose| |curve| |karatsubaOnce|
- |integralBasisAtInfinity| |GospersMethod| |internalDecompose|
- |jvmStrict| |c06eaf| |script| |showArrayValues| |status|
- |jvmTransient| |library| |unravel| |extendedIntegrate| |plus|
- |collectUnder| |rationalPoint?| |graphs| |mkAnswer| |rCoord|
- |getVariableOrder| |jvmNative| |PDESolve| |fortranLinkerArgs| |df2st|
- |upDateBranches| |weierstrass| |character?| |rowEch|
- |changeThreshhold| |singularitiesOf| |iCompose| |value| |compound?|
- |BumInSepFFE| |isPlus| |curryLeft| |newline| |jvmFloatConstantTag|
- |repeating| |argumentList!| |replace| |expenseOfEvaluation|
- |clearFortranOutputStack| |tex| |safeFloor| |OMputEndBind| |bitCoef|
- |critB| |cTan| |s17aef| |stFuncN| |box| |times| |power!| |name|
- |LyndonWordsList1| |reset| |mr| |nativeModuleExtension| |cycleEntry|
- |sparsityIF| |solve1| |cCosh| |setLength!| |alphanumeric| |hclf|
- |direction| |bandedJacobian| |body| |e04ycf| |basisOfLeftNucleus|
- |outputGeneral| |f04axf| |makeSUP| |rootPower| |csubst| |makeop|
- |showTheSymbolTable| |leftMinimalPolynomial| |positiveRemainder|
- |write| |removeRedundantFactorsInContents| |factors| |s17acf|
- |derivationCoordinates| |numberOfComposites| |nor|
- |jvmNameAndTypeConstantTag| |elements| |getPickedPoints| |sizeLess?|
- |saturate| |save| |setFormula!| |useEisensteinCriterion?|
- |primintfldpoly| |symmetric?| |deepestInitial| |cross| |kind| |index|
- |round| |fintegrate| |truncate| |monom| |radicalOfLeftTraceForm|
- |extractIndex| |color| |d02bhf| |componentUpperBound| |gderiv|
- |complexNormalize| |rightCharacteristicPolynomial| |gensym|
- |createLowComplexityTable| |youngDiagram| |setAttributeButtonStep|
- |palgLODE0| |getStream| |doubleRank| |routines| |getIdentifier|
- |rightExactQuotient| |setValue!| |cyclotomicDecomposition| |cAcsch|
- |pair| |integralRepresents| |printTypes| |increasePrecision| **
- |padicFraction| |leftDiscriminant| |setUnion| |padecf| |sqfree|
- |removeSuperfluousCases| |common| UP2UTS |elem?| |hdmpToDmp| |setelt!|
- |hermiteH| |rotatez| |morphism| |curry| |rotatex| |monomial?|
- |clikeUniv| |create| |complexExpand| |mainSquareFreePart|
- |uncouplingMatrices| |entry?| |besselJ| |s21baf| |cycleRagits|
- |doubleResultant| |nextsubResultant2| |convergents| |modTree|
- |lfextendedint| |bombieriNorm| |generalizedInverse| |shiftLeft| |port|
- |ramifiedAtInfinity?| |factorByRecursion| |intensity| |listOfMonoms|
- |wholeRadix| |quadratic| |show| |reverse| |bytes| |c06gcf|
- |repeating?| |d03edf| |selectNonFiniteRoutines| |rootBound| |ODESolve|
- |degreeSubResultantEuclidean| |jordanAlgebra?| |stopTable!| |s19aaf|
- |basisOfNucleus| |rightDivide| |OMgetEndBVar| |prologue| |say|
- |patternMatchTimes| |leadingIndex| |listBranches| |prepareDecompose|
- |divisor| |rightRegularRepresentation| |wholeRagits| |trace|
- |selectFiniteRoutines| |OMputVariable| |univariateSolve| |imaginary|
- |multiplyExponents| |irreducibleRepresentation| |measure|
- |antisymmetricTensors| |zeroDimPrime?| |stopTableInvSet!| |groebSolve|
- |algebraicSort| |just| |f04qaf| |critMonD1| |chineseRemainder|
- |radicalEigenvectors| |arbitrary| |setref| |bracket|
- |squareFreeFactors| |graphCurves| |arguments| |shallowCopy|
- |nilFactor| |internalSubQuasiComponent?| |s15adf| |mainMonomial|
- |graphImage| |exponential| |sinh2csch| |s13adf| |nullSpace|
- |makeViewport3D| |adaptive3D?| |imagE| |mapmult| |divideIfCan!|
- |solveLinear| |removeConstantTerm| |removeSuperfluousQuasiComponents|
- |quartic| |dflist| |relerror| |gcdPrimitive| |subspace| |moebiusMu|
- |modifyPoint| |principalAncestors| |LazardQuotient| |OMread| |parents|
- |search| |f02awf| |simplifyExp| |e01sef| |setAdaptive|
- |removeRoughlyRedundantFactorsInPol| |radicalEigenvalues|
- |stiffnessAndStabilityFactor| |iicosh| |wronskianMatrix|
- |createNormalPoly| |isOr| |ref| |fortranLiteral| |fortranLiteralLine|
- |quote| |purelyAlgebraicLeadingMonomial?| |qfactor| |enterInCache|
- |union| |clipSurface| |adaptive| |roughBasicSet| |external?|
- |commutator| |spherical| |powmod| |lfinfieldint| |precision|
- |computeCycleLength| |nextNormalPrimitivePoly| |createIrreduciblePoly|
- |partialDenominators| |changeName| |hasoln| |critM| |distFact|
- |d02gaf| |numberOfCycles| |characteristicSet| |nthExponent|
- |wordInStrongGenerators| |associator| |checkRur| |nullary| |maxdeg|
- |sortConstraints| |clipPointsDefault| |constantToUnaryFunction|
- |arrayStack| |datalist| |inverseLaplace| |iiacoth| |lazyEvaluate|
- |completeEchelonBasis| |iiperm| |rightLcm| |plot| |unit| |heap|
- |f01qcf| |iicsc| |expint| |setMaxPoints3D| |removeZeroes| |close!|
- |setProperty| |e02baf| |lquo| |log2| |leftScalarTimes!| |btwFact|
- |powern| |mapdiv| |setErrorBound| |rightQuotient| |pointPlot|
- |putColorInfo| |insertRoot!| |linearlyDependent?| |freeOf?| |sec2cos|
- |e02ajf| |rule| |complexZeros| |difference|
- |createLowComplexityNormalBasis| |cyclic?| |chvar|
- |shanksDiscLogAlgorithm| |toScale| |rightFactorIfCan|
- |numberOfComputedEntries| |s14baf| |jokerMode| |reducedForm| |cos2sec|
- |e02ddf| |merge| |recolor| |sh| |elliptic?| |noKaratsuba|
- |jvmInterfaceMethodConstantTag| |hostByteOrder| |getRef| |setRow!|
- |composites| |setAdaptive3D| |resultantReduit| |constantRight|
- |rationalApproximation| |e02dcf| |plusInfinity| |OMputSymbol|
- |callForm?| |showFortranOutputStack| |principal?| |sylvesterSequence|
- |bat| |baseRDEsys| |reduceByQuasiMonic| |dfRange| |hypergeometric0F1|
- |fillPascalTriangle| |totolex| |minusInfinity| |jvmSynchronized|
- |semiResultantReduitEuclidean| |quadraticForm| |solid?| |getProperty|
- |octon| |iisqrt3| |cAsec| |degree| |scaleRoots| |critBonD| |sechIfCan|
- |disjunction| |imagI| |mathieu23| |normalizeAtInfinity| |harmonic|
- |e04fdf| |elaboration| |linSolve| |cCsch| |startTableGcd!| |f02bbf|
- |solveLinearlyOverQ| |collectUpper| |extendIfCan| |pseudoDivide|
- |makeGraphImage| |d01ajf| |OMgetEndObject| |bfEntry| |setsubMatrix!|
- |product| |integralCoordinates| |inGroundField?| |recip| |inverse|
- |pattern| |debug| |exportedOperators| |cSec| |upperCase?| |myDegree|
- |reverse!| |iisec| |checkPrecision| |doubleFloatFormat| |redPo|
- |twist| D |any| |socf2socdf| |e04gcf| |dAndcExp| |s21bdf|
- |rationalIfCan| |type| |laplacian| |cosSinInfo| |insertMatch|
- |monicDecomposeIfCan| |e04naf| |rightGcd| |readUInt32!|
- |semiResultantEuclidean2| |intersect| |euclideanGroebner| |aQuadratic|
- |scalarTypeOf| |genericLeftTrace| |critMTonD1| |maxColIndex|
- |subresultantSequence| |completeEval| |rightRankPolynomial| |dim|
- |maxPoints| |discriminantEuclidean| |UnVectorise| |rdHack1| |lazyPrem|
- |univariatePolynomials| |concat| |complexIntegrate|
- |rectangularMatrix| |leftPower| |rootOf| |satisfy?| |hex|
- |strongGenerators| |alternative?| |shiftRoots| |pr2dmp| |plenaryPower|
- |blankSeparate| |goodPoint| |getExplanations| |completeSmith|
- |OMputError| |mapUnivariateIfCan| |denomRicDE| |clearCache| |iicot|
- |bezoutMatrix| |integers| |qinterval| |bfKeys| |const| |setleaves!|
- |sech2cosh| F2FG |irForm| |OMUnknownSymbol?| |d01fcf| |charClass|
- |unitCanonical| |noLinearFactor?| |cartesian| |limitedIntegrate|
- |clipParametric| |antisymmetric?| |weighted| |absolutelyIrreducible?|
- |genericLeftNorm| |s21bbf| |oddintegers| |print| |s17agf| |jvmSuper|
- |inf| |pole?| |formfeed| |OMlistSymbols| |resolve| |subMatrix|
- |rubiksGroup| |setvalue!| |writeInt8!| |iiGamma| |extractIfCan|
- |remainder| |removeIrreducibleRedundantFactors| |convert| |toroidal|
- |characteristicPolynomial| |numer| |subscript| |unitNormal| |mapCoef|
- |evenlambert| |transform| |horizConcat| |leftZero| |complete| |denom|
- |allRootsOf| |s17def| |ptree| |zeroVector| |binaryFunction| |s17aff|
- |primeFactor| |findBinding| |e01bgf| |cPower| |enqueue!| |c05nbf|
- |splitNodeOf!| |genericLeftMinimalPolynomial| |supersub| |title|
- |fill!| |pi| |iibinom| |argument| |outputList| |makeYoungTableau|
- |reduction| |shiftRight| |cCoth| |infinity| |bumptab| |simplify|
- |triangularSystems| |possiblyNewVariety?| |prepareSubResAlgo|
- |idealiser| |permutationGroup| |univariatePolynomialsGcds| |fracPart|
- |e02dff| |numberOfFactors| |polygamma| |rootRadius| |s18dcf| |e|
- |tryFunctionalDecomposition?| |lastSubResultantElseSplit| |ceiling|
- |length| |quotientByP| |sumOfKthPowerDivisors| |contractSolve|
- |restorePrecision| |hue| |antiCommutative?| |kernel| |c06fqf|
- |pseudoQuotient| |scripts| |mainContent| |minimumDegree| |divideIfCan|
- |s18def| |constant?| |nil| |infinite| |arbitraryExponent|
- |approximate| |complex| |shallowMutable| |canonical| |noetherian|
- |central| |partiallyOrderedSet| |arbitraryPrecision|
- |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary|
- |additiveValuation| |unitsKnown| |canonicalUnitNormal|
- |multiplicativeValuation| |finiteAggregate| |shallowlyMutable|
- |commutative|) 
\ No newline at end of file
+ |Enumeration| |Mapping| |Record| |Union| |e01daf| |postfix|
+ |jokerMode| |monicRightFactorIfCan| |Si| |mapUnivariateIfCan| |lexico|
+ |numericIfCan| |leftTrim| |sayLength| |setValue!| |alphanumeric|
+ |numberOfFactors| |rquo| |ip4Address| |showClipRegion| |d02kef| |kind|
+ |copyInto!| |physicalLength!| |minRowIndex| |conjugates| |shiftRight|
+ |makeGraphImage| |redmat| |chineseRemainder|
+ |resultantReduitEuclidean| |maxPoints| |positiveRemainder|
+ |safeCeiling| FG2F |OMsend| |positive?| |leftTraceMatrix|
+ |fractionFreeGauss!| |expenseOfEvaluation| |complementaryBasis|
+ |graeffe| |asecIfCan| |compactFraction| |pToDmp| |localReal?| |minus!|
+ |rightScalarTimes!| |rombergo| |representationType|
+ |viewWriteAvailable| |antiAssociative?| |setProperty|
+ |isAbsolutelyIrreducible?| |dimensionsOf|
+ |degreeSubResultantEuclidean| |slex| |zeroSetSplit| |qfactor|
+ |aromberg| |yCoord| |nil?| |cschIfCan| |anfactor| |leastMonomial|
+ |jvmPublic| |myDegree| |removeRoughlyRedundantFactorsInPol|
+ |resultantReduit| |bsolve| |subResultantChain| |mesh| |taylorRep|
+ |cycleRagits| |binding| |systemSizeIF| |rst| |newTypeLists| |optimize|
+ |operation| |key?| |transcendentalDecompose| |complexNormalize|
+ |OMlistSymbols| |algebraic?| |rightZero| |tryFunctionalDecomposition|
+ |pdct| |shuffle| |union| |associatedSystem| |bubbleSort!| |cCsc|
+ |indicialEquationAtInfinity| |generalizedContinuumHypothesisAssumed?|
+ |reducedForm| |e04mbf| |semiResultantReduitEuclidean|
+ |extendedIntegrate| |clearTheIFTable| |pack!| |rroot| |OMgetInteger|
+ |lazyPremWithDefault| |constantLeft| |rename| |associatedEquations|
+ |nextIrreduciblePoly| |denomLODE| |denomRicDE|
+ |cyclotomicDecomposition| |binomial| |mix| |polygamma|
+ |stoseIntegralLastSubResultant| |initTable!| |infRittWu?| |shade|
+ |mainKernel| |OMgetError| |extension| |cCoth| |imagi|
+ |mainPrimitivePart| |radicalEigenvectors| |initials| |reverse|
+ |discriminantEuclidean| |startTable!| |expintegrate| |triangSolve|
+ |frobenius| |leadingCoefficientRicDE| |cLog| |d01ajf|
+ |differentialVariables| |leastAffineMultiple| |dmp2rfi| |numFunEvals|
+ |subtractIfCan| |reducedSystem| |mdeg| |SturmHabichtCoefficients|
+ |hash| |intcompBasis| |froot| |insertBottom!| |mkPrim|
+ |stoseInvertibleSetsqfreg| |li| |removeRedundantFactorsInContents|
+ |jordanAlgebra?| |trueEqual| |polarCoordinates| |henselFact| |count|
+ |rank| |super| |enterInCache| |stoseSquareFreePart| |leftRank|
+ |clearFortranOutputStack| |ode2| |rightUnits| |e02baf| |e02def|
+ |setRealSteps| |lazyPseudoRemainder| |d01apf| |bumprow| |bit?|
+ |negative?| |doubleResultant| |constructor| |f02wef| |zeroDim?|
+ |less?| |radicalEigenvalues| |nextPartition|
+ |rightCharacteristicPolynomial| |besselK| |subMatrix| |f04mcf|
+ |flexible?| |scripted?| |conjug| |setMaxPoints| |validExponential|
+ |reverse!| |before?| |rewriteSetWithReduction| |rspace|
+ |mainCoefficients| |cycleElt| |virtualDegree| |degreeSubResultant|
+ |nthRoot| |genus| |imagJ| |trace2PowMod| |generalPosition| |cos2sec|
+ |removeSinhSq| |dualSignature| |viewDeltaYDefault| |iicot|
+ |removeDuplicates!| |lSpaceBasis| |complement| EQ |rootRadius|
+ |lighting| |makeSeries| |unitVector| |selectMultiDimensionalRoutines|
+ |category| |cCosh| |quadraticForm| |collectUnder| |integer?|
+ |showTheIFTable| |coefficients| |maximumExponent| |endSubProgram|
+ |arbitrary| |mathieu22| |relativeApprox| |domain| |hcrf| |e02daf|
+ |apply| |isAnd| |permutationRepresentation| |makeCos| |cAcsch|
+ |associatorDependence| |intChoose| |getSyntaxFormsFromFile| |lists|
+ |basisOfMiddleNucleus| |entries| |UnVectorise| |package| |wholePart|
+ |first| |factorSFBRlcUnit| |linearDependenceOverZ| |series|
+ |squareFreeLexTriangular| |bumptab| |s17ahf| |OMgetEndObject|
+ |branchIfCan| |safeFloor| |extractProperty| |binomThmExpt| |rest|
+ |iteratedInitials| |fibonacci| |stopTable!| |cCos| |atrapezoidal|
+ |ratPoly| |bezoutResultant| |clipSurface| |decreasePrecision|
+ |aLinear| |region| |binarySearchTree| |setProperties|
+ |nextLatticePermutation| |complexNumericIfCan| |odd?|
+ |sylvesterMatrix| |capacity| |nextsousResultant2| |flexibleArray|
+ |logIfCan| |rightTrace| |factors| |lowerCase| |lquo| |doubleDisc|
+ |cyclicSubmodule| |deriv| |writeLine!| |rubiksGroup| |besselI|
+ |nextsubResultant2| |bag| |rationalPoint?| |prod| |min|
+ |stiffnessAndStabilityFactor| |figureUnits| |computeCycleEntry|
+ |Vectorise| |rootProduct| |genericRightTrace| |edf2efi| |iomode|
+ |f07fef| |selectOrPolynomials| |charthRoot| |pseudoRemainder|
+ |leftUnits| |epilogue| |realZeros| |normal01| |signatureAst| |prefix|
+ |toseLastSubResultant| |bezoutMatrix| |outlineRender| |iisec|
+ |readIfCan!| |arg1| |s18dcf| |monomials| |reflect| |commonDenominator|
+ |credPol| |optional?| |elementary| |mainVariable?| |vedf2vef| |binary|
+ |iidprod| |predicate| |arg2| |cyclicParents| |e02ddf| |setref|
+ |symmetricPower| |denominators| |createZechTable| |redpps|
+ |parseString| |selectIntegrationRoutines| |FormatArabic| |outputList|
+ |bfEntry| |kmax| |irCtor| |halfExtendedSubResultantGcd2| |rdHack1|
+ |solid?| |limitedint| |jvmProtected| |meshPar2Var| |setFieldInfo|
+ |simplify| |next| |conditions| |rarrow| |hdmpToP| |parametersOf|
+ |medialSet| |viewDefaults| |shrinkable| |e01bhf| |s19aaf|
+ |integralRepresents| |OMconnOutDevice| |adaptive| |match|
+ |prefixRagits| |brillhartTrials| |lyndonIfCan| |euclideanNormalForm|
+ |returnType!| |forLoop| |dequeue!| |normalizeIfCan| |unvectorise|
+ |localAbs| |subCase?| |OMputEndBind| |resetNew| |sn| |e01bef| |fmecg|
+ |balancedFactorisation| |genericLeftDiscriminant| |s18aff| |largest|
+ |d01gaf| |selectPDERoutines| |indiceSubResultant| |setvalue!|
+ |bernoulli| |s17acf| |exponentialOrder| |every?| |rk4a| |calcRanges|
+ |pattern| |iicos| |upperCase!| |elliptic| |clearTheSymbolTable|
+ |convergents| |log2| |diophantineSystem| |digamma| |rationalPower|
+ |iicosh| |currentSubProgram| |shellSort| |univcase|
+ |basisOfLeftAnnihilator| |maxPoints3D| |linGenPos| |extractBottom!|
+ |setMinPoints3D| |integers| |parabolic| |doubleFloatFormat|
+ |tryFunctionalDecomposition?| |fortranTypeOf| |pop!| |readLine!|
+ |elRow2!| |bat| |OMgetBVar| |laguerreL| |fortranCharacter|
+ |fixedPoint| |parameters| |isobaric?| |deleteRoutine!| |bracket|
+ |merge| |nodes| |simpsono| |ravel| |approxNthRoot| |true| |supRittWu?|
+ |sinhIfCan| |floor| |cAcosh| |standardBasisOfCyclicSubmodule|
+ |variable?| |setchildren!| |invertible?| |lazy?| |reshape| |f04adf|
+ |mathieu12| |orthonormalBasis| |csch2sinh| |logical?| |OMbindTCP|
+ |lazyPrem| |oddInfiniteProduct| |basisOfNucleus| |pdf2ef| |tab1|
+ |primeFrobenius| |printTypes| |comparison| |makeSin| |map|
+ |shallowExpand| |scale| |d02raf| |fortranCompilerName| |f04axf|
+ |singularAtInfinity?| |leadingIdeal| |polyRDE| |row|
+ |triangularSystems| |makeSketch| |e04ucf| |mat| |factorOfDegree|
+ |randomLC| |cycles| |colorDef| |moduloP| |graphs| |goto|
+ |var2StepsDefault| |identity| |parametric?| |possiblyNewVariety?|
+ |iilog| |writeInt8!| |setAdaptive3D| |selectSumOfSquaresRoutines|
+ |mainDefiningPolynomial| |unary?| |outputSpacing| |OMreceive| |wreath|
+ |zeroDimensional?| |setlast!| |basisOfCenter| |convert|
+ |perfectSquare?| |jacobian| |OMputSymbol| |stFunc2| |polynomialZeros|
+ |rightRemainder| |list?| |OMputEndAttr| |normalise| |backOldPos|
+ |trigs| |littleEndian| |changeVar| |modTree| |cothIfCan| |groebgen|
+ |makeprod| |generalSqFr| |redPo| |buildSyntax| |remove!| |truncate|
+ |recolor| |inverseIntegralMatrixAtInfinity| |option?| |log10|
+ |selectAndPolynomials| |droot| |rewriteIdealWithRemainder| |sorted?|
+ |id| |wronskianMatrix| |iitan| |upperCase| |reorder| |baseRDEsys|
+ |bitand| |heap| |c05pbf| |binaryTournament| |internalIntegrate| |lo|
+ |lazyIntegrate| |oddlambert| |genericLeftNorm| |viewSizeDefault|
+ |asinhIfCan| |messagePrint| |bitior| |explimitedint| |composite|
+ |cAtan| |s20adf| |step| |Aleph| |createNormalPoly| |palgint0|
+ |Frobenius| |specialTrigs| |primextintfrac|
+ |factorSquareFreeByRecursion| |perspective| |increasePrecision|
+ |palgextint0| |iicoth| |sturmSequence| |orbits| |cyclic?|
+ |univariatePolynomials| |second| |diagonals| |numerator| |squareFree|
+ |iisech| |infinite?| |basisOfLeftNucloid| |polyred| |algint|
+ |removeRoughlyRedundantFactorsInContents| |third| |ranges| |checkRur|
+ |splitLinear| |OMputAttr| |systemCommand| |s17dgf| |stack|
+ |startTableGcd!| |key| |edf2ef| |zeroDimPrime?| |qPot| |makeSUP|
+ |factorList| |internalDecompose| |supersub| |UpTriBddDenomInv|
+ |lowerPolynomial| |gcdprim| |categoryFrame| |e02gaf| |rotate!|
+ |jordanAdmissible?| |iExquo| |endOfFile?| |explogs2trigs|
+ |userOrdered?| |derivative| |filename| |normal| |OMReadError?|
+ |reseed| |setEpilogue!| |tan2trig| |extendedint| |lastSubResultant|
+ |integralCoordinates| |jvmStatic| |conjunction| |prepareSubResAlgo|
+ |mapUp!| |isPlus| |halfExtendedResultant1| |setMinPoints|
+ |eigenvectors| |car| |f2st| |abs| |radicalOfLeftTraceForm| |prem|
+ |parse| |acotIfCan| |maxRowIndex| |semiIndiceSubResultantEuclidean|
+ |notelem| |hermite| |lagrange| |LazardQuotient| |eq| |subTriSet?|
+ |nextPrimitivePoly| |lepol| |copy!| |s21bbf| |BasicMethod| |polar|
+ |reduceByQuasiMonic| |iter| |f01qcf| |e02zaf| |rationalFunction|
+ |lowerCase?| |e01bff| |lift| |isOpen?| |column| |expandLog|
+ |palgLODE0| |perfectSqrt| |eyeDistance| |certainlySubVariety?| |value|
+ |cycleEntry| |rotate| |reduce| |ParCond| |defineProperty| |chvar|
+ |perfectNthRoot| |genericLeftTrace| |exprHasLogarithmicWeights|
+ |infieldIntegrate| |d02ejf| |bivariate?| |numberOfPrimitivePoly|
+ |sequence| |isOr| |replaceKthElement| |printCode| |secIfCan|
+ |createPrimitiveElement| |f01ref| |f04atf| |asechIfCan| |OMreadStr|
+ |psolve| |f02bbf| |semiResultantEuclideannaif| |generateIrredPoly|
+ |stopTableInvSet!| |stoseInvertible?reg| |rootPower| |palgRDE| |fill!|
+ |jvmStrict| |linear| |monicModulo| |OMclose| |headReduced?|
+ |linearAssociatedLog| |d01gbf| |lineColorDefault| |initiallyReduced?|
+ |f01bsf| |expt| |bits| |recoverAfterFail| |ksec| |listRepresentation|
+ |noncommutativeJordanAlgebra?| |curryLeft| |complexExpand|
+ |outputMeasure| |createNormalElement| |unaryFunction| |readBytes!|
+ |rule| |polynomial| |OMsetEncoding| Y |OMgetEndAttr| |opeval|
+ |selectfirst| |nextColeman| |LyndonWordsList| |hasHi| |xCoord|
+ |enumerate| |setDifference| |inGroundField?| |applyRules| |coshIfCan|
+ |safetyMargin| |untab| |ScanArabic| |innerint| |factorsOfDegree|
+ |dimension| |squareTop| |squareFreePrim| |idealiser| |prime?|
+ |totalLex| |oddintegers| |palglimint0| |twoFactor| |c06gcf| |atom?|
+ |OMread| |generators| |index| |extractIndex| |tanh2trigh|
+ |innerSolve1| |integralLastSubResultant| |toseInvertibleSet| |dfRange|
+ |cyclotomicFactorization| |iicsc| |shufflein| |modifyPointData|
+ |units| |realRoots| |children| |c02aff| |c02agf| |critMTonD1| |eulerE|
+ |minset| |merge!| |getStream| |lowerCase!| |functorData| |discreteLog|
+ |pair| |shanksDiscLogAlgorithm| |typeLists| |isNot| |qelt| |returns|
+ |tan| |setPoly| |pquo| |Nul| |zeroDimPrimary?| |newReduc| |ref|
+ |setColumn!| |groebSolve| |chainSubResultants| |qsetelt|
+ |createGenericMatrix| |janko2| |cot| |sort| |explicitlyFinite?|
+ |commutative?| |latex| |coord| |tanAn| |newline|
+ |topFortranOutputStack| |collectQuasiMonic| |xRange| |Lazard2| |sec|
+ |c06eaf| |completeHermite| |iibinom| |rootOfIrreduciblePoly| |cAtanh|
+ |monicLeftDivide| |directSum| |e02bef| |mainSquareFreePart|
+ |leadingSupport| |yRange| |csubst| |csc| |random| |pointSizeDefault|
+ |incrementKthElement| |headReduce| |code|
+ |leftCharacteristicPolynomial| |omError| |cardinality| |points|
+ |jvmInterface| |nary?| |zRange| |indicialEquations| |asin| |top!|
+ |monicRightDivide| |result| |recip| |addMatch| |symmetricGroup|
+ |romberg| |quotedOperators| |superscript| |map!| |leftExtendedGcd|
+ |acos| |repeating?| |karatsubaDivide| |exprToXXP| |OMParseError?|
+ |permutationGroup| |primes| |oneDimensionalArray| |s17agf|
+ |complexEigenvectors| |multinomial| |qsetelt!| |name| |atan|
+ |pointColorPalette| |integralMatrixAtInfinity| |hyperelliptic|
+ |nsqfree| |inconsistent?| |solveLinearlyOverQ| |rk4| |fixedPoints|
+ |tanSum| |setprevious!| |search| |body| |acot| |maxrank| |simplifyLog|
+ |exprToGenUPS| |trunc| |nullary?| |reset| |scopes| |input|
+ |insertTop!| |fractRadix| |maxColIndex| |hypergeometric0F1| |asec|
+ |normalDenom| |expint| |doubleRank| |f02awf| |curveColor| |library|
+ |head| |toScale| |linearAssociatedExp| |gethi| BY |getlo|
+ |integralDerivationMatrix| |acsc| |coth2tanh| |readUInt8!|
+ |extractPoint| |charpol| |size| |write| |f02agf| |s13aaf| |hexDigit?|
+ |algebraicSort| |diagonalProduct| |parabolicCylindrical|
+ |constantRight| |hessian| |sinh| |root?| |printInfo!| |primintegrate|
+ |rewriteIdealWithQuasiMonicGenerators| |save| |separateDegrees|
+ |decompose| |sumOfDivisors| |palgextint| |sin2csc| |acsch|
+ |invmultisect| |cosh| |repSq| |leftRemainder| |equiv| |pushNewContour|
+ |fortranLiteral| |color| |jvmFloatConstantTag| |enterPointData|
+ |uncouplingMatrices| |makeop| |tanh| |writeByte!| |tableau|
+ |constantIfCan| |extensionDegree| |algintegrate| |zCoord| |lifting1|
+ |split| |partialFraction| |symbolTableOf| |coth| |d03edf|
+ |showArrayValues| |mapUnivariate| |inverse|
+ |halfExtendedSubResultantGcd1| |getOperator| |startStats!| |cot2tan|
+ |Beta| |copies| |iiacsc| |sech| |compBound| |constant| |argument|
+ |LyndonBasis| NOT |escape| |dequeue| |jvmSuper| |makeUnit|
+ |gcdPolynomial| |ratpart| |port| |mainCharacterization| |csch|
+ |closed| |getOrder| |setButtonValue| |pmintegrate| OR |ideal| |f01brf|
+ |readLineIfCan!| |solve1| |OMopenFile| |unitsColorDefault| |newLine|
+ |asinh| |iroot| |interval| |property| |resultantEuclidean| AND
+ |univariatePolynomialsGcds| |curve?| |nthFlag| |LagrangeInterpolation|
+ |subresultantSequence| |df2mf| |genericPosition| |acosh| |OMserve|
+ |subResultantGcd| |OMUnknownCD?| |routines| |node| |edf2df|
+ |collectUpper| |generalInfiniteProduct| |rightFactorIfCan|
+ |fillPascalTriangle| |expandPower| |lfunc| |t| |signature| |atanh|
+ |setMaxPoints3D| |initiallyReduce| |nthFractionalTerm| |simplifyExp|
+ |palglimint| |argumentListOf| |exprToUPS| |just| |makeEq|
+ |finiteBound| |acoth| |rationalPoints| |double?|
+ |showTheRoutinesTable| |transcendent?| |nothing|
+ |brillhartIrreducible?| |f02bjf| |isExpt| |universe| |assert|
+ |definingInequation| |inHallBasis?| |mapBivariate| |asech| |unparse|
+ |green| |categories| |minrank| |poisson| |quasiComponent| |normalize|
+ |repeating| |entry?| |delete!| |simpson| |selectNonFiniteRoutines|
+ |OMputFloat| |dihedralGroup| |regularRepresentation|
+ |fortranLiteralLine| |show| |basisOfRightNucloid| |dictionary|
+ |zeroOf| |binaryTree| |sturmVariationsOf| |multiple|
+ |setLegalFortranSourceExtensions| |screenResolution3D|
+ |exportedOperators| |predicates| |quickSort| |d02bhf|
+ |intermediateResultsIF| |elColumn2!| |mesh?| |applyQuote|
+ |factorGroebnerBasis| |seriesToOutputForm| |cyclicEntries| |status|
+ |mirror| |totalDegree| |integerBound| |cAsin| |trace| |inf|
+ |resultantEuclideannaif| |equality| |countable?| |tower| |c06frf|
+ |f02axf| |functionIsFracPolynomial?| |makeYoungTableau| |expPot|
+ |string?| |useNagFunctions| |numberOfComputedEntries| |OMgetObject|
+ |cAsech| |normFactors| |nodeOf?| |OMputInteger| |direction| *
+ |makeMulti| |lazyPseudoDivide| |choosemon| |symFunc| |llprop|
+ |tubePoints| |ruleset| |OMencodingUnknown| |completeSmith|
+ |getIdentifier| |e01saf| |fracPart| |compiledFunction| |corrPoly|
+ |f04qaf| |completeEval| |highCommonTerms| |leftAlternative?|
+ |externalList| |divisors| |OMconnInDevice| |s01eaf| |OMwrite|
+ |whitePoint| |quasiMonicPolynomials| |nextNormalPoly| |OMencodingXML|
+ |removeZeroes| |fortranInteger| |subResultantGcdEuclidean|
+ |composites| |primintfldpoly| |concat| |leastPower| |argumentList!|
+ |changeNameToObjf| |unitNormalize| |loadNativeModule| |complexNumeric|
+ |suchThat| |pushup| |nonQsign| |e01sef| |coerceImages| |pleskenSplit|
+ = |macroExpand| |norm| |cycleSplit!| |sts2stst| |callForm?| |cond|
+ |outputFixed| |rootBound| |firstSubsetGray| |selectODEIVPRoutines|
+ |equation| |trigs2explogs| |pdf2df| |reduceLODE| |besselJ| |kernels|
+ |cSec| |selectOptimizationRoutines| |chebyshevT| |RittWuCompare| <
+ |component| |usingTable?| |expintfldpoly| |ord| |operator|
+ |graphState| |dihedral| |swap!| |f02aaf| |subSet| > |f04faf| |pole?|
+ |optAttributes| |iisqrt2| |plusInfinity| |varList| |univariate|
+ |divideIfCan| |substitute| |symbolTable|
+ |zeroSetSplitIntoTriangularSystems| |ratDsolve| |dn|
+ |normalizeAtInfinity| <= |rightRank| |s14baf| |patternMatch|
+ |minusInfinity| |d01alf| |viewPhiDefault| |xn| |reduction| |subHeight|
+ |ef2edf| |finiteBasis| >= |distribute| |bivariateSLPEBR|
+ |factorSquareFreePolynomial| |pushFortranOutputStack| |bandedJacobian|
+ |rightExactQuotient| |LiePolyIfCan| |rightMinimalPolynomial| |rowEch|
+ |lazyVariations| |lieAlgebra?| |factor| |getMatch| |leftFactorIfCan|
+ |leftUnit| |popFortranOutputStack| |hMonic| |gcdcofactprim|
+ |viewDeltaXDefault| |cartesian| |stosePrepareSubResAlgo| |edf2fi|
+ |rightRankPolynomial| |splitConstant| |distFact| |sqrt| |title|
+ |overlap| |outputAsFortran| |localIntegralBasis| |fractionPart|
+ |reducedContinuedFraction| |support| + |f04jgf| |fortran|
+ |RemainderList| |s14aaf| |normalizedAssociate| |real| |iFTable| |red|
+ |symmetric?| - |sizeMultiplication| |inR?| |schwerpunkt| |mapGen|
+ |type| |processTemplate| |imag| |divide| |f02fjf| |symbol?|
+ |showAllElements| |palgRDE0| / |f01qdf| |OMputEndApp| |e|
+ |removeRoughlyRedundantFactorsInPols| |directProduct| |gramschmidt|
+ |augment| |characteristicSerie| |relerror| |e02aef|
+ |showFortranOutputStack| |viewThetaDefault| |sinIfCan| |bat1| |s21baf|
+ |hostByteOrder| |getMultiplicationTable| |completeEchelonBasis|
+ |writeUInt8!| |firstUncouplingMatrix| |irreducible?| |jvmAbstract|
+ |sec2cos| |univariateSolve| |musserTrials| |c06ebf| |fTable| |brace|
+ |complete| |squareFreePart| |pointLists| |formula| |duplicates?|
+ |reindex| |geometric| |squareFreePolynomial| |erf| |plus| |s18def|
+ |leftDivide| |destruct| |OMsupportsSymbol?| |normalDeriv| |airyBi|
+ |rational?| |char| |harmonic| |eigenvalues| |subQuasiComponent?|
+ |rotatez| |numericalOptimization| |OMputEndObject|
+ |multiplyCoefficients| |complexLimit| |interReduce| |df2fi| |bottom!|
+ |baseRDE| |axesColorDefault| |stoseInternalLastSubResultant| |iiasinh|
+ |mapExpon| |d02gaf| |cPower| RF2UTS |e04ycf| |headAst| |whatInfinity|
+ |exponential1| |taylorIfCan| |dilog| |LyndonWordsList1| |times|
+ |euler| |transpose| |imagE| |tanhIfCan| |uniform| |inverseColeman|
+ |localUnquote| |evaluateInverse| |limitedIntegrate| |changeThreshhold|
+ |radPoly| |index?| |generalizedEigenvector| |solveid| |monomial| |sin|
+ |tab| |removeRedundantFactors| |vector| |options| |coHeight| |init|
+ |skewSFunction| |innerSolve| |float| |power| |weakBiRank|
+ |getOperands| |branchPoint?| |testModulus| |lifting| |cos|
+ |multivariate| |definingEquations| |createPrimitivePoly|
+ |differentiate| |goodPoint| |separateFactors| |deepestInitial|
+ |basisOfRightAnnihilator| |numberOfNormalPoly| |readUInt32!| |ran|
+ |rationalApproximation| |variables| |variationOfParameters|
+ |OMputBind| |goodnessOfFit| |string| |getGraph| |implies|
+ |subscriptedVariables| |times!| |collect| |script| |e04dgf| |monom|
+ |mappingMode| |legendreP| |gcdPrimitive| |changeMeasure| |principal?|
+ |critB| |algebraicOf| |imaginary| |eigenvector| |rk4qc| |iiperm|
+ |constant?| |diag| |allRootsOf| |cExp| |expIfCan| |d02gbf| |e02bbf|
+ |stoseInvertible?sqfreg| |torsionIfCan| |dual| |SturmHabicht|
+ |besselY| |dimensions| |f01qef| |numFunEvals3D| |e02ajf|
+ |stopTableGcd!| |OMgetVariable| |tex| |morphism| |common|
+ |exprHasWeightCosWXorSinWX| |rotatey| |normalizedDivide|
+ |OMgetEndError| |viewPosDefault| |printHeader| |e04fdf|
+ |singularitiesOf| |lyndon?| |f04arf| |environment| |rightPower|
+ |taylor| |over| |definingPolynomial| |basisOfLeftNucleus|
+ |insertionSort!| |partition| |mergeFactors| |optpair| |mindegTerm|
+ |leaves| |verticalTab| |laurent| |resetBadValues| |ridHack1|
+ |numberOfCycles| |exp| |level| |push!| |karatsuba| |clipParametric|
+ |makeFloatFunction| |lazyPquo| |keys| GE |branchPointAtInfinity?|
+ |curve| |maxrow| |modularGcdPrimitive| |enqueue!| |critT| |rational|
+ |s19abf| |smith| |lprop| GT |selectsecond| |normInvertible?|
+ |LowTriBddDenomInv| |thenBranch| |cyclotomic| |findCycle|
+ |discriminant| |measure2Result| |outputFloating| |OMputBVar| LE
+ |semiResultantEuclidean2| |evaluate| |stopMusserTrials| |nrows|
+ |bright| |is?| |preprocess| |readInt16!| |mr| |sign| |getExplanations|
+ |label| |cross| |purelyTranscendental?| LT |loopPoints| |conical|
+ |toseInvertible?| |ncols| |elseBranch| |createRandomElement|
+ |singRicDE| |primPartElseUnitCanonical| |divisorCascade|
+ |generalTwoFactor| |cosh2sech| |reopen!| |multiplyExponents|
+ |operators| |kroneckerDelta| |commaSeparate| |s17def| |subspace|
+ |f2df| |sylvesterSequence| LODO2FUN |tanIfCan| |reducedDiscriminant|
+ |divergence| |fullDisplay| |rightLcm| |symmetricProduct| |totalfract|
+ |setClipValue| |removeCoshSq| |meshPar1Var| |mulmod| |addPoint2|
+ |curry| |jvmVolatile| |unrankImproperPartitions1| |cscIfCan| |mvar|
+ |summation| |removeZero| |semiDegreeSubResultantEuclidean| |Is|
+ |areEquivalent?| |iflist2Result| |c06fpf| SEGMENT |characteristicSet|
+ |increase| |isEquiv| |cCot| |cTan| |elaboration| |complexZeros|
+ |setPredicates| |roughEqualIdeals?| |numerators| |d03faf| |crushedSet|
+ |cn| |null?| |outputGeneral| |controlPanel| |cAcos| |read!|
+ |antisymmetric?| |minColIndex| |rootSplit| |null| |closedCurve|
+ |gensym| |c05nbf| |e02bcf| |split!| |option| |iCompose| |regime|
+ |OMreadFile| |nlde| |contours| |exponent| |d01aqf| |karatsubaOnce|
+ |not| |jvmLongConstantTag| |isTimes| |computeBasis|
+ |expandTrigProducts| |getRef| |order| |rowEchelonLocal| |laguerre|
+ |intersect| |inputOutputBinaryFile| |frst| |boundOfCauchy| |and|
+ |plotPolar| |uniform01| |createMultiplicationMatrix| |getGoodPrime|
+ |drawToScale| |splitSquarefree| |cubic| |failed?| |rischDEsys|
+ |cycleTail| |or| |firstNumer| |removeRedundantFactorsInPols|
+ |getMultiplicationMatrix| |addMatchRestricted| |interpret| |round|
+ |irreducibleRepresentation| |mainExpression| |FormatRoman|
+ |linkToFortran| |light| |xor| |pair?| |mapSolve| |exprex| |putGraph|
+ |digit?| |eisensteinIrreducible?| |pol| |writeBytes!|
+ |linearlyDependentOverZ?| |airyAi| |quoByVar| |case| |zeroVector|
+ |moebiusMu| |logpart| |fi2df| |jvmMethodrefConstantTag|
+ |rewriteIdealWithHeadRemainder| |idealSimplify| |rotatex|
+ |nthExponent| |plot| |Zero| |iisinh| |stripCommentsAndBlanks|
+ |leftReducedSystem| |drawComplexVectorField| |linSolve| |comp|
+ |showAll?| |heapSort| |showSummary| |s17dcf| |OMgetBind| |One|
+ |extendedEuclidean| |lambert| |groebner| |someBasis| |function|
+ |coerceL| |rightRecip| |indiceSubResultantEuclidean| |setPosition|
+ |cosIfCan| |block| |zoom| |s17aef| |legendre| |weighted| |difference|
+ |countRealRootsMultiple| |extractTop!| |showAttributes| |setStatus|
+ |createLowComplexityTable| |f02adf| |multiple?| |condition|
+ |quasiAlgebraicSet| |createPrimitiveNormalPoly| |multisect| |shape|
+ |integralBasisAtInfinity| |sizePascalTriangle| |f02xef| |monomRDEsys|
+ |child| |csc2sin| |d01anf| |leaf?| |euclideanGroebner| |module|
+ |algebraicDecompose| |indicialEquation| |splitNodeOf!|
+ |tableForDiscreteLogarithm| |leader| |exactQuotient!| |OMgetFloat|
+ |queue| |paren| |cRationalPower| |delete| |wordInStrongGenerators|
+ |elt| |findConstructor| |rur| |clearTable!| |fintegrate| |measure|
+ |compound?| |slash| |printStatement| |modulus| |setScreenResolution|
+ |s13acf| |sum| |noKaratsuba| |makeVariable| |elaborate| |more?|
+ |qroot| |checkForZero| |iterationVar| |removeSquaresIfCan|
+ |subresultantVector| |explicitlyEmpty?| |OMgetSymbol| |lfintegrate|
+ |asimpson| |monomial?| |dim| |lazyResidueClass| |setrest!|
+ |binaryFunction| |modifyPoint| |s21bcf| |jacobiIdentity?| |irDef|
+ |outputAsTex| |factorial| |yCoordinates| |unit| |element?| |midpoint|
+ |s20acf| |inRadical?| |acschIfCan| |determinant| |constDsolve|
+ |balancedBinaryTree| |iiacot| |lazyGintegrate| |elaborateFile|
+ |coordinates| |debug| |parts| |cCsch| |absolutelyIrreducible?|
+ |stFunc1| |submod| |genericRightMinimalPolynomial| |minPol|
+ |pointColor| |clip| D |stFuncN| |mapExponents| |ddFact|
+ |createLowComplexityNormalBasis| |lcm| |coth2trigh| |f07fdf|
+ |characteristic| |monicCompleteDecompose| |youngDiagram| |belong?|
+ |hexDigit| |exteriorDifferential| |aQuadratic| |GospersMethod|
+ |outputAsScript| |underscore| |minimumExponent| |blue|
+ |taylorQuoByVar| |append| |d01bbf| |low| |eigenMatrix|
+ |PollardSmallFactor| |associator| |genericLeftMinimalPolynomial|
+ |subNodeOf?| |digit| |numer| |upperBound| |antisymmetricTensors| |gcd|
+ |numberOfChildren| |rootNormalize| |updatF| |quotient| |d03eef|
+ |pureLex| |countRealRoots| |zero?| |prevPrime| |denom| |var1Steps|
+ |false| |BumInSepFFE| |polygon| |vark| |solveRetract|
+ |nativeModuleExtension| |jvmInterfaceMethodConstantTag| |subset?|
+ |exptMod| |OMputEndError| |clikeUniv| |invertIfCan| |getDatabase|
+ |jvmPrivate| |LazardQuotient2| |compile| |pushuconst| |pi|
+ |viewport2D| |s19adf| |ScanFloatIgnoreSpaces| |coercePreimagesImages|
+ |sequences| |hasPredicate?| |principalAncestors| |voidMode|
+ |magnitude| |infinity| |getPickedPoints| |inc| |numericalIntegration|
+ |point?| |adaptive?| |linearElement| |leftRegularRepresentation|
+ |var1StepsDefault| |associates?| |diagonal?| |minordet|
+ |fortranComplex| |bezoutDiscriminant| |weights| |clipPointsDefault|
+ |f02akf| |setAttributeButtonStep| |wrregime| |readInt32!| |print|
+ |autoReduced?| |interactiveEnv| |rightQuotient| |Ei| |startPolynomial|
+ |hue| |extract!| |deepCopy| |resolve| |power!| |stirling1| |kernel|
+ |denominator| |extend| |scalarTypeOf| |iiexp| |e02agf|
+ |reciprocalPolynomial| |setVariableOrder| |homogeneous?| |groebner?|
+ |list| |irForm| |triangulate| |tanintegrate| |d01akf| |f01maf| |draw|
+ |critBonD| |iiasech| |createThreeSpace| |integralMatrix| |setLength!|
+ |nextNormalPrimitivePoly| |debug3D| |alternating| |subscript| |pow|
+ |hitherPlane| |f07aef| |lhs| |call| |OMputString| |prindINFO|
+ |OMgetEndApp| |acoshIfCan| |zeroSquareMatrix| |modularFactor| |center|
+ |find| |fortranLinkerArgs| |showIntensityFunctions| |rhs| |create|
+ |purelyAlgebraic?| |member?| |groebnerFactorize| |solveLinear|
+ |roughBase?| |OMputAtp| |prepareDecompose| |setImagSteps| |normDeriv2|
+ |ParCondList| |cyclicEqual?| |dioSolve| |makeObject| |sizeLess?|
+ |width| |getBadValues| |host| |rootPoly| |antiCommutator| |ScanRoman|
+ |graphImage| |declare| |extractClosed| |coef| |permutation| |e02adf|
+ |subst| |isConnected?| |antiCommutative?| |lfextlimint|
+ |palgintegrate| |resultant| |normalElement| |clearTheFTable| |tRange|
+ |constantCoefficientRicDE| |root| |front| |attributeData|
+ |screenResolution| |semiSubResultantGcdEuclidean2| |pointPlot|
+ |limitPlus| |solveLinearPolynomialEquationByRecursion| |delta|
+ |constantToUnaryFunction| |createMultiplicationTable| |rootSimp|
+ |cyclePartition| |e02bdf| |initial| |symbolIfCan| |singular?|
+ |OMUnknownSymbol?| |laplacian| |shift| |bipolarCylindrical|
+ |leftTrace| |f02aff| |normalForm| |strongGenerators| |quasiMonic?|
+ |signAround| |unrankImproperPartitions0| |swapRows!| |objects|
+ |createIrreduciblePoly| |matrixGcd| |unitNormal| |mainVariable|
+ |sncndn| |packageCall| |sechIfCan| |symmetricSquare| |optional|
+ |exprHasAlgebraicWeight| |base| |getZechTable| |maxIndex|
+ |infinityNorm| |squareMatrix| |multiEuclidean| |curveColorPalette|
+ |s15aef| |acosIfCan| |SturmHabichtMultiple| |imagk| |acothIfCan|
+ |exponential| |normalized?| |f04mbf| |iipow| |df2st| |divisor| UP2UTS
+ |logGamma| |drawComplex| |jvmStringConstantTag| |removeConstantTerm|
+ |lp| |listOfMonoms| |log| |useEisensteinCriterion| |setnext!|
+ |factorsOfCyclicGroupSize| |lazyPseudoQuotient| |pushdown|
+ |stronglyReduce| |digits| |monomRDE| |laplace| |saturate| |cSinh|
+ |subPolSet?| |permutations| |printInfo| |lambda| |hasSolution?|
+ |c06fqf| |coerceP| |reducedQPowers| |one?| |say| |nthFactor|
+ |clipBoolean| |traverse| |contains?| |left| |weight| |errorInfo|
+ |minPoints| |float?| |dmpToP| |multiEuclideanTree| |minimize|
+ |nthRootIfCan| |presub| |right| |rootKerSimp| |cup| |factorSquareFree|
+ |point| |mapCoef| |minPoints3D| |alternative?| |linearMatrix| |d01fcf|
+ |ReduceOrder| |cosSinInfo| |df2ef| |e02dcf| |alternatingGroup|
+ |pointColorDefault| |cache| |primitiveElement| |badValues|
+ |deepExpand| |updatD| |putColorInfo| |close| |laurentRep| |arrayStack|
+ |partialDenominators| |iiasec| |s17aff| |primlimitedint| |isList|
+ |problemPoints| |leftMult| |c06ecf| |mapDown!| |sinhcosh|
+ |simplifyPower| |cdr| |patternVariable| |e04jaf| |disjunction|
+ |distance| |display| |qqq| |cyclic| |range| |leviCivitaSymbol|
+ |sinh2csch| |wholeRadix| |sumSquares| |rightRegularRepresentation|
+ |sup| |previous| |elem?| |simpleBounds?| |identification|
+ |numberOfHues| |doubleComplex?| |ptFunc| |unknown| |roughUnitIdeal?|
+ |HermiteIntegrate| |pile| |Ci| |unit?| |makeResult| |indices|
+ |conditionP| |powers| |parents| |invertibleElseSplit?| |s19acf|
+ |leftFactor| |prolateSpheroidal| |coerceListOfPairs| |htrigs|
+ |multiset| |particularSolution| |roman| |setFormula!| |exQuo|
+ |upDateBranches| |hasTopPredicate?| |currentEnv| |totalDifferential|
+ |pseudoQuotient| |distdfact| |hostPlatform| |probablyZeroDim?|
+ |d01asf| |e02ahf| |quatern| |eq?| |inspect| |s18acf|
+ |removeSuperfluousQuasiComponents| |evenlambert| |square?|
+ |properties| |consnewpol| |charClass| |fixedPointExquo| |hconcat|
+ |padicallyExpand| |symbol| |quadratic?| |ffactor| |realElementary|
+ |toseSquareFreePart| |shiftRoots| |translate| |output| |separate|
+ |critpOrder| |mainValue| |factorials| |insertMatch| |expression|
+ |trim| |viewport3D| |genericRightNorm| |primaryDecomp| |bandedHessian|
+ |test| |lexTriangular| |bitTruth| |linear?| |generator|
+ |extendedResultant| |integer| |changeName| |inverseLaplace|
+ |physicalLength| |trivialIdeal?| |orbit| |remove| |delay|
+ |insertRoot!| |symmetricDifference| |ldf2vmf| |functionIsOscillatory|
+ |tracePowMod| |s13adf| UTS2UP |infLex?| |imagI| |wholeRagits|
+ |printStats!| |sdf2lst| |complexRoots| |primeFactor| |entry| |dark|
+ |symmetricRemainder| |expr| |quadratic| |last| |dmpToHdmp|
+ |commutativeEquality| |c06gsf| |hdmpToDmp| |decimal| |se2rfi|
+ |tablePow| |complexForm| |traceMatrix| |assoc| |knownInfBasis|
+ |message| |OMencodingBinary| |complexElementary| |insert!| |pushucoef|
+ |mainContent| |f04asf| |errorKind| |drawStyle| |changeWeightLevel|
+ |polyPart| |acscIfCan| |polyRicDE| |aQuartic| |rootDirectory|
+ |jvmIntegerConstantTag| |tensorProduct| |normal?|
+ |useEisensteinCriterion?| |pointData| |weierstrass|
+ |lastSubResultantEuclidean| |alphanumeric?| |horizontalTab|
+ |jvmClassConstantTag| |transform| |variable| |OMputObject| |polygon?|
+ |unitCanonical| |explicitEntries?| |diagonal| |iicsch| |partitions|
+ |coefficient| |iterators| |quartic| |pr2dmp| |setleft!| |refine|
+ |typeList| |extractSplittingLeaf| |substring?| |getButtonValue|
+ |hasoln| |cylindrical| |overbar| |radicalSimplify| |OMgetString|
+ |eulerPhi| |high| |monicDecomposeIfCan| |useSingleFactorBound|
+ |asinIfCan| |LiePoly| |birth| |readByte!| |generalizedEigenvectors|
+ |gradient| |rightMult| |mainMonomials| |checkPrecision| |incr|
+ |iiacoth| |suffix?| |invertibleSet| |top| |nullSpace| |empty|
+ |reverseLex| |makingStats?| |linearlyDependent?|
+ |selectFiniteRoutines| |ocf2ocdf| |hi| |continue| |rules| |firstDenom|
+ |isAtom| |OMgetEndAtp| |tubeRadiusDefault| |bytes| |mathieu23|
+ |character?| |solveInField| |nthCoef| |numeric| |prefix?| |rightOne|
+ |internalLastSubResultant| |complexEigenvalues|
+ |algebraicCoefficients?| |OMgetType| |linearAssociatedOrder| |eof?|
+ |startTableInvSet!| |radical| |stoseInvertible?| |makeCrit|
+ |overlabel| |horizConcat| |f02ajf| |positiveSolve| |rightAlternative?|
+ |mergeDifference| |numberOfImproperPartitions| |setelt!| |algDsolve|
+ |minimumDegree| |findBinding| |setClosed| |UP2ifCan|
+ |conditionsForIdempotents| |s17akf| |tube| |extendedSubResultantGcd|
+ |rightTraceMatrix| |radicalSolve| |linearPart| |isOp| |compdegd|
+ |irVar| |precision| |noLinearFactor?| |rename!| |integrate| |minIndex|
+ |triangular?| |readInt8!| |OMlistCDs| |plenaryPower| |ldf2lst|
+ |noValueMode| |closed?| |setCondition!| |critM| |listYoungTableaus|
+ |e01sff| |makeViewport3D| |exponents| |identitySquareMatrix|
+ |removeCosSq| |laurentIfCan| |infix?| |nonSingularModel|
+ |quadraticNorm| |dflist| |intPatternMatch| |sub| |s17dhf| |mkcomm|
+ |integral| |e04naf| |nextPrimitiveNormalPoly| |mask| |bothWays|
+ |ptree| |palgint| |monomialIntegrate| |topPredicate| |OMconnectTCP|
+ |OMputVariable| |symmetricTensors| |primextendedint|
+ |fullPartialFraction| |lazyEvaluate| |computePowers| |e02akf| |f07adf|
+ |deref| |freeOf?| |resize| |chebyshevU| |Lazard|
+ |stoseLastSubResultant| |iifact| |cons| |dominantTerm| |att2Result|
+ |decomposeFunc| |raisePolynomial| |setsubMatrix!|
+ |initializeGroupForWordProblem| |iiacsch| |mindeg| |divideExponents|
+ |getProperty| |beauzamyBound| |OMgetApp| |c06fuf| |generate|
+ |inverseIntegralMatrix| |roughBasicSet| |leftZero| |middle| |finite?|
+ |setright!| |readable?| |radicalEigenvector| |hermiteH| |iiatan|
+ |fglmIfCan| |e01bgf| |addPointLast| |resultantnaif| |OMgetAttr| |rem|
+ |encodingDirectory| |incrementBy| |argscript| |mpsode| |associative?|
+ |s17ajf| |iisin| |euclideanSize| |coerceS| |f02aef| |quo| |varselect|
+ |expand| |mkIntegral| |getCurve|
+ |generalizedContinuumHypothesisAssumed| |adaptive3D?| |integral?|
+ |dimensionOfIrreducibleRepresentation| |source| |nextSublist|
+ |structuralConstants| |ratDenom| |filterWhile| |B1solve| |monicDivide|
+ |pushdterm| |s18aef| |blankSeparate| |derivationCoordinates| |space|
+ |qinterval| |div| |leftLcm| |filterUntil|
+ |functionIsContinuousAtEndPoints| |lastSubResultantElseSplit|
+ |bitCoef| |any| |nextPrime| |OMmakeConn| |supDimElseRittWu?| |exquo|
+ |rightGcd| |select| |singleFactorBound| |arity| |realEigenvectors|
+ |squareFreeFactors| |directory| |OMsupportsCD?| |target|
+ |quasiRegular?| |leftScalarTimes!| |phiCoord| ~= |doublyTransitive?|
+ |fprindINFO| |stoseInvertibleSet| |exists?| |revert| |components|
+ |back| |internal?| |position| |evenInfiniteProduct| |#|
+ |inputBinaryFile| |mainForm| |numberOfComponents| |resetVariableOrder|
+ |connect| |lflimitedint| |lookupFunction| |tanNa| |leftExactQuotient|
+ |rightDivide| ~ |external?| |isQuotient| |product| |coerce| |ipow|
+ |increment| |var2Steps| |integralAtInfinity?| |octon| |f01rcf|
+ |generalLambert| |genericRightTraceForm| |accuracyIF| |curryRight|
+ |construct| |elRow1!| |real?| |palginfieldint| |putProperty| |sin?|
+ |nextItem| |basicSet| |zerosOf| |plus!| |showRegion| |iiGamma|
+ |aspFilename| |setIntersection| |subNode?| |nand| |mkAnswer| |lookup|
+ |/\\| |c06gbf| |cycleLength| |algSplitSimple| |continuedFraction|
+ |vectorise| |update| |d02cjf| |primitivePart!| |\\/| |lllp|
+ |rischNormalize| |jvmUTF8ConstantTag| |quoted?| |matrixConcat3D|
+ |content| |lfextendedint| |roughSubIdeal?| |bfKeys| |removeSinSq|
+ |twist| |ignore?| |trapezoidalo| |height| |ceiling|
+ |algebraicVariables| |graphCurves| |fixedDivisor| |numberOfComposites|
+ |bigEndian| |Gamma| |any?| |clipWithRanges| |genericRightDiscriminant|
+ |tubeRadius| |sh| |semiSubResultantGcdEuclidean1| |recur|
+ |lieAdmissible?| |rowEchLocal| |coordinate| |listConjugateBases|
+ |s17dlf| |factorPolynomial| |tubePointsDefault| |complexIntegrate|
+ |moebius| |btwFact| |univariate?| |addBadValue| |completeHensel|
+ |setTopPredicate| |factorAndSplit| |palgLODE| |returnTypeOf|
+ |appendPoint| |mantissa| |OMgetEndBVar| |viewWriteDefault|
+ |padicFraction| |commutator| |create3Space|
+ |ScanFloatIgnoreSpacesIfCan| |semicolonSeparate| |primlimintfrac|
+ |stronglyReduced?| |neglist| |imagK| |numberOfDivisors| |bernoulliB|
+ |conjugate| |max| |extractIfCan| |cfirst| |iisqrt3| |vspace|
+ |moreAlgebraic?| |closedCurve?| |fortranCarriageReturn|
+ |outputBinaryFile| |irreducibleFactor| |solve| |bombieriNorm|
+ |linefeed| |imagj| |isImplies| |internalIntegrate0| |sparsityIF|
+ |leftQuotient| |irreducibleFactors| |setOfMinN| |isMult|
+ |OMgetEndBind| |rangePascalTriangle| |yellow| |c05adf| |rCoord|
+ |atoms| |matrixDimensions| |pade|
+ |rewriteSetByReducingWithParticularGenerators| |radix| |iprint|
+ |infix| |randnum| |seriesSolve| |gcdcofact| |length| |infiniteProduct|
+ |socf2socdf| |quotientByP| |seed| |combineFeatureCompatibility|
+ |shallowCopy| |leftNorm| |nor| |const| |match?| |scripts| |pastel|
+ |updateStatus!| |rightUnit| |internalSubPolSet?| |setelt| |invmod|
+ |jvmFinal| |makeTerm| |sumOfSquares| |bivariatePolynomials| |set|
+ |thetaCoord| |partialNumerators| |alphabetic| |showTheFTable|
+ |elliptic?| |pToHdmp| |rectangularMatrix| |jvmDoubleConstantTag|
+ |connectTo| |ListOfTerms| |depth| |kovacic| |sqfrFactor|
+ |pascalTriangle| |copy| |nonLinearPart| |swap| |meshFun2Var|
+ |scalarMatrix| |exactQuotient| |powern| |leftDiscriminant| |spherical|
+ |principalIdeal| |lyndon| |mappingAst| |iidsum| |datalist|
+ |integerIfCan| |stirling2| |prologue| |nthExpon| |cAcoth| |nullary|
+ |autoCoerce| |e01baf| |remainder| |fortranDoubleComplex|
+ |setLabelValue| |An| |closeComponent| |tail| |isPower|
+ |basisOfRightNucleus| |cSin| |linearForm| |c06gqf|
+ |generalizedInverse| |cAsec| |d02bbf| |ode| |bitLength|
+ |relationsIdeal| |realEigenvalues| |mathieu24| |number?| |ode1|
+ |lllip| |semiDiscriminantEuclidean| |subResultantsChain| |hspace|
+ |coleman| |numberOfMonomials| |void| |leftGcd| |companionBlocks|
+ |leadingBasisTerm| |midpoints| |possiblyInfinite?| |infieldint|
+ |newSubProgram| |getVariableOrder| |e04gcf| |basisOfCentroid|
+ |sumOfKthPowerDivisors| |nilFactor| |perfectNthPower?| |exp1|
+ |interpolate| |retract| |cap| |torsion?| |repeatUntilLoop| |setEmpty!|
+ |nullity| |KrullNumber| |oblateSpheroidal| |badNum| ** |setfirst!|
+ |separant| |setleaves!| |leadingTerm| |bringDown|
+ |stiffnessAndStabilityOfODEIF| |linears| |stoseInvertibleSetreg|
+ |cAcot| |semiLastSubResultantEuclidean| |leftPower| |decrease|
+ |jvmNameAndTypeConstantTag| |basisOfCommutingElements| |iiabs|
+ |cyclicGroup| |totalGroebner| |move| |iiasin| |rightDiscriminant|
+ |minGbasis| |constantOpIfCan| |internalInfRittWu?| |f02abf|
+ |univariatePolynomial| |setUnion| |writable?| |powmod| |whileLoop|
+ |complex?| |HenselLift| |complexSolve| |flatten|
+ |halfExtendedResultant2| |mapdiv| |approximants| |minimalPolynomial|
+ |wordInGenerators| |rightNorm| |removeIrreducibleRedundantFactors|
+ |e01sbf| |zag| |retractable?| |patternMatchTimes| |getMeasure|
+ |pmComplexintegrate| |maxdeg| |box| |numberOfOperations|
+ |factorFraction| |shiftLeft| |bindings| |headRemainder|
+ |rightExtendedGcd| |assign| |unknownEndian| |backspace| |makeFR|
+ |rischDE| |leftRecip| |retractIfCan| |iitanh| |degree| |setTex!|
+ |qualifier| |OMcloseConn| |listexp| |po| |empty?| |double|
+ |deepestTail| |OMputEndBVar| |removeDuplicates| |getProperties|
+ |jvmNative| |dAndcExp| |s14abf| |contractSolve| |push|
+ |internalSubQuasiComponent?| |s17adf| |getConstant| |cAcsc| |tan2cot|
+ |tubePlot| |adjoint| |meatAxe| |fortranDouble| |prinb| |npcoef|
+ |failed| |youngGroup| |select!| |sech2cosh| |zeroMatrix| |error|
+ |surface| |splitDenominator| |unprotectedRemoveRedundantFactors|
+ |lowerBound| |rootOf| |computeInt| |vconcat| |fortranReal| |dec|
+ |lazyIrreducibleFactors| |scanOneDimSubspaces| |viewpoint| |toroidal|
+ |mapmult| |schema| |nthr| |constantKernel| |internalZeroSetSplit|
+ |padecf| |lfinfieldint| |graphStates| |leadingExponent| |coefChoose|
+ |ramifiedAtInfinity?| |cAsinh| |elements| |outerProduct| |cyclicCopy|
+ |cTanh| |central?| |factor1| |monomialIntPoly| |atanIfCan|
+ |putProperties| |prime| |leadingIndex| |diagonalMatrix| |scan|
+ |biRank| |mightHaveRoots| |check| |factorset| |setStatus!| |declare!|
+ |basis| |withPredicates| |setErrorBound| |powerAssociative?|
+ |fortranLogical| |c06ekf| |sortConstraints| |minPoly| |cSech| |s15adf|
+ |groebnerIdeal| |insert| |linearPolynomials| |sort!| |lex| |byte|
+ |degreePartition| |puiseux| |pomopo!| |polCase| |ellipticCylindrical|
+ |setOrder| |OMencodingSGML| |bumptab1| |tanQ| |ricDsolve| |s21bdf|
+ |stop| |restorePrecision| |open?| |iiacos| |f01mcf| |lintgcd|
+ |scaleRoots| |OMputApp| |showScalarValues| |lexGroebner| |outputForm|
+ |inv| |resetAttributeButtons| |superHeight| |clearDenominator|
+ |LyndonCoordinates| |eval| |satisfy?| F2FG |PDESolve| |inrootof|
+ |has?| |ground?| |zero| |swapColumns!| |compose| |anticoord| |s18adf|
+ |d01amf| |showTheSymbolTable| |deleteProperty!| |hclf| |printingInfo?|
+ |unexpand| |ground| |drawCurves| |quasiRegular|
+ |characteristicPolynomial| |dot| |moduleSum| |powerSum| |alphabetic?|
+ |typeForm| |testDim| |presuper| |sqfree| |leadingMonomial|
+ |computeCycleLength| |And| |expenseOfEvaluationIF| |divideIfCan!|
+ |SturmHabichtSequence| |segment| |cycle| |reduceBasisAtInfinity|
+ |identityMatrix| |f01rdf| |mainVariables| |leadingCoefficient| |Or|
+ |jacobi| |vertConcat| |factorByRecursion| |SFunction| |listBranches|
+ |primPartElseUnitCanonical!| |int| |child?| |iiacosh|
+ |primitiveMonomials| |extendIfCan| |Not| |OMunhandledSymbol|
+ |currentScope| |trailingCoefficient| |getCode| |expextendedint|
+ |reduced?| |listOfLists| |reductum| |iiatanh| |bounds| |mainMonomial|
+ |primitivePart| |setScreenResolution3D| |totolex| |matrix| |tanh2coth|
+ |transcendenceDegree| |prinshINFO| |trapezoidal| |internalAugment|
+ |carriageReturn| |wordsForStrongGenerators| |style| |byteBuffer|
+ |contract| F |quote| |cotIfCan| |rk4f| |rowEchelon| |chiSquare|
+ |chiSquare1| |currentCategoryFrame| |prinpolINFO| |addmod|
+ |rationalIfCan| |createNormalPrimitivePoly| |duplicates|
+ |rangeIsFinite| |mathieu11| |solid| |hex| |write!| |idealiserMatrix|
+ |jvmTransient| |redPol| |even?| |componentUpperBound|
+ |solveLinearPolynomialEquationByFractions| |outputArgs| |in?|
+ |overset?| |f04maf| |rightFactorCandidate| |monic?| |open|
+ |useSingleFactorBound?| |generic| |sincos| |viewZoomDefault|
+ |leftMinimalPolynomial| |modularGcd| |unmakeSUP| |crest| |setRow!|
+ |build| |jvmFieldrefConstantTag| |flagFactor| |OMputEndAtp|
+ |colorFunction| |semiResultantEuclidean1| |OMputError| |rdregime|
+ |nil| |removeSuperfluousCases| |e02dff| |pseudoDivide| |randomR|
+ |makeViewport2D| |listLoops| |arguments| |represents|
+ |partialQuotients| |fractRagits| |size?| |OMgetAtp| |changeBase|
+ |critMonD1| |concat!| |intensity| |comment| |categoryMode|
+ |mapMatrixIfCan| |cot2trig| |addiag| |operations| |reify| |primitive?|
+ |generic?| |makeRecord| |replace| |domainTemplate| |close!| |gbasis|
+ |linearDependence| |integralBasis| |tree| |node?| |numberOfVariables|
+ |approximate| |dom| |table| |imports| |setPrologue!| |readUInt16!|
+ |terms| |complex| |radicalRoots| |members| |setAdaptive| |ODESolve|
+ |Hausdorff| |addPoint| |parent| |obj| |new| |tValues|
+ |purelyAlgebraicLeadingMonomial?| |sPol| |interpretString| |limit|
+ |rootsOf| |numberOfFractionalTerms| |paraboloidal| |innerEigenvectors|
+ |upperCase?| |leftOne| |position!| |gderiv| |leftRankPolynomial|
+ |expressIdealMember| |jvmSynchronized| |diff| |part?| GF2FG
+ |fixPredicate| |op| |maxint| |OMopenString| |formfeed| |approxSqrt|
+ |selectPolynomials| |constantOperator| |unravel|
+ |numberOfIrreduciblePoly| |clearCache| |bipolar| |abelianGroup|
+ |genericLeftTraceForm| |atanhIfCan| |aCubic| |realSolve| |axes|
+ |ramified?| |multMonom| |solveLinearPolynomialEquation| |rightTrim|
+ |permanent| |sample| |nextSubsetGray| |nil| |infinite|
+ |arbitraryExponent| |approximate| |complex| |shallowMutable|
+ |canonical| |noetherian| |central| |partiallyOrderedSet|
+ |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors|
+ |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown|
+ |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate|
+ |shallowlyMutable| |commutative|) 
\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 22a184dd..3cd9c6c9 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5489 +1,5493 @@
 
-(3471998 . 3508766252)       
-((-2280 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-3119 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-2696 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1265 (-560)) |#2|) 44 T ELT)) (-4318 (($ $) 80 T ELT)) (-2108 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-2533 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-1559 (((-663 |#2|) $) 13 T ELT)) (-4246 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-3459 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-2067 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-1726 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3327 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-2667 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-1495 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1265 (-560))) 66 T ELT)) (-3435 (($ $ (-560)) 76 T ELT) (($ $ (-1265 (-560))) 75 T ELT)) (-3150 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-2877 (($ $ $ (-560)) 69 T ELT)) (-2721 (($ $) 68 T ELT)) (-2548 (($ (-663 |#2|)) 73 T ELT)) (-4357 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-2539 (((-887) $) 92 T ELT)) (-1657 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2329 (((-114) $ $) 95 T ELT)) (-2349 (((-114) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -2329 ((-114) |#1| |#1|)) (-15 -2539 ((-887) |#1|)) (-15 -2349 ((-114) |#1| |#1|)) (-15 -3119 (|#1| |#1|)) (-15 -3119 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -4318 (|#1| |#1|)) (-15 -2877 (|#1| |#1| |#1| (-560))) (-15 -2280 ((-114) |#1|)) (-15 -4246 (|#1| |#1| |#1|)) (-15 -2533 ((-560) |#2| |#1| (-560))) (-15 -2533 ((-560) |#2| |#1|)) (-15 -2533 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -2280 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -4246 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -2696 (|#2| |#1| (-1265 (-560)) |#2|)) (-15 -1726 (|#1| |#1| |#1| (-560))) (-15 -1726 (|#1| |#2| |#1| (-560))) (-15 -3435 (|#1| |#1| (-1265 (-560)))) (-15 -3435 (|#1| |#1| (-560))) (-15 -2067 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4357 (|#1| (-663 |#1|))) (-15 -4357 (|#1| |#1| |#1|)) (-15 -4357 (|#1| |#2| |#1|)) (-15 -4357 (|#1| |#1| |#2|)) (-15 -1495 (|#1| |#1| (-1265 (-560)))) (-15 -2548 (|#1| (-663 |#2|))) (-15 -3327 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -1495 (|#2| |#1| (-560))) (-15 -1495 (|#2| |#1| (-560) |#2|)) (-15 -2696 (|#2| |#1| (-560) |#2|)) (-15 -3150 ((-793) |#2| |#1|)) (-15 -1559 ((-663 |#2|) |#1|)) (-15 -3150 ((-793) (-1 (-114) |#2|) |#1|)) (-15 -2667 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -1657 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -3459 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2067 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2721 (|#1| |#1|))) (-19 |#2|) (-1248)) (T -18)) 
+(3473074 . 3508838164)       
+((-1860 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-4235 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3986 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1266 (-560)) |#2|) 44 T ELT)) (-1518 (($ $) 80 T ELT)) (-1995 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3817 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-3086 (((-663 |#2|) $) 13 T ELT)) (-1762 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2173 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-1793 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-4233 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3237 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-1723 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-3034 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-560)) NIL T ELT) (($ $ (-1266 (-560))) 66 T ELT)) (-3032 (($ $ (-560)) 76 T ELT) (($ $ (-1266 (-560))) 75 T ELT)) (-1485 (((-793) (-1 (-114) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-1352 (($ $ $ (-560)) 69 T ELT)) (-4007 (($ $) 68 T ELT)) (-3845 (($ (-663 |#2|)) 73 T ELT)) (-2465 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-663 $)) 85 T ELT)) (-3834 (((-888) $) 92 T ELT)) (-3894 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-2478 (((-114) $ $) 95 T ELT)) (-2499 (((-114) $ $) 99 T ELT))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -2478 ((-114) |#1| |#1|)) (-15 -3834 ((-888) |#1|)) (-15 -2499 ((-114) |#1| |#1|)) (-15 -4235 (|#1| |#1|)) (-15 -4235 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -1518 (|#1| |#1|)) (-15 -1352 (|#1| |#1| |#1| (-560))) (-15 -1860 ((-114) |#1|)) (-15 -1762 (|#1| |#1| |#1|)) (-15 -3817 ((-560) |#2| |#1| (-560))) (-15 -3817 ((-560) |#2| |#1|)) (-15 -3817 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -1860 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -1762 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -3986 (|#2| |#1| (-1266 (-560)) |#2|)) (-15 -4233 (|#1| |#1| |#1| (-560))) (-15 -4233 (|#1| |#2| |#1| (-560))) (-15 -3032 (|#1| |#1| (-1266 (-560)))) (-15 -3032 (|#1| |#1| (-560))) (-15 -1793 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -2465 (|#1| (-663 |#1|))) (-15 -2465 (|#1| |#1| |#1|)) (-15 -2465 (|#1| |#2| |#1|)) (-15 -2465 (|#1| |#1| |#2|)) (-15 -3034 (|#1| |#1| (-1266 (-560)))) (-15 -3845 (|#1| (-663 |#2|))) (-15 -3237 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1995 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3034 (|#2| |#1| (-560))) (-15 -3034 (|#2| |#1| (-560) |#2|)) (-15 -3986 (|#2| |#1| (-560) |#2|)) (-15 -1485 ((-793) |#2| |#1|)) (-15 -3086 ((-663 |#2|) |#1|)) (-15 -1485 ((-793) (-1 (-114) |#2|) |#1|)) (-15 -1723 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -3894 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2173 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1793 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4007 (|#1| |#1|))) (-19 |#2|) (-1249)) (T -18)) 
 NIL 
-(-10 -8 (-15 -2329 ((-114) |#1| |#1|)) (-15 -2539 ((-887) |#1|)) (-15 -2349 ((-114) |#1| |#1|)) (-15 -3119 (|#1| |#1|)) (-15 -3119 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -4318 (|#1| |#1|)) (-15 -2877 (|#1| |#1| |#1| (-560))) (-15 -2280 ((-114) |#1|)) (-15 -4246 (|#1| |#1| |#1|)) (-15 -2533 ((-560) |#2| |#1| (-560))) (-15 -2533 ((-560) |#2| |#1|)) (-15 -2533 ((-560) (-1 (-114) |#2|) |#1|)) (-15 -2280 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -4246 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -2696 (|#2| |#1| (-1265 (-560)) |#2|)) (-15 -1726 (|#1| |#1| |#1| (-560))) (-15 -1726 (|#1| |#2| |#1| (-560))) (-15 -3435 (|#1| |#1| (-1265 (-560)))) (-15 -3435 (|#1| |#1| (-560))) (-15 -2067 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4357 (|#1| (-663 |#1|))) (-15 -4357 (|#1| |#1| |#1|)) (-15 -4357 (|#1| |#2| |#1|)) (-15 -4357 (|#1| |#1| |#2|)) (-15 -1495 (|#1| |#1| (-1265 (-560)))) (-15 -2548 (|#1| (-663 |#2|))) (-15 -3327 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2108 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -1495 (|#2| |#1| (-560))) (-15 -1495 (|#2| |#1| (-560) |#2|)) (-15 -2696 (|#2| |#1| (-560) |#2|)) (-15 -3150 ((-793) |#2| |#1|)) (-15 -1559 ((-663 |#2|) |#1|)) (-15 -3150 ((-793) (-1 (-114) |#2|) |#1|)) (-15 -2667 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -1657 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -3459 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2067 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2721 (|#1| |#1|))) 
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-(((-19 |#1|) (-142) (-1248)) (T -19)) 
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+(((-19 |#1|) (-142) (-1249)) (T -19)) 
 NIL 
-(-13 (-385 |t#1|) (-10 -7 (-6 -4510))) 
-(((-34) . T) ((-102) -2191 (|has| |#1| (-1132)) (|has| |#1| (-871)) (|has| |#1| (-102))) ((-632 (-887)) -2191 (|has| |#1| (-1132)) (|has| |#1| (-871)) (|has| |#1| (-632 (-887)))) ((-153 |#1|) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-298 #0=(-560) |#1|) . T) ((-298 (-1265 (-560)) $) . T) ((-300 #0# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-385 |#1|) . T) ((-503 |#1|) . T) ((-618 #0# |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-673 |#1|) . T) ((-871) |has| |#1| (-871)) ((-874) |has| |#1| (-871)) ((-1132) -2191 (|has| |#1| (-1132)) (|has| |#1| (-871))) ((-1248) . T)) 
-((-2494 (((-3 $ "failed") $ $) 12 T ELT)) (-2426 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-948) $) NIL T ELT) (($ (-793) $) 16 T ELT) (($ (-560) $) 26 T ELT))) 
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+(-13 (-385 |t#1|) (-10 -7 (-6 -4511))) 
+(((-34) . T) ((-102) -2309 (|has| |#1| (-1133)) (|has| |#1| (-872)) (|has| |#1| (-102))) ((-632 (-888)) -2309 (|has| |#1| (-1133)) (|has| |#1| (-872)) (|has| |#1| (-632 (-888)))) ((-153 |#1|) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-298 #0=(-560) |#1|) . T) ((-298 (-1266 (-560)) $) . T) ((-300 #0# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-385 |#1|) . T) ((-503 |#1|) . T) ((-618 #0# |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-673 |#1|) . T) ((-872) |has| |#1| (-872)) ((-875) |has| |#1| (-872)) ((-1133) -2309 (|has| |#1| (-1133)) (|has| |#1| (-872))) ((-1249) . T)) 
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 NIL 
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 (((-21) (-142)) (T -21)) 
-((-2426 (*1 *1 *1) (-4 *1 (-21))) (-2426 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-133) (-668 (-560)) (-10 -8 (-15 -2426 ($ $)) (-15 -2426 ($ $ $)))) 
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+((-3544 (*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1133)) (-4 *4 (-1133)) (-5 *2 (-2 (|:| -1919 *3) (|:| -3529 *4)))))) 
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+(((-34) . T) ((-107 #0=(-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((-102) -2309 (|has| |#2| (-1133)) (|has| |#2| (-102)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-102))) ((-632 (-888)) -2309 (|has| |#2| (-1133)) (|has| |#2| (-632 (-888))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-632 (-888)))) ((-153 #1=(-2 (|:| -1919 |#1|) (|:| -3529 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1266 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . T) ((-321 #1#) -12 (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-294 #1#) . T) ((-385 #1#) . T) ((-503 #1#) . T) ((-503 |#2|) . T) ((-618 #2# #1#) . T) ((-618 |#1| |#2|) . T) ((-528 #1# #1#) -12 (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-321 (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)))) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-629 |#1| |#2|) . T) ((-673 #1#) . T) ((-688 #1#) . T) ((-872) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) ((-875) |has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872)) ((-1042 #1#) . T) ((-1133) -2309 (|has| |#2| (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-1133)) (|has| (-2 (|:| -1919 |#1|) (|:| -3529 |#2|)) (-872))) ((-1182 #1#) . T) ((-1226 |#1| |#2|) . T) ((-1249) . T) ((-1288 #1#) . T)) 
+((-3834 (((-888) $) NIL T ELT) (($ (-560)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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+NIL 
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 (((-38 |#1|) (-142) (-175)) (T -38)) 
 NIL 
-(-13 (-1080) (-739 |t#1|) (-635 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-632 (-887)) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 |#1|) . T) ((-670 $) . T) ((-662 |#1|) . T) ((-739 |#1|) . T) ((-748) . T) ((-1082 |#1|) . T) ((-1087 |#1|) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T)) 
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-NIL 
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 NIL 
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 NIL 
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 NIL 
 (((-98) (-142)) (T -98)) 
 NIL 
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-NIL 
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-(-10 -7 (-15 -4022 ((-663 (-1202 (-560))) (-560))) (-15 -1945 ((-1202 (-560)) (-560))) (-15 -2013 ((-419 (-1202 (-560))) (-560)))) 
-((-3927 (((-1186 (-229)) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 132 T ELT)) (-2290 (((-663 (-1190)) (-1186 (-229))) NIL T ELT)) (-3817 (((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 109 T ELT)) (-2350 (((-663 (-229)) (-326 (-229)) (-1208) (-1120 (-864 (-229)))) NIL T ELT)) (-2892 (((-663 (-1190)) (-663 (-229))) NIL T ELT)) (-1605 (((-229) (-1120 (-864 (-229)))) 31 T ELT)) (-3397 (((-229) (-1120 (-864 (-229)))) 32 T ELT)) (-2151 (((-391) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 126 T ELT)) (-2921 (((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 67 T ELT)) (-3921 (((-1190) (-229)) NIL T ELT)) (-2482 (((-1190) (-663 (-1190))) 27 T ELT)) (-4181 (((-1066) (-1208) (-1208) (-1066)) 13 T ELT))) 
-(((-195) (-10 -7 (-15 -3817 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2921 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1605 ((-229) (-1120 (-864 (-229))))) (-15 -3397 ((-229) (-1120 (-864 (-229))))) (-15 -2151 ((-391) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2350 ((-663 (-229)) (-326 (-229)) (-1208) (-1120 (-864 (-229))))) (-15 -3927 ((-1186 (-229)) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3921 ((-1190) (-229))) (-15 -2892 ((-663 (-1190)) (-663 (-229)))) (-15 -2290 ((-663 (-1190)) (-1186 (-229)))) (-15 -2482 ((-1190) (-663 (-1190)))) (-15 -4181 ((-1066) (-1208) (-1208) (-1066))))) (T -195)) 
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-(-10 -7 (-15 -3817 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2921 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1605 ((-229) (-1120 (-864 (-229))))) (-15 -3397 ((-229) (-1120 (-864 (-229))))) (-15 -2151 ((-391) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2350 ((-663 (-229)) (-326 (-229)) (-1208) (-1120 (-864 (-229))))) (-15 -3927 ((-1186 (-229)) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3921 ((-1190) (-229))) (-15 -2892 ((-663 (-1190)) (-663 (-229)))) (-15 -2290 ((-663 (-1190)) (-1186 (-229)))) (-15 -2482 ((-1190) (-663 (-1190)))) (-15 -4181 ((-1066) (-1208) (-1208) (-1066)))) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 61 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 33 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
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+((-2088 (((-419 (-1203 (-560))) (-560)) 38 T ELT)) (-1440 (((-663 (-1203 (-560))) (-560)) 33 T ELT)) (-2808 (((-1203 (-560)) (-560)) 28 T ELT))) 
+(((-194) (-10 -7 (-15 -1440 ((-663 (-1203 (-560))) (-560))) (-15 -2808 ((-1203 (-560)) (-560))) (-15 -2088 ((-419 (-1203 (-560))) (-560))))) (T -194)) 
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+(-10 -7 (-15 -1440 ((-663 (-1203 (-560))) (-560))) (-15 -2808 ((-1203 (-560)) (-560))) (-15 -2088 ((-419 (-1203 (-560))) (-560)))) 
+((-2764 (((-1187 (-229)) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 132 T ELT)) (-3526 (((-663 (-1191)) (-1187 (-229))) NIL T ELT)) (-4359 (((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 109 T ELT)) (-3409 (((-663 (-229)) (-326 (-229)) (-1209) (-1121 (-866 (-229)))) NIL T ELT)) (-3677 (((-663 (-1191)) (-663 (-229))) NIL T ELT)) (-2226 (((-229) (-1121 (-866 (-229)))) 31 T ELT)) (-2224 (((-229) (-1121 (-866 (-229)))) 32 T ELT)) (-3518 (((-391) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 126 T ELT)) (-3788 (((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 67 T ELT)) (-3334 (((-1191) (-229)) NIL T ELT)) (-2845 (((-1191) (-663 (-1191))) 27 T ELT)) (-3508 (((-1067) (-1209) (-1209) (-1067)) 13 T ELT))) 
+(((-195) (-10 -7 (-15 -4359 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3788 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2226 ((-229) (-1121 (-866 (-229))))) (-15 -2224 ((-229) (-1121 (-866 (-229))))) (-15 -3518 ((-391) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3409 ((-663 (-229)) (-326 (-229)) (-1209) (-1121 (-866 (-229))))) (-15 -2764 ((-1187 (-229)) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3334 ((-1191) (-229))) (-15 -3677 ((-663 (-1191)) (-663 (-229)))) (-15 -3526 ((-663 (-1191)) (-1187 (-229)))) (-15 -2845 ((-1191) (-663 (-1191)))) (-15 -3508 ((-1067) (-1209) (-1209) (-1067))))) (T -195)) 
+((-3508 (*1 *2 *3 *3 *2) (-12 (-5 *2 (-1067)) (-5 *3 (-1209)) (-5 *1 (-195)))) (-2845 (*1 *2 *3) (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-1191)) (-5 *1 (-195)))) (-3526 (*1 *2 *3) (-12 (-5 *3 (-1187 (-229))) (-5 *2 (-663 (-1191))) (-5 *1 (-195)))) (-3677 (*1 *2 *3) (-12 (-5 *3 (-663 (-229))) (-5 *2 (-663 (-1191))) (-5 *1 (-195)))) (-3334 (*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1191)) (-5 *1 (-195)))) (-2764 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-1187 (-229))) (-5 *1 (-195)))) (-3409 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1209)) (-5 *5 (-1121 (-866 (-229)))) (-5 *2 (-663 (-229))) (-5 *1 (-195)))) (-3518 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-391)) (-5 *1 (-195)))) (-2224 (*1 *2 *3) (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-2226 (*1 *2 *3) (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-3788 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (-5 *1 (-195)))) (-4359 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-195))))) 
+(-10 -7 (-15 -4359 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3788 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2226 ((-229) (-1121 (-866 (-229))))) (-15 -2224 ((-229) (-1121 (-866 (-229))))) (-15 -3518 ((-391) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3409 ((-663 (-229)) (-326 (-229)) (-1209) (-1121 (-866 (-229))))) (-15 -2764 ((-1187 (-229)) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -3334 ((-1191) (-229))) (-15 -3677 ((-663 (-1191)) (-663 (-229)))) (-15 -3526 ((-663 (-1191)) (-1187 (-229)))) (-15 -2845 ((-1191) (-663 (-1191)))) (-15 -3508 ((-1067) (-1209) (-1209) (-1067)))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 61 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 33 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-196) (-809)) (T -196)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 66 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 66 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-197) (-809)) (T -197)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 81 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 81 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-198) (-809)) (T -198)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 63 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 63 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-199) (-809)) (T -199)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 76 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-200) (-809)) (T -200)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 93 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 93 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-201) (-809)) (T -201)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 90 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 90 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-202) (-809)) (T -202)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 78 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3170 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 78 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3039 (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3039 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-3834 (((-888) $) NIL T ELT)) (-1519 (((-114) $ $) NIL T ELT)) (-2478 (((-114) $ $) NIL T ELT))) 
 (((-203) (-809)) (T -203)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 76 T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 35 T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
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 (((-204) (-809)) (T -204)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 77 T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 42 T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
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 (((-205) (-809)) (T -205)) 
 NIL 
 (-809) 
-((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 105 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 86 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) 
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 (((-206) (-809)) (T -206)) 
 NIL 
 (-809) 
-((-2155 (((-3 (-2 (|:| -2994 (-115)) (|:| |w| (-229))) "failed") (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 109 T ELT)) (-3048 (((-560) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 59 T ELT)) (-3380 (((-3 (-663 (-229)) "failed") (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 90 T ELT))) 
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-((-3048 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-560)) (-5 *1 (-207)))) (-3380 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-663 (-229))) (-5 *1 (-207)))) (-2155 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| -2994 (-115)) (|:| |w| (-229)))) (-5 *1 (-207))))) 
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+NIL 
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+(((-233 |#1|) (-142) (-1133)) (T -233)) 
 NIL 
 (-13 (-242 |t#1|)) 
-(((-34) . T) ((-107 |#1|) . T) ((-102) -2191 (|has| |#1| (-1132)) (|has| |#1| (-102))) ((-632 (-887)) -2191 (|has| |#1| (-1132)) (|has| |#1| (-632 (-887)))) ((-153 |#1|) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-242 |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-503 |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-1132) |has| |#1| (-1132)) ((-1248) . T)) 
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-(((-234 |#1|) (-142) (-1080)) (T -234)) 
-NIL 
-(-13 (-1080) (-274 |t#1|) (-10 -7 (IF (|has| |t#1| (-240)) (-6 (-240)) |%noBranch|) (IF (|has| |t#1| (-927 (-1208))) (-6 (-927 (-1208))) |%noBranch|))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-635 (-560)) . T) ((-632 (-887)) . T) ((-236 $) -2191 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-240) |has| |#1| (-240)) ((-239) -2191 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-668 (-560)) . T) ((-668 $) . T) ((-670 $) . T) ((-748) . T) ((-921 $ #0=(-1208)) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-929 #0#) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T)) 
-((-4324 ((|#2| $) 9 T ELT))) 
-(((-235 |#1| |#2|) (-10 -8 (-15 -4324 (|#2| |#1|))) (-236 |#2|) (-1248)) (T -235)) 
-NIL 
-(-10 -8 (-15 -4324 (|#2| |#1|))) 
-((-2457 ((|#1| $) 7 T ELT)) (-4324 ((|#1| $) 6 T ELT))) 
-(((-236 |#1|) (-142) (-1248)) (T -236)) 
-((-2457 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1248)))) (-4324 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1248))))) 
-(-13 (-1248) (-10 -8 (-15 -2457 (|t#1| $)) (-15 -4324 (|t#1| $)))) 
-(((-1248) . T)) 
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-(((-237 |#1|) (-142) (-1080)) (T -237)) 
+(((-34) . T) ((-107 |#1|) . T) ((-102) -2309 (|has| |#1| (-1133)) (|has| |#1| (-102))) ((-632 (-888)) -2309 (|has| |#1| (-1133)) (|has| |#1| (-632 (-888)))) ((-153 |#1|) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-242 |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-503 |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-1133) |has| |#1| (-1133)) ((-1249) . T)) 
+((-3808 (((-114) $ $) 7 T ELT)) (-3136 (((-114) $) 21 T ELT)) (-1469 (((-3 $ "failed") $ $) 25 T ELT)) (-4489 (($) 22 T CONST)) (-2167 (((-3 $ "failed") $) 42 T ELT)) (-3363 (((-114) $) 40 T ELT)) (-2128 (((-1191) $) 11 T ELT)) (-1473 (((-1152) $) 12 T ELT)) (-2703 (($ $ (-1 |#1| |#1|) (-793)) 62 T ELT) (($ $ (-1 |#1| |#1|)) 61 T ELT) (($ $ (-1209)) 60 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-663 (-1209))) 58 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-1209) (-793)) 57 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 56 (|has| |#1| (-930 (-1209))) ELT) (($ $) 52 (|has| |#1| (-239)) ELT) (($ $ (-793)) 50 (|has| |#1| (-239)) ELT)) (-3834 (((-888) $) 13 T ELT) (($ (-560)) 38 T ELT)) (-3103 (((-793)) 37 T CONST)) (-1519 (((-114) $ $) 6 T ELT)) (-2971 (($) 23 T CONST)) (-2983 (($) 39 T CONST)) (-3095 (($ $ (-1 |#1| |#1|) (-793)) 64 T ELT) (($ $ (-1 |#1| |#1|)) 63 T ELT) (($ $ (-1209)) 59 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-663 (-1209))) 55 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-1209) (-793)) 54 (|has| |#1| (-930 (-1209))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 53 (|has| |#1| (-930 (-1209))) ELT) (($ $) 51 (|has| |#1| (-239)) ELT) (($ $ (-793)) 49 (|has| |#1| (-239)) ELT)) (-2478 (((-114) $ $) 8 T ELT)) (-2581 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-2571 (($ $ $) 18 T ELT)) (** (($ $ (-949)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT))) 
+(((-234 |#1|) (-142) (-1081)) (T -234)) 
+NIL 
+(-13 (-1081) (-274 |t#1|) (-10 -7 (IF (|has| |t#1| (-240)) (-6 (-240)) |%noBranch|) (IF (|has| |t#1| (-928 (-1209))) (-6 (-928 (-1209))) |%noBranch|))) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-635 (-560)) . T) ((-632 (-888)) . T) ((-236 $) -2309 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-240) |has| |#1| (-240)) ((-239) -2309 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-668 (-560)) . T) ((-668 $) . T) ((-670 $) . T) ((-748) . T) ((-922 $ #0=(-1209)) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #0#) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T)) 
+((-3095 ((|#2| $) 9 T ELT))) 
+(((-235 |#1| |#2|) (-10 -8 (-15 -3095 (|#2| |#1|))) (-236 |#2|) (-1249)) (T -235)) 
+NIL 
+(-10 -8 (-15 -3095 (|#2| |#1|))) 
+((-2703 ((|#1| $) 7 T ELT)) (-3095 ((|#1| $) 6 T ELT))) 
+(((-236 |#1|) (-142) (-1249)) (T -236)) 
+((-2703 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1249)))) (-3095 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1249))))) 
+(-13 (-1249) (-10 -8 (-15 -2703 (|t#1| $)) (-15 -3095 (|t#1| $)))) 
+(((-1249) . T)) 
+((-3808 (((-114) $ $) 7 T ELT)) (-3136 (((-114) $) 21 T ELT)) (-1469 (((-3 $ "failed") $ $) 25 T ELT)) (-4489 (($) 22 T CONST)) (-2128 (((-1191) $) 11 T ELT)) (-1473 (((-1152) $) 12 T ELT)) (-2703 (($ $ (-793)) 42 T ELT) (($ $) 40 T ELT)) (-3834 (((-888) $) 13 T ELT)) (-1519 (((-114) $ $) 6 T ELT)) (-2971 (($) 23 T CONST)) (-3095 (($ $ (-793)) 43 T ELT) (($ $) 41 T ELT)) (-2478 (((-114) $ $) 8 T ELT)) (-2581 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-2571 (($ $ $) 18 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ |#1| $) 32 T ELT) (($ $ |#1|) 36 T ELT))) 
+(((-237 |#1|) (-142) (-1081)) (T -237)) 
 NIL 
 (-13 (-111 |t#1| |t#1|) (-239) (-10 -7 (IF (|has| |t#1| (-175)) (-6 (-739 |t#1|)) |%noBranch|))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-632 (-887)) . T) ((-236 $) . T) ((-239) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-670 |#1|) . T) ((-662 |#1|) |has| |#1| (-175)) ((-739 |#1|) |has| |#1| (-175)) ((-1082 |#1|) . T) ((-1087 |#1|) . T) ((-1132) . T) ((-1248) . T)) 
-((-2457 (($ $) NIL T ELT) (($ $ (-793)) 9 T ELT)) (-4324 (($ $) NIL T ELT) (($ $ (-793)) 11 T ELT))) 
-(((-238 |#1|) (-10 -8 (-15 -4324 (|#1| |#1| (-793))) (-15 -2457 (|#1| |#1| (-793))) (-15 -4324 (|#1| |#1|)) (-15 -2457 (|#1| |#1|))) (-239)) (T -238)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-632 (-888)) . T) ((-236 $) . T) ((-239) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-670 |#1|) . T) ((-662 |#1|) |has| |#1| (-175)) ((-739 |#1|) |has| |#1| (-175)) ((-1083 |#1|) . T) ((-1088 |#1|) . T) ((-1133) . T) ((-1249) . T)) 
+((-2703 (($ $) NIL T ELT) (($ $ (-793)) 9 T ELT)) (-3095 (($ $) NIL T ELT) (($ $ (-793)) 11 T ELT))) 
+(((-238 |#1|) (-10 -8 (-15 -3095 (|#1| |#1| (-793))) (-15 -2703 (|#1| |#1| (-793))) (-15 -3095 (|#1| |#1|)) (-15 -2703 (|#1| |#1|))) (-239)) (T -238)) 
 NIL 
-(-10 -8 (-15 -4324 (|#1| |#1| (-793))) (-15 -2457 (|#1| |#1| (-793))) (-15 -4324 (|#1| |#1|)) (-15 -2457 (|#1| |#1|))) 
-((-2457 (($ $) 7 T ELT) (($ $ (-793)) 10 T ELT)) (-4324 (($ $) 6 T ELT) (($ $ (-793)) 9 T ELT))) 
+(-10 -8 (-15 -3095 (|#1| |#1| (-793))) (-15 -2703 (|#1| |#1| (-793))) (-15 -3095 (|#1| |#1|)) (-15 -2703 (|#1| |#1|))) 
+((-2703 (($ $) 7 T ELT) (($ $ (-793)) 10 T ELT)) (-3095 (($ $) 6 T ELT) (($ $ (-793)) 9 T ELT))) 
 (((-239) (-142)) (T -239)) 
-((-2457 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-793)))) (-4324 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-793))))) 
-(-13 (-236 $) (-10 -8 (-15 -2457 ($ $ (-793))) (-15 -4324 ($ $ (-793))))) 
-(((-236 $) . T) ((-1248) . T)) 
-((-2294 (((-114) $ $) 7 T ELT)) (-3626 (((-114) $) 21 T ELT)) (-2494 (((-3 $ "failed") $ $) 25 T ELT)) (-3366 (($) 22 T CONST)) (-4310 (((-3 $ "failed") $) 42 T ELT)) (-1871 (((-114) $) 40 T ELT)) (-3049 (((-1190) $) 11 T ELT)) (-3139 (((-1151) $) 12 T ELT)) (-2457 (($ $ (-793)) 47 T ELT) (($ $) 45 T ELT)) (-2539 (((-887) $) 13 T ELT) (($ (-560)) 38 T ELT)) (-3418 (((-793)) 37 T CONST)) (-3860 (((-114) $ $) 6 T ELT)) (-1427 (($) 23 T CONST)) (-1439 (($) 39 T CONST)) (-4324 (($ $ (-793)) 48 T ELT) (($ $) 46 T ELT)) (-2329 (((-114) $ $) 8 T ELT)) (-2426 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-2413 (($ $ $) 18 T ELT)) (** (($ $ (-948)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-948) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT))) 
+((-2703 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-793)))) (-3095 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-793))))) 
+(-13 (-236 $) (-10 -8 (-15 -2703 ($ $ (-793))) (-15 -3095 ($ $ (-793))))) 
+(((-236 $) . T) ((-1249) . T)) 
+((-3808 (((-114) $ $) 7 T ELT)) (-3136 (((-114) $) 21 T ELT)) (-1469 (((-3 $ "failed") $ $) 25 T ELT)) (-4489 (($) 22 T CONST)) (-2167 (((-3 $ "failed") $) 42 T ELT)) (-3363 (((-114) $) 40 T ELT)) (-2128 (((-1191) $) 11 T ELT)) (-1473 (((-1152) $) 12 T ELT)) (-2703 (($ $ (-793)) 47 T ELT) (($ $) 45 T ELT)) (-3834 (((-888) $) 13 T ELT) (($ (-560)) 38 T ELT)) (-3103 (((-793)) 37 T CONST)) (-1519 (((-114) $ $) 6 T ELT)) (-2971 (($) 23 T CONST)) (-2983 (($) 39 T CONST)) (-3095 (($ $ (-793)) 48 T ELT) (($ $) 46 T ELT)) (-2478 (((-114) $ $) 8 T ELT)) (-2581 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-2571 (($ $ $) 18 T ELT)) (** (($ $ (-949)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT))) 
 (((-240) (-142)) (T -240)) 
 NIL 
-(-13 (-1080) (-239)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-635 (-560)) . T) ((-632 (-887)) . T) ((-236 $) . T) ((-239) . T) ((-668 (-560)) . T) ((-668 $) . T) ((-670 $) . T) ((-748) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T)) 
-((-2694 (($) 12 T ELT) (($ (-663 |#2|)) NIL T ELT)) (-2721 (($ $) 14 T ELT)) (-2548 (($ (-663 |#2|)) 10 T ELT)) (-2539 (((-887) $) 21 T ELT))) 
-(((-241 |#1| |#2|) (-10 -8 (-15 -2539 ((-887) |#1|)) (-15 -2694 (|#1| (-663 |#2|))) (-15 -2694 (|#1|)) (-15 -2548 (|#1| (-663 |#2|))) (-15 -2721 (|#1| |#1|))) (-242 |#2|) (-1132)) (T -241)) 
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+(-13 (-1081) (-239)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-635 (-560)) . T) ((-632 (-888)) . T) ((-236 $) . T) ((-239) . T) ((-668 (-560)) . T) ((-668 $) . T) ((-670 $) . T) ((-748) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T)) 
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+NIL 
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+(((-246 |#1| |#2|) (-245 |#1| |#2|) (-793) (-1249)) (T -246)) 
 NIL 
 (-245 |#1| |#2|) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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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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-(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2191 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-302) |has| |#1| (-571)) ((-426 |#1|) . T) ((-571) |has| |#1| (-571)) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-571)) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-571)) ((-748) . T) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T)) 
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-((-3808 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1248)) (-5 *1 (-339 *3)))) (-2727 (*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-339 *3)) (-4 *3 (-1248)))) (-1706 (*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-339 *3)) (-4 *3 (-1248)))) (-1612 (*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-339 *3)) (-4 *3 (-1248))))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+NIL 
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 NIL 
 (-13 (-660 |t#1|) (-10 -7 (IF (|has| |t#1| (-660 (-560))) (-6 (-660 (-560))) |%noBranch|))) 
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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 
 (-349 |#1| |#2| |#3| |#4|) 
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 NIL 
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 NIL 
 (-57 |#1| |#4| |#5|) 
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 NIL 
 (-688 |#1|) 
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 NIL 
 (-708 |#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) 
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-NIL 
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+NIL 
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 (((-541) (-142)) (T -541)) 
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 (((-176) . T)) 
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+NIL 
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-((-2660 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-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| (-1186 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2132 (-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 (-574)))) (-3155 (*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| -3818 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2660 (-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| (-1186 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2132 (-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 (-574)))) (-3655 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-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| (-1186 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2132 (-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 (-574)))) (-1368 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -3818 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2660 (-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| (-1186 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2132 (-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 (-574)))) (-3878 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -3818 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| 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+(((-670 |#1|) (-142) (-1089)) (T -670)) 
 NIL 
 (-13 (-21) (-668 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-632 (-887)) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-1132) . T) ((-1248) . T)) 
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-NIL 
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-(((-34) . T) ((-102) -2191 (|has| |#1| (-1132)) (|has| |#1| (-102))) ((-632 (-887)) -2191 (|has| |#1| (-1132)) (|has| |#1| (-632 (-887)))) ((-153 |#1|) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-298 #0=(-560) |#1|) . T) ((-298 (-1265 (-560)) $) . T) ((-300 #0# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-503 |#1|) . T) ((-618 #0# |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-1132) |has| |#1| (-1132)) ((-1248) . T)) 
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-((-3824 (((-3 |#2| "failed") |#3| |#2| (-1208) |#2| (-663 |#2|)) 174 T ELT) (((-3 (-2 (|:| |particular| |#2|) (|:| -1868 (-663 |#2|))) "failed") |#3| |#2| (-1208)) 44 T ELT))) 
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 NIL 
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 (((-677 |#1|) (-680 |#1|) (-240)) (T -677)) 
 NIL 
 (-680 |#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 
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-NIL 
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-NIL 
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-NIL 
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 (((-871) (-142)) (T -871)) 
 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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+(((-1002) (-13 (-1115) (-10 -8 (-15 -3495 ((-1167) $)) (-15 -3804 ((-1250) $))))) (T -1002)) 
+((-3495 (*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1002)))) (-3804 (*1 *2 *1) (-12 (-5 *2 (-1250)) (-5 *1 (-1002))))) 
+(-13 (-1115) (-10 -8 (-15 -3495 ((-1167) $)) (-15 -3804 ((-1250) $)))) 
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+NIL 
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+(((-632 (-888)) . T)) 
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+NIL 
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 NIL 
 (-13 (-93)) 
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-NIL 
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+NIL 
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 NIL 
 (-277 |#1|) 
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-NIL 
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 NIL 
 (-440 |#1|) 
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-NIL 
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-NIL 
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-(((-1134) (-1135 (-1190) (-1208) (-560) (-229) (-887))) (T -1134)) 
-NIL 
-(-1135 (-1190) (-1208) (-560) (-229) (-887)) 
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-(((-102) . T) ((-632 (-887)) . T) ((-637 (-663 $)) . T) ((-637 |#1|) . T) ((-637 |#2|) . T) ((-637 |#3|) . T) ((-637 |#4|) . T) ((-637 |#5|) . T) ((-298 (-560) $) . T) ((-298 (-663 (-560)) $) . T) ((-1132) . T) ((-1248) . T)) 
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-NIL 
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 NIL 
 (-245 |#1| |#3|) 
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-NIL 
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+NIL 
+(-13 (-1141 |t#1| |t#2| |t#3| |t#4|) (-806 |t#1| |t#2| |t#3| |t#4|)) 
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 NIL 
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-NIL 
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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1208) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1208) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2191 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2191 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1208)) -2191 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-927 (-1208)) -2191 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-929 #4#) -2191 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-911 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-560)))) ((-909 |#2|) |has| |#1| (-376)) ((-939) -12 (|has| |#1| (-376)) (|has| |#2| (-939))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1208)))) ((-1069 |#2|) . T) ((-1082 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1253) |has| |#1| (-376)) ((-1260 |#1|) . T) ((-1277 |#1| #0#) . T)) 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-793) (-1143)) ((-302) |has| |#1| (-571)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) |has| |#1| (-571)) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-571)) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-571)) ((-748) . T) ((-921 $ #2=(-1208)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208)))) ((-1004 |#1| #0# (-1113)) . T) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1277 |#1| #0#) . T)) 
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-NIL 
-(((-1294) (-142)) (T -1294)) 
-NIL 
-(-13 (-10 -7 (-6 -2908))) 
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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 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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"WFFINTBS" 3417155 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1307 3414100 3414563 3415025 "WEIER" 3415804 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1306 3413024 3413582 3413624 "VSPACE" 3413760 NIL VSPACE (NIL T) -9 NIL 3413834 NIL) (-1305 3412856 3412889 3412980 "VSPACE-" 3412985 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1304 3412653 3412707 3412775 "VOID" 3412810 T VOID (NIL) -8 NIL NIL NIL) (-1303 3408921 3409716 3410453 "VIEWDEF" 3411938 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1302 3397865 3400469 3402642 "VIEW3D" 3406770 T VIEW3D (NIL) -8 NIL NIL NIL) (-1301 3389882 3391776 3393355 "VIEW2D" 3396308 T VIEW2D (NIL) -8 NIL NIL NIL) (-1300 3387982 3388377 3388783 "VIEW" 3389498 T VIEW (NIL) -7 NIL NIL NIL) (-1299 3386535 3386818 3387136 "VECTOR2" 3387712 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1298 3381441 3386305 3386397 "VECTOR" 3386478 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3374386 3379145 3379188 "VECTCAT" 3380183 NIL VECTCAT (NIL T) -9 NIL 3380770 NIL) (-1296 3373328 3373654 3374044 "VECTCAT-" 3374049 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1295 3372734 3372979 3373099 "VARIABLE" 3373243 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1294 3372667 3372672 3372702 "UTYPE" 3372707 T UTYPE (NIL) -9 NIL NIL NIL) (-1293 3371475 3371651 3371913 "UTSODETL" 3372493 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1292 3368867 3369375 3369899 "UTSODE" 3371016 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1291 3358877 3364800 3364843 "UTSCAT" 3365955 NIL UTSCAT (NIL T) -9 NIL 3366713 NIL) (-1290 3356003 3356947 3357936 "UTSCAT-" 3357941 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1289 3355624 3355673 3355806 "UTS2" 3355954 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1288 3346941 3353385 3353865 "UTS" 3355202 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1287 3340808 3343751 3343794 "URAGG" 3345864 NIL URAGG (NIL T) -9 NIL 3346587 NIL) (-1286 3337531 3338610 3339733 "URAGG-" 3339738 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1285 3332907 3336166 3336631 "UPXSSING" 3337195 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1284 3325336 3332811 3332883 "UPXSCONS" 3332888 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1283 3314094 3321538 3321600 "UPXSCCA" 3322174 NIL UPXSCCA (NIL T T) -9 NIL 3322407 NIL) (-1282 3313714 3313817 3313991 "UPXSCCA-" 3313996 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1281 3302372 3309541 3309584 "UPXSCAT" 3310232 NIL UPXSCAT (NIL T) -9 NIL 3310841 NIL) (-1280 3301796 3301881 3302060 "UPXS2" 3302287 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1279 3293288 3301178 3301442 "UPXS" 3301590 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1278 3291924 3292195 3292546 "UPSQFREE" 3293031 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1277 3284755 3288190 3288245 "UPSCAT" 3289325 NIL UPSCAT (NIL T T) -9 NIL 3290091 NIL) (-1276 3283911 3284166 3284493 "UPSCAT-" 3284498 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1275 3283532 3283581 3283714 "UPOLYC2" 3283862 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3267680 3276659 3276702 "UPOLYC" 3278803 NIL UPOLYC (NIL T) -9 NIL 3280024 NIL) (-1273 3258549 3261448 3264588 "UPOLYC-" 3264593 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3257870 3257995 3258159 "UPMP" 3258438 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1271 3257417 3257504 3257643 "UPDIVP" 3257783 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1270 3255955 3256234 3256550 "UPDECOMP" 3257166 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1269 3255168 3255298 3255484 "UPCDEN" 3255839 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1268 3254681 3254756 3254905 "UP2" 3255093 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1267 3245277 3254364 3254493 "UP" 3254600 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1266 3244482 3244619 3244824 "UNISEG2" 3245120 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1265 3242835 3243686 3243963 "UNISEG" 3244240 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3241877 3242075 3242301 "UNIFACT" 3242651 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1263 3228608 3241781 3241853 "ULSCONS" 3241858 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1262 3208425 3221688 3221750 "ULSCCAT" 3222388 NIL ULSCCAT (NIL T T) -9 NIL 3222677 NIL) (-1261 3207421 3207720 3208108 "ULSCCAT-" 3208113 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1260 3195876 3202967 3203010 "ULSCAT" 3203873 NIL ULSCAT (NIL T) -9 NIL 3204604 NIL) (-1259 3195300 3195385 3195564 "ULS2" 3195791 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1258 3177131 3194612 3194854 "ULS" 3195116 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1257 3176050 3176750 3176864 "UINT8" 3176975 T UINT8 (NIL) -8 NIL NIL 3177067) (-1256 3174968 3175668 3175782 "UINT64" 3175893 T UINT64 (NIL) -8 NIL NIL 3175985) (-1255 3173886 3174586 3174700 "UINT32" 3174811 T UINT32 (NIL) -8 NIL NIL 3174903) (-1254 3172804 3173504 3173618 "UINT16" 3173729 T UINT16 (NIL) -8 NIL NIL 3173821) (-1253 3170883 3172050 3172080 "UFD" 3172292 T UFD (NIL) -9 NIL 3172406 NIL) (-1252 3170665 3170723 3170818 "UFD-" 3170823 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1251 3169723 3169930 3170146 "UDVO" 3170471 T UDVO (NIL) -7 NIL NIL NIL) (-1250 3167489 3167948 3168419 "UDPO" 3169287 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1249 3167201 3167444 3167475 "TYPEAST" 3167480 T TYPEAST (NIL) -8 NIL NIL NIL) (-1248 3167134 3167139 3167169 "TYPE" 3167174 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3166087 3166307 3166547 "TWOFACT" 3166928 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1246 3165062 3165496 3165731 "TUPLE" 3165887 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1245 3162699 3163272 3163811 "TUBETOOL" 3164545 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1244 3161505 3161746 3161988 "TUBE" 3162492 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1243 3149640 3154262 3154359 "TSETCAT" 3159628 NIL TSETCAT (NIL T T T T) -9 NIL 3161160 NIL) (-1242 3144108 3145972 3147863 "TSETCAT-" 3147868 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1241 3138294 3143080 3143363 "TS" 3143860 NIL TS (NIL T) -8 NIL NIL NIL) (-1240 3132767 3133780 3134709 "TRMANIP" 3137430 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1239 3132196 3132271 3132434 "TRIMAT" 3132699 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1238 3130008 3130299 3130656 "TRIGMNIP" 3131945 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1237 3129492 3129641 3129671 "TRIGCAT" 3129884 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1236 3129137 3129240 3129381 "TRIGCAT-" 3129386 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1235 3125751 3127995 3128276 "TREE" 3128891 NIL TREE (NIL T) -8 NIL NIL NIL) (-1234 3124857 3125553 3125583 "TRANFUN" 3125618 T TRANFUN (NIL) -9 NIL 3125684 NIL) (-1233 3124076 3124327 3124607 "TRANFUN-" 3124612 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1232 3123874 3123912 3123973 "TOPSP" 3124037 T TOPSP (NIL) -7 NIL NIL NIL) (-1231 3123204 3123337 3123491 "TOOLSIGN" 3123755 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1230 3121718 3122381 3122620 "TEXTFILE" 3122987 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1229 3121493 3121530 3121602 "TEX1" 3121681 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1228 3119297 3119946 3120375 "TEX" 3121086 T TEX (NIL) -8 NIL NIL NIL) (-1227 3118933 3119008 3119098 "TEMUTL" 3119229 T TEMUTL (NIL) -7 NIL NIL NIL) (-1226 3117027 3117367 3117692 "TBCMPPK" 3118656 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1225 3108347 3115113 3115169 "TBAGG" 3115569 NIL TBAGG (NIL T T) -9 NIL 3115780 NIL) (-1224 3103231 3104905 3106659 "TBAGG-" 3106664 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1223 3102597 3102722 3102867 "TANEXP" 3103120 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1222 3102048 3102372 3102462 "TALGOP" 3102542 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1221 3101442 3101559 3101697 "TABLEAU" 3101945 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1220 3094456 3101299 3101392 "TABLE" 3101397 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3088986 3090284 3091532 "TABLBUMP" 3093242 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1218 3088196 3088355 3088536 "SYSTEM" 3088827 T SYSTEM (NIL) -8 NIL NIL NIL) (-1217 3084601 3085354 3086137 "SYSSOLP" 3087447 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1216 3084363 3084556 3084587 "SYSPTR" 3084592 T SYSPTR (NIL) -8 NIL NIL NIL) (-1215 3083202 3083894 3084020 "SYSNNI" 3084206 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084298) (-1214 3082409 3082964 3083043 "SYSINT" 3083103 NIL SYSINT (NIL NIL) -8 NIL NIL 3083148) (-1213 3078507 3079687 3080397 "SYNTAX" 3081721 T SYNTAX (NIL) -8 NIL NIL NIL) (-1212 3075587 3076267 3076899 "SYMTAB" 3077897 T SYMTAB (NIL) -8 NIL NIL NIL) (-1211 3070686 3071738 3072721 "SYMS" 3074626 T SYMS (NIL) -8 NIL NIL NIL) (-1210 3067592 3070137 3070370 "SYMPOLY" 3070488 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1209 3067097 3067184 3067307 "SYMFUNC" 3067504 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1208 3062895 3064409 3065222 "SYMBOL" 3066306 T SYMBOL (NIL) -8 NIL NIL NIL) (-1207 3056368 3058123 3059843 "SWITCH" 3061197 T SWITCH (NIL) -8 NIL NIL NIL) (-1206 3049129 3055324 3055618 "SUTS" 3056132 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040621 3048511 3048775 "SUPXS" 3048923 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3039768 3039907 3040124 "SUPFRACF" 3040489 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1203 3039383 3039448 3039561 "SUP2" 3039703 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1202 3029927 3039001 3039127 "SUP" 3039292 NIL SUP (NIL T) -8 NIL NIL NIL) (-1201 3028351 3028649 3029005 "SUMRF" 3029626 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1200 3027674 3027752 3027944 "SUMFS" 3028272 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1199 3009540 3026986 3027228 "SULS" 3027490 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 3009088 3009362 3009432 "SUCHTAST" 3009492 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1197 3008329 3008613 3008753 "SUCH" 3008996 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1196 3001968 3003235 3004194 "SUBSPACE" 3007417 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1195 3001388 3001488 3001652 "SUBRESP" 3001856 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1194 2995399 2996681 2997828 "STTFNC" 3000288 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1193 2988593 2990064 2991375 "STTF" 2994135 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2979710 2981775 2983569 "STTAYLOR" 2986834 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1191 2972464 2979574 2979657 "STRTBL" 2979662 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1190 2966861 2972173 2972272 "STRING" 2972387 T STRING (NIL) -8 NIL NIL NIL) (-1189 2966365 2966448 2966592 "STREAM3" 2966778 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1188 2965329 2965530 2965765 "STREAM2" 2966178 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1187 2965011 2965069 2965162 "STREAM1" 2965271 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1186 2957125 2962630 2963241 "STREAM" 2964435 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1185 2956117 2956322 2956553 "STINPROD" 2956941 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1184 2955232 2955606 2955754 "STEPAST" 2955991 T STEPAST (NIL) -8 NIL NIL NIL) (-1183 2954728 2954973 2955003 "STEP" 2955097 T STEP (NIL) -9 NIL 2955168 NIL) (-1182 2947784 2954627 2954704 "STBL" 2954709 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1181 2942334 2946947 2946990 "STAGG" 2947143 NIL STAGG (NIL T) -9 NIL 2947232 NIL) (-1180 2939886 2940638 2941510 "STAGG-" 2941515 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1179 2937858 2939656 2939748 "STACK" 2939829 NIL STACK (NIL T) -8 NIL NIL NIL) (-1178 2937175 2937688 2937718 "SRING" 2937723 T SRING (NIL) -9 NIL 2937743 NIL) (-1177 2929182 2935316 2935772 "SREGSET" 2936805 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2921529 2922976 2924489 "SRDCMPK" 2927788 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2913829 2918888 2918918 "SRAGG" 2920221 T SRAGG (NIL) -9 NIL 2920829 NIL) (-1174 2912780 2913101 2913480 "SRAGG-" 2913485 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2906364 2911727 2912148 "SQMATRIX" 2912406 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2899776 2903082 2903809 "SPLTREE" 2905709 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2895601 2896432 2897078 "SPLNODE" 2899202 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2894576 2894881 2894911 "SPFCAT" 2895355 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2893271 2893523 2893787 "SPECOUT" 2894334 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2883917 2886235 2886265 "SPADXPT" 2890943 T SPADXPT (NIL) -9 NIL 2893109 NIL) (-1167 2883672 2883718 2883787 "SPADPRSR" 2883870 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2881275 2883627 2883658 "SPADAST" 2883663 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2872876 2874979 2875022 "SPACEC" 2879395 NIL SPACEC (NIL T) -9 NIL 2881211 NIL) (-1164 2870676 2872808 2872857 "SPACE3" 2872862 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2869408 2869599 2869890 "SORTPAK" 2870481 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2867470 2867803 2868215 "SOLVETRA" 2869072 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2866508 2866742 2867003 "SOLVESER" 2867243 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2861740 2862700 2863695 "SOLVERAD" 2865560 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2857465 2858164 2858893 "SOLVEFOR" 2861107 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2851069 2856813 2856910 "SNTSCAT" 2856915 NIL SNTSCAT (NIL T T T T) -9 NIL 2856985 NIL) (-1157 2844620 2849392 2849783 "SMTS" 2850759 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2838342 2844508 2844585 "SMP" 2844590 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2836471 2836802 2837200 "SMITH" 2838039 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2827996 2833050 2833153 "SMATCAT" 2834504 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835054 NIL) (-1153 2824768 2825759 2826937 "SMATCAT-" 2826942 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2822237 2823976 2824019 "SKAGG" 2824280 NIL SKAGG (NIL T) -9 NIL 2824415 NIL) (-1151 2817755 2821720 2821897 "SINT" 2822049 T SINT (NIL) -8 NIL NIL 2822204) (-1150 2817521 2817565 2817631 "SIMPAN" 2817711 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2816341 2816580 2816855 "SIGNRF" 2817280 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2815156 2815325 2815609 "SIGNEF" 2816170 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2814396 2814739 2814863 "SIGAST" 2815054 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2813621 2813931 2814071 "SIG" 2814278 T SIG (NIL) -8 NIL NIL NIL) (-1145 2811273 2811765 2812271 "SHP" 2813162 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2804646 2811174 2811250 "SHDP" 2811255 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2804157 2804397 2804427 "SGROUP" 2804520 T SGROUP (NIL) -9 NIL 2804582 NIL) (-1142 2804009 2804041 2804114 "SGROUP-" 2804119 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2800728 2801498 2802221 "SGCF" 2803308 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2794430 2800174 2800271 "SFRTCAT" 2800276 NIL SFRTCAT (NIL T T T T) -9 NIL 2800315 NIL) (-1139 2787749 2788869 2790005 "SFRGCD" 2793413 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2780767 2781948 2783134 "SFQCMPK" 2786682 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2780369 2780476 2780587 "SFORT" 2780708 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2779295 2780209 2780330 "SEXOF" 2780335 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2774884 2775791 2775886 "SEXCAT" 2778508 NIL SEXCAT (NIL T T T T T) -9 NIL 2779068 NIL) (-1134 2773799 2774765 2774833 "SEX" 2774838 T SEX (NIL) -8 NIL NIL NIL) (-1133 2771921 2772512 2772817 "SETMN" 2773540 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2771451 2771639 2771669 "SETCAT" 2771786 T SETCAT (NIL) -9 NIL 2771871 NIL) (-1131 2771219 2771283 2771382 "SETCAT-" 2771387 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2767322 2769680 2769723 "SETAGG" 2770593 NIL SETAGG (NIL T) -9 NIL 2770933 NIL) (-1129 2766744 2766896 2767133 "SETAGG-" 2767138 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2763553 2766678 2766726 "SET" 2766731 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2762936 2763249 2763350 "SEQAST" 2763474 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2762063 2762429 2762490 "SEGXCAT" 2762776 NIL SEGXCAT (NIL T T) -9 NIL 2762896 NIL) (-1125 2760988 2761256 2761299 "SEGCAT" 2761821 NIL SEGCAT (NIL T) -9 NIL 2762042 NIL) (-1124 2760603 2760668 2760781 "SEGBIND2" 2760923 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2759493 2759966 2760174 "SEGBIND" 2760430 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759012 2759294 2759371 "SEGAST" 2759438 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2758221 2758357 2758561 "SEG2" 2758856 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2757137 2757887 2758069 "SEG" 2758074 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2756370 2757072 2757119 "SDVAR" 2757124 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2747728 2756140 2756270 "SDPOL" 2756275 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2746297 2746587 2746906 "SCPKG" 2747443 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2745419 2745633 2745825 "SCOPE" 2746127 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2744615 2744773 2744952 "SCACHE" 2745274 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2744199 2744433 2744463 "SASTCAT" 2744468 T SASTCAT (NIL) -9 NIL 2744481 NIL) (-1113 2743602 2744034 2744110 "SAOS" 2744145 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2743161 2743202 2743375 "SAERFFC" 2743561 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2742748 2742789 2742948 "SAEFACT" 2743120 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2735796 2742645 2742725 "SAE" 2742730 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2734099 2734431 2734832 "RURPK" 2735462 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2732676 2733042 2733347 "RULESET" 2733933 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2732246 2732470 2732553 "RULECOLD" 2732628 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2729361 2729999 2730457 "RULE" 2731927 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2729145 2729179 2729250 "RTVALUE" 2729312 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2728556 2728862 2728956 "RSTRCAST" 2729073 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2723326 2724199 2725119 "RSETGCD" 2727755 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2711890 2717634 2717731 "RSETCAT" 2721850 NIL RSETCAT (NIL T T T T) -9 NIL 2722947 NIL) (-1101 2709709 2710356 2711180 "RSETCAT-" 2711185 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2702017 2703471 2704991 "RSDCMPK" 2708308 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2699886 2700449 2700523 "RRCC" 2701609 NIL RRCC (NIL T T) -9 NIL 2701953 NIL) (-1098 2699207 2699411 2699690 "RRCC-" 2699695 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2698590 2698903 2699004 "RPTAST" 2699128 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2670976 2681702 2681769 "RPOLCAT" 2692435 NIL RPOLCAT (NIL T T T) -9 NIL 2695595 NIL) (-1095 2661946 2664814 2667936 "RPOLCAT-" 2667941 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2652399 2660157 2660639 "ROUTINE" 2661486 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2648462 2652025 2652165 "ROMAN" 2652281 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2646574 2647322 2647582 "ROIRC" 2648267 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2642294 2645063 2645093 "RNS" 2645397 T RNS (NIL) -9 NIL 2645671 NIL) (-1090 2640701 2641186 2641720 "RNS-" 2641795 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2639662 2640066 2640268 "RNGBIND" 2640552 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2638955 2639459 2639489 "RNG" 2639494 T RNG (NIL) -9 NIL 2639515 NIL) (-1087 2638250 2638728 2638771 "RMODULE" 2638776 NIL RMODULE (NIL T) -9 NIL 2638803 NIL) (-1086 2637074 2637180 2637516 "RMCAT2" 2638151 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2633576 2636420 2636717 "RMATRIX" 2636836 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2626075 2628663 2628778 "RMATCAT" 2632137 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633119 NIL) (-1083 2625414 2625597 2625904 "RMATCAT-" 2625909 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2624987 2625201 2625244 "RLINSET" 2625306 NIL RLINSET (NIL T) -9 NIL 2625350 NIL) (-1081 2624548 2624629 2624757 "RINTERP" 2624906 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2623472 2624146 2624176 "RING" 2624232 T RING (NIL) -9 NIL 2624324 NIL) (-1079 2623252 2623308 2623405 "RING-" 2623410 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2622063 2622330 2622588 "RIDIST" 2623016 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2612688 2621531 2621737 "RGCHAIN" 2621911 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2611946 2612430 2612471 "RGBCSPC" 2612529 NIL RGBCSPC (NIL T) -9 NIL 2612581 NIL) (-1075 2611012 2611471 2611512 "RGBCMDL" 2611744 NIL RGBCMDL (NIL T) -9 NIL 2611858 NIL) (-1074 2610652 2610721 2610824 "RFFACTOR" 2610943 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2610371 2610412 2610509 "RFFACT" 2610611 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2608422 2608852 2609234 "RFDIST" 2610011 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2605362 2606030 2606700 "RF" 2607786 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2604809 2604907 2605070 "RETSOL" 2605264 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2604427 2604525 2604568 "RETRACT" 2604701 NIL RETRACT (NIL T) -9 NIL 2604788 NIL) (-1068 2604270 2604301 2604388 "RETRACT-" 2604393 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2603818 2604092 2604162 "RETAST" 2604222 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2596168 2603471 2603598 "RESULT" 2603713 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2594603 2595437 2595636 "RESRING" 2596071 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2594227 2594288 2594386 "RESLATC" 2594540 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2593926 2593967 2594074 "REPSQ" 2594186 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2593617 2593658 2593769 "REPDB" 2593885 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2587449 2588906 2590129 "REP2" 2592429 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2583752 2584507 2585315 "REP1" 2586676 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2581132 2581754 2582356 "REP" 2583172 T REP (NIL) -7 NIL NIL NIL) (-1058 2573140 2579273 2579729 "REGSET" 2580762 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2571849 2572288 2572538 "REF" 2572925 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2571214 2571329 2571496 "REDORDER" 2571733 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2566585 2570427 2570654 "RECLOS" 2571042 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2565619 2565818 2566033 "REALSOLV" 2566392 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2562066 2562904 2563788 "REAL0Q" 2564784 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2557619 2558655 2559716 "REAL0" 2561047 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2557453 2557506 2557536 "REAL" 2557541 T REAL (NIL) -9 NIL 2557576 NIL) (-1050 2556864 2557170 2557264 "RDUCEAST" 2557381 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2556263 2556341 2556548 "RDIV" 2556786 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2555313 2555505 2555718 "RDIST" 2556085 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2553898 2554197 2554569 "RDETRS" 2555021 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2551692 2552164 2552702 "RDETR" 2553440 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2550311 2550595 2550992 "RDEEFS" 2551408 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2548814 2549126 2549551 "RDEEF" 2549999 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2542293 2545768 2545798 "RCFIELD" 2547093 T RCFIELD (NIL) -9 NIL 2547824 NIL) (-1042 2540249 2540861 2541557 "RCFIELD-" 2541632 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2536301 2538322 2538365 "RCAGG" 2539449 NIL RCAGG (NIL T) -9 NIL 2539914 NIL) (-1040 2535911 2536023 2536186 "RCAGG-" 2536191 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2535228 2535358 2535523 "RATRET" 2535795 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2534769 2534848 2534969 "RATFACT" 2535156 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2534047 2534197 2534349 "RANDSRC" 2534639 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2533775 2533825 2533898 "RADUTIL" 2533996 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2525920 2532606 2532917 "RADIX" 2533498 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2515535 2525762 2525892 "RADFF" 2525897 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2515164 2515257 2515287 "RADCAT" 2515447 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2514934 2514994 2515094 "RADCAT-" 2515099 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2512845 2514704 2514796 "QUEUE" 2514877 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2512470 2512519 2512650 "QUATCT2" 2512796 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2504848 2508893 2508935 "QUATCAT" 2509726 NIL QUATCAT (NIL T) -9 NIL 2510492 NIL) (-1028 2500729 2502024 2503414 "QUATCAT-" 2503510 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2496575 2500662 2500710 "QUAT" 2500715 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2493831 2495623 2495666 "QUAGG" 2496047 NIL QUAGG (NIL T) -9 NIL 2496222 NIL) (-1025 2493379 2493653 2493723 "QQUTAST" 2493783 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2492290 2492892 2493057 "QFORM" 2493260 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2491915 2491964 2492095 "QFCAT2" 2492241 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2481612 2487762 2487804 "QFCAT" 2488472 NIL QFCAT (NIL T) -9 NIL 2489473 NIL) (-1021 2476946 2478394 2479981 "QFCAT-" 2480077 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2476377 2476511 2476643 "QEQUAT" 2476836 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2469395 2470576 2471762 "QCMPACK" 2475310 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2468624 2468806 2469042 "QALGSET2" 2469213 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2466074 2466610 2467040 "QALGSET" 2468279 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2464741 2464983 2465302 "PWFFINTB" 2465847 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2462886 2463084 2463440 "PUSHVAR" 2464555 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2458613 2459829 2459872 "PTRANFN" 2461783 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2456950 2457295 2457619 "PTPACK" 2458324 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2456573 2456636 2456747 "PTFUNC2" 2456887 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2450489 2455362 2455405 "PTCAT" 2455705 NIL PTCAT (NIL T) -9 NIL 2455858 NIL) (-1010 2450138 2450179 2450305 "PSQFR" 2450448 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2448710 2449026 2449362 "PSEUDLIN" 2449836 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2435230 2437805 2440131 "PSETPK" 2446470 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2427938 2430966 2431064 "PSETCAT" 2434105 NIL PSETCAT (NIL T T T T) -9 NIL 2434919 NIL) (-1006 2425663 2426405 2427229 "PSETCAT-" 2427234 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2424976 2425171 2425201 "PSCURVE" 2425473 T PSCURVE (NIL) -9 NIL 2425640 NIL) (-1004 2420699 2422466 2422533 "PSCAT" 2423385 NIL PSCAT (NIL T T T) -9 NIL 2423625 NIL) (-1003 2419693 2419975 2420378 "PSCAT-" 2420383 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2417892 2418752 2419017 "PRTITION" 2419450 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2417303 2417609 2417703 "PRTDAST" 2417820 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2406147 2408569 2410759 "PRS" 2415165 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2403767 2405469 2405509 "PRQAGG" 2405692 NIL PRQAGG (NIL T) -9 NIL 2405794 NIL) (-998 2402946 2403395 2403423 "PROPLOG" 2403562 T PROPLOG (NIL) -9 NIL 2403677 NIL) (-997 2402544 2402607 2402730 "PROPFUN2" 2402869 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2401841 2401980 2402152 "PROPFUN1" 2402405 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2399822 2400588 2400885 "PROPFRML" 2401577 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2399267 2399398 2399526 "PROPERTY" 2399714 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2393155 2397433 2398253 "PRODUCT" 2398493 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2392945 2392983 2393042 "PRINT" 2393116 T PRINT (NIL) -7 NIL NIL NIL) (-991 2392261 2392402 2392554 "PRIMES" 2392825 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2390308 2390727 2391193 "PRIMELT" 2391840 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2390025 2390086 2390114 "PRIMCAT" 2390238 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2389014 2389210 2389438 "PRIMARR2" 2389843 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2384736 2388952 2388997 "PRIMARR" 2389002 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2384373 2384435 2384546 "PREASSOC" 2384674 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2381338 2383831 2384065 "PR" 2384184 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2380789 2380946 2380974 "PPCURVE" 2381179 T PPCURVE (NIL) -9 NIL 2381315 NIL) (-983 2380336 2380584 2380667 "PORTNUM" 2380726 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2377673 2378094 2378686 "POLYROOT" 2379917 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2377050 2377114 2377348 "POLYLIFT" 2377609 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2373271 2373774 2374403 "POLYCATQ" 2376595 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2358919 2365018 2365083 "POLYCAT" 2368597 NIL POLYCAT (NIL T T T) -9 NIL 2370475 NIL) (-978 2352059 2354244 2356621 "POLYCAT-" 2356626 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2351640 2351714 2351834 "POLY2UP" 2351985 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2351266 2351329 2351438 "POLY2" 2351577 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2344481 2350870 2351030 "POLY" 2351139 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2343142 2343405 2343681 "POLUTIL" 2344255 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2341461 2341774 2342105 "POLTOPOL" 2342864 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2336457 2341395 2341442 "POINT" 2341447 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2334590 2335001 2335376 "PNTHEORY" 2336102 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333036 2333345 2333744 "PMTOOLS" 2334288 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2332623 2332707 2332824 "PMSYM" 2332952 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2332125 2332200 2332375 "PMQFCAT" 2332548 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2331506 2331604 2331766 "PMPREDFS" 2332026 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2330849 2330971 2331127 "PMPRED" 2331383 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2329503 2329721 2330099 "PMPLCAT" 2330611 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329029 2329114 2329266 "PMLSAGG" 2329418 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2328496 2328578 2328760 "PMKERNEL" 2328947 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328107 2328188 2328301 "PMINS" 2328415 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2327543 2327618 2327827 "PMFS" 2328032 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2326759 2326889 2327094 "PMDOWN" 2327420 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326008 2326142 2326305 "PMASSFS" 2326646 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2325151 2325333 2325514 "PMASS" 2325847 T PMASS (NIL) -7 NIL NIL NIL) (-957 2324800 2324874 2324968 "PLOTTOOL" 2325077 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320452 2321646 2322568 "PLOT3D" 2323898 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2319340 2319541 2319776 "PLOT1" 2320256 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2313761 2315151 2316299 "PLOT" 2318212 T PLOT (NIL) -8 NIL NIL NIL) (-953 2288936 2293827 2298678 "PLEQN" 2309027 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2288623 2288676 2288779 "PINTERPA" 2288883 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2287929 2288063 2288243 "PINTERP" 2288488 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2286013 2287179 2287207 "PID" 2287404 T PID (NIL) -9 NIL 2287531 NIL) (-949 2285758 2285801 2285876 "PICOERCE" 2285970 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2284854 2285522 2285609 "PI" 2285649 T PI (NIL) -8 NIL NIL 2285716) (-947 2284162 2284313 2284489 "PGROEB" 2284710 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2279601 2280560 2281466 "PGE" 2283276 T PGE (NIL) -7 NIL NIL NIL) (-945 2277682 2277971 2278337 "PGCD" 2279318 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277008 2277123 2277284 "PFRPAC" 2277566 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2273266 2275556 2275909 "PFR" 2276687 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2271619 2271899 2272224 "PFOTOOLS" 2273013 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270134 2270391 2270742 "PFOQ" 2271376 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2268617 2268847 2269203 "PFO" 2269918 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2265701 2267207 2267235 "PFECAT" 2267828 T PFECAT (NIL) -9 NIL 2268205 NIL) (-938 2265149 2265314 2265521 "PFECAT-" 2265526 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2263722 2264004 2264305 "PFBRU" 2264898 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2261551 2261940 2262372 "PFBR" 2263373 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2257497 2261440 2261509 "PF" 2261514 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2252551 2253704 2254574 "PERMGRP" 2256660 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2250463 2251575 2251616 "PERMCAT" 2252016 NIL PERMCAT (NIL T) -9 NIL 2252314 NIL) (-932 2250110 2250157 2250281 "PERMAN" 2250416 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2245912 2247619 2248267 "PERM" 2249495 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2243153 2245577 2245699 "PENDTREE" 2245823 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242034 2242297 2242338 "PDSPC" 2242871 NIL PDSPC (NIL T) -9 NIL 2243116 NIL) (-928 2241089 2241355 2241717 "PDSPC-" 2241722 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2239803 2240739 2240780 "PDRING" 2240785 NIL PDRING (NIL T) -9 NIL 2240813 NIL) (-926 2238546 2239308 2239362 "PDMOD" 2239367 NIL PDMOD (NIL T T) -9 NIL 2239471 NIL) (-925 2235713 2236539 2237207 "PDEPROB" 2237898 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2233222 2233762 2234317 "PDEPACK" 2235178 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232110 2232324 2232575 "PDECOMP" 2233021 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2229627 2230518 2230546 "PDECAT" 2231333 T PDECAT (NIL) -9 NIL 2232046 NIL) (-921 2229244 2229311 2229365 "PDDOM" 2229530 NIL PDDOM (NIL T T) -9 NIL 2229610 NIL) (-920 2229057 2229093 2229200 "PDDOM-" 2229205 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2228802 2228841 2228931 "PCOMP" 2229018 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2226842 2227603 2227900 "PBWLB" 2228531 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2226468 2226531 2226640 "PATTERN2" 2226779 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2224177 2224613 2225070 "PATTERN1" 2226057 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2216356 2218250 2219588 "PATTERN" 2222860 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2215914 2215987 2216119 "PATRES2" 2216283 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2213180 2213863 2214344 "PATRES" 2215479 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211033 2211468 2211875 "PATMATCH" 2212847 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2210487 2210738 2210779 "PATMAB" 2210886 NIL PATMAB (NIL T) -9 NIL 2210969 NIL) (-910 2208933 2209341 2209599 "PATLRES" 2210292 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2208471 2208602 2208643 "PATAB" 2208648 NIL PATAB (NIL T) -9 NIL 2208820 NIL) (-908 2206611 2207048 2207471 "PARTPERM" 2208068 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2206220 2206295 2206397 "PARSURF" 2206542 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2205846 2205909 2206018 "PARSU2" 2206157 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2205604 2205650 2205717 "PARSER" 2205799 T PARSER (NIL) -7 NIL NIL NIL) (-904 2205213 2205288 2205390 "PARSCURV" 2205535 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2204839 2204902 2205011 "PARSC2" 2205150 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2204466 2204536 2204633 "PARPCURV" 2204775 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204092 2204155 2204264 "PARPC2" 2204403 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203081 2203465 2203647 "PARAMAST" 2203930 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2202589 2202687 2202806 "PAN2EXPR" 2202982 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2201282 2201710 2201938 "PALETTE" 2202381 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2199627 2200287 2200647 "PAIR" 2200968 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2192560 2198884 2199079 "PADICRC" 2199481 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2184817 2191904 2192089 "PADICRAT" 2192407 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2181614 2183477 2183517 "PADICCT" 2184098 NIL PADICCT (NIL NIL) -9 NIL 2184380 NIL) (-893 2179630 2181551 2181596 "PADIC" 2181601 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2178575 2178787 2179055 "PADEPAC" 2179417 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2177775 2177920 2178126 "PADE" 2178437 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176008 2176983 2177263 "OWP" 2177579 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2175453 2175714 2175811 "OVERSET" 2175931 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2174373 2175058 2175230 "OVAR" 2175321 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2162609 2165482 2167682 "OUTFORM" 2172193 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2161891 2162206 2162333 "OUTBFILE" 2162502 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2161168 2161363 2161391 "OUTBCON" 2161709 T OUTBCON (NIL) -9 NIL 2161875 NIL) (-884 2160751 2160881 2161038 "OUTBCON-" 2161043 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2159991 2160136 2160297 "OUT" 2160610 T OUT (NIL) -7 NIL NIL NIL) (-882 2159287 2159720 2159809 "OSI" 2159922 T OSI (NIL) -8 NIL NIL NIL) (-881 2158706 2159128 2159156 "OSGROUP" 2159161 T OSGROUP (NIL) -9 NIL 2159183 NIL) (-880 2157417 2157678 2157963 "ORTHPOL" 2158453 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2154668 2157252 2157373 "OREUP" 2157378 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2151771 2154359 2154486 "ORESUP" 2154610 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2149271 2149799 2150360 "OREPCTO" 2151260 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2142649 2145144 2145185 "OREPCAT" 2147533 NIL OREPCAT (NIL T) -9 NIL 2148637 NIL) (-875 2139622 2140578 2141636 "OREPCAT-" 2141641 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2138814 2139092 2139120 "ORDTYPE" 2139429 T ORDTYPE (NIL) -9 NIL 2139592 NIL) (-873 2138115 2138331 2138586 "ORDTYPE-" 2138591 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2137471 2137854 2138012 "ORDSTRCT" 2138017 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2136969 2137339 2137367 "ORDSET" 2137372 T ORDSET (NIL) -9 NIL 2137394 NIL) (-870 2135327 2136298 2136326 "ORDRING" 2136528 T ORDRING (NIL) -9 NIL 2136653 NIL) (-869 2134948 2135066 2135210 "ORDRING-" 2135215 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2134199 2134764 2134792 "ORDMON" 2134797 T ORDMON (NIL) -9 NIL 2134818 NIL) (-867 2133343 2133508 2133703 "ORDFUNS" 2134048 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2132558 2133073 2133101 "ORDFIN" 2133166 T ORDFIN (NIL) -9 NIL 2133240 NIL) (-865 2131812 2131951 2132137 "ORDCOMP2" 2132418 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2128159 2130398 2130807 "ORDCOMP" 2131436 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2124680 2125650 2126464 "OPTPROB" 2127365 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2121422 2122121 2122825 "OPTPACK" 2123996 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119035 2119861 2119889 "OPTCAT" 2120708 T OPTCAT (NIL) -9 NIL 2121358 NIL) (-860 2118353 2118712 2118817 "OPSIG" 2118950 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118115 2118160 2118226 "OPQUERY" 2118307 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2117421 2117701 2117742 "OPERCAT" 2117954 NIL OPERCAT (NIL T) -9 NIL 2118051 NIL) (-857 2117164 2117232 2117349 "OPERCAT-" 2117354 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114080 2115475 2115979 "OP" 2116693 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2113373 2113500 2113674 "ONECOMP2" 2113952 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2109986 2112170 2112539 "ONECOMP" 2113037 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2109387 2109511 2109641 "OMSERVER" 2109876 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2105901 2108827 2108867 "OMSAGG" 2108928 NIL OMSAGG (NIL T) -9 NIL 2108992 NIL) (-851 2104476 2104787 2105069 "OMPKG" 2105639 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2102823 2104025 2104194 "OMLO" 2104357 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2101759 2101930 2102150 "OMEXPR" 2102649 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2100844 2101180 2101340 "OMERRK" 2101619 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100081 2100390 2100526 "OMERR" 2100728 T OMERR (NIL) -8 NIL NIL NIL) (-846 2099472 2099758 2099866 "OMENC" 2099993 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093109 2094552 2095723 "OMDEV" 2098321 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2092142 2092349 2092543 "OMCONN" 2092935 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2091548 2091675 2091703 "OM" 2092002 T OM (NIL) -9 NIL NIL NIL) (-842 2089826 2091018 2091046 "OINTDOM" 2091051 T OINTDOM (NIL) -9 NIL 2091072 NIL) (-841 2086901 2088514 2088851 "OFMONOID" 2089521 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086135 2086838 2086883 "ODVAR" 2086888 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2083279 2085880 2086035 "ODR" 2086040 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2074691 2083055 2083181 "ODPOL" 2083186 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068034 2074563 2074668 "ODP" 2074673 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2066776 2067015 2067290 "ODETOOLS" 2067808 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2063719 2064401 2065117 "ODESYS" 2066109 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2058549 2059509 2060534 "ODERTRIC" 2062794 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2057969 2058057 2058251 "ODERED" 2058461 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2054821 2055405 2056082 "ODERAT" 2057392 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2051737 2052245 2052842 "ODEPRRIC" 2054350 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2049632 2050276 2050762 "ODEPROB" 2051271 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046098 2046637 2047284 "ODEPRIM" 2049111 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2045341 2045449 2045709 "ODEPAL" 2045990 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2041443 2042294 2043158 "ODEPACK" 2044497 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2040486 2040611 2040833 "ODEINT" 2041332 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2034551 2036012 2037459 "ODEIFTBL" 2039059 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2029901 2030735 2031687 "ODEEF" 2033710 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2029244 2029339 2029562 "ODECONST" 2029806 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2027307 2028016 2028044 "ODECAT" 2028649 T ODECAT (NIL) -9 NIL 2029180 NIL) (-821 2026939 2026988 2027115 "OCTCT2" 2027258 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2023439 2026644 2026766 "OCT" 2026849 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2022662 2023232 2023260 "OCAMON" 2023265 T OCAMON (NIL) -9 NIL 2023286 NIL) (-818 2016933 2019705 2019745 "OC" 2020842 NIL OC (NIL T) -9 NIL 2021700 NIL) (-817 2013968 2014908 2015898 "OC-" 2015992 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2013388 2013813 2013841 "OASGP" 2013846 T OASGP (NIL) -9 NIL 2013866 NIL) (-815 2012514 2013111 2013139 "OAMONS" 2013179 T OAMONS (NIL) -9 NIL 2013222 NIL) (-814 2011805 2012334 2012362 "OAMON" 2012367 T OAMON (NIL) -9 NIL 2012387 NIL) (-813 2010916 2011554 2011582 "OAGROUP" 2011587 T OAGROUP (NIL) -9 NIL 2011607 NIL) (-812 2010598 2010654 2010743 "NUMTUBE" 2010860 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004117 2005689 2007225 "NUMQUAD" 2009082 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1999797 2000831 2001866 "NUMODE" 2003102 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997078 1998018 1998046 "NUMINT" 1998969 T NUMINT (NIL) -9 NIL 1999733 NIL) (-808 1995990 1996223 1996441 "NUMFMT" 1996880 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982173 1985294 1987826 "NUMERIC" 1993497 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1975877 1981621 1981716 "NTSCAT" 1981721 NIL NTSCAT (NIL T T T T) -9 NIL 1981760 NIL) (-805 1975057 1975236 1975429 "NTPOLFN" 1975716 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1974683 1974746 1974855 "NSUP2" 1974994 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961465 1971508 1972320 "NSUP" 1973904 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950308 1961239 1961372 "NSMP" 1961377 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1948716 1949041 1949398 "NREP" 1949996 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947295 1947559 1947917 "NPCOEF" 1948459 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946343 1946476 1946692 "NORMRETR" 1947176 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944354 1944674 1945083 "NORMPK" 1946051 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944033 1944067 1944191 "NORMMA" 1944320 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1943816 1943851 1943920 "NONE1" 1943997 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1943580 1943773 1943802 "NONE" 1943807 T NONE (NIL) -8 NIL NIL NIL) (-794 1943071 1943139 1943318 "NODE1" 1943512 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941163 1942194 1942449 "NNI" 1942796 T NNI (NIL) -8 NIL NIL 1943031) (-792 1939559 1939896 1940260 "NLINSOL" 1940831 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1935740 1936795 1937694 "NIPROB" 1938680 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934479 1934731 1935033 "NFINTBAS" 1935502 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1933563 1934129 1934170 "NETCLT" 1934342 NIL NETCLT (NIL T) -9 NIL 1934424 NIL) (-788 1932235 1932502 1932783 "NCODIV" 1933331 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1931991 1932034 1932109 "NCNTFRAC" 1932192 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930147 1930535 1930955 "NCEP" 1931616 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1928810 1929757 1929785 "NASRING" 1929895 T NASRING (NIL) -9 NIL 1929975 NIL) (-784 1928593 1928649 1928743 "NASRING-" 1928748 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1927560 1928211 1928239 "NARNG" 1928356 T NARNG (NIL) -9 NIL 1928447 NIL) (-782 1927234 1927319 1927453 "NARNG-" 1927458 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926071 1926320 1926555 "NAGSP" 1927019 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917115 1919027 1920700 "NAGS" 1924418 T NAGS (NIL) -7 NIL NIL NIL) (-779 1915639 1915971 1916302 "NAGF07" 1916804 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910111 1911468 1912775 "NAGF04" 1914352 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1902983 1904693 1906326 "NAGF02" 1908498 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898147 1899307 1900424 "NAGF01" 1901886 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1891727 1893341 1894926 "NAGE04" 1896582 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1882788 1885017 1887147 "NAGE02" 1889617 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1878681 1879688 1880652 "NAGE01" 1881844 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876458 1877010 1877568 "NAGD03" 1878143 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868154 1870136 1872090 "NAGD02" 1874524 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1861893 1863390 1864830 "NAGD01" 1866734 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858030 1858924 1859761 "NAGC06" 1861076 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856477 1856827 1857183 "NAGC05" 1857694 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1855841 1855972 1856116 "NAGC02" 1856353 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1854642 1855369 1855409 "NAALG" 1855488 NIL NAALG (NIL T) -9 NIL 1855549 NIL) (-765 1854471 1854506 1854596 "NAALG-" 1854601 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848343 1849529 1850716 "MULTSQFR" 1853367 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1847650 1847737 1847921 "MULTFACT" 1848255 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1839795 1844233 1844286 "MTSCAT" 1845356 NIL MTSCAT (NIL T T) -9 NIL 1845872 NIL) (-761 1839501 1839561 1839653 "MTHING" 1839735 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839287 1839326 1839386 "MSYSCMD" 1839461 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836032 1838848 1838889 "MSETAGG" 1838894 NIL MSETAGG (NIL T) -9 NIL 1838928 NIL) (-758 1831746 1834787 1835107 "MSET" 1835745 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827345 1829125 1829870 "MRING" 1831046 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1826905 1826978 1827109 "MRF2" 1827272 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826517 1826558 1826702 "MRATFAC" 1826864 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824087 1824424 1824855 "MPRFF" 1826222 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817421 1823941 1824038 "MPOLY" 1824043 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1816905 1816946 1817154 "MPCPF" 1817380 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816413 1816462 1816646 "MPC3" 1816856 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1815596 1815689 1815910 "MPC2" 1816328 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1813873 1814234 1814624 "MONOTOOL" 1815256 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813018 1813401 1813429 "MONOID" 1813648 T MONOID (NIL) -9 NIL 1813795 NIL) (-747 1812534 1812683 1812864 "MONOID-" 1812869 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801507 1808354 1808413 "MONOGEN" 1809087 NIL MONOGEN (NIL T T) -9 NIL 1809543 NIL) (-745 1798557 1799460 1800460 "MONOGEN-" 1800579 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797274 1797822 1797850 "MONADWU" 1798242 T MONADWU (NIL) -9 NIL 1798480 NIL) (-743 1796604 1796805 1797053 "MONADWU-" 1797058 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1795889 1796193 1796221 "MONAD" 1796428 T MONAD (NIL) -9 NIL 1796540 NIL) (-741 1795556 1795652 1795784 "MONAD-" 1795789 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1793695 1794469 1794748 "MOEBIUS" 1795309 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1792863 1793363 1793403 "MODULE" 1793408 NIL MODULE (NIL T) -9 NIL 1793447 NIL) (-738 1792401 1792527 1792717 "MODULE-" 1792722 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1789931 1790765 1791092 "MODRING" 1792225 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1786660 1788036 1788557 "MODOP" 1789460 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785146 1785727 1786004 "MODMONOM" 1786523 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1773907 1783437 1783851 "MODMON" 1784783 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1770740 1772751 1773027 "MODFIELD" 1773782 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1769651 1770021 1770211 "MMLFORM" 1770570 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769171 1769220 1769399 "MMAP" 1769602 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767064 1768003 1768044 "MLO" 1768467 NIL MLO (NIL T) -9 NIL 1768709 NIL) (-729 1764412 1764946 1765548 "MLIFT" 1766545 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1763791 1763887 1764041 "MKUCFUNC" 1764323 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763384 1763460 1763583 "MKRECORD" 1763714 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762407 1762593 1762821 "MKFUNC" 1763195 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1761783 1761899 1762055 "MKFLCFN" 1762290 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761048 1761162 1761347 "MKBCFUNC" 1761676 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757045 1760602 1760738 "MINT" 1760932 T MINT (NIL) -8 NIL NIL NIL) (-722 1755827 1756100 1756377 "MHROWRED" 1756800 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1750578 1754362 1754767 "MFLOAT" 1755442 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1749923 1750011 1750182 "MFINFACT" 1750490 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746202 1747086 1747970 "MESH" 1749059 T MESH (NIL) -7 NIL NIL NIL) (-718 1744556 1744904 1745257 "MDDFACT" 1745889 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741092 1743687 1743728 "MDAGG" 1743983 NIL MDAGG (NIL T) -9 NIL 1744126 NIL) (-716 1728815 1740385 1740592 "MCMPLX" 1740905 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1727934 1728098 1728299 "MCDEN" 1728664 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1725782 1726094 1726474 "MCALCFN" 1727664 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1724659 1724947 1725180 "MAYBE" 1725588 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722217 1722794 1723356 "MATSTOR" 1724130 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1717639 1721589 1721837 "MATRIX" 1722002 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713339 1714112 1714848 "MATLIN" 1716996 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1711915 1712086 1712419 "MATCAT2" 1713174 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701254 1704972 1705049 "MATCAT" 1710081 NIL MATCAT (NIL T T T) -9 NIL 1711553 NIL) (-707 1697207 1698517 1699930 "MATCAT-" 1699935 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695283 1695643 1696027 "MAPPKG3" 1696882 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694240 1694437 1694659 "MAPPKG2" 1695107 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1692697 1693023 1693350 "MAPPKG1" 1693946 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1691698 1692103 1692280 "MAPPAST" 1692540 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691303 1691367 1691490 "MAPHACK3" 1691634 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1690883 1690956 1691070 "MAPHACK2" 1691235 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690309 1690424 1690566 "MAPHACK1" 1690774 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688232 1689009 1689313 "MAGMA" 1690037 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1687651 1687956 1688047 "MACROAST" 1688161 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1683894 1685890 1686351 "M3D" 1687223 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677366 1682205 1682246 "LZSTAGG" 1683028 NIL LZSTAGG (NIL T) -9 NIL 1683323 NIL) (-695 1673048 1674497 1675954 "LZSTAGG-" 1675959 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1669961 1670939 1671426 "LWORD" 1672593 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669483 1669765 1669840 "LSTAST" 1669906 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661411 1669254 1669388 "LSQM" 1669393 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1660629 1660774 1661002 "LSPP" 1661266 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657366 1658082 1658812 "LSMP1" 1659931 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655148 1655479 1655935 "LSMP" 1657055 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648276 1654238 1654279 "LSAGG" 1654341 NIL LSAGG (NIL T) -9 NIL 1654419 NIL) (-687 1644785 1645895 1647108 "LSAGG-" 1647113 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642080 1643929 1644178 "LPOLY" 1644580 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1641656 1641747 1641870 "LPEFRAC" 1641989 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641339 1641418 1641446 "LOGIC" 1641557 T LOGIC (NIL) -9 NIL 1641639 NIL) (-683 1641195 1641224 1641295 "LOGIC-" 1641300 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640370 1640528 1640721 "LODOOPS" 1641051 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1638894 1639143 1639496 "LODOF" 1640117 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1634770 1637529 1637570 "LODOCAT" 1638008 NIL LODOCAT (NIL T) -9 NIL 1638219 NIL) (-679 1634485 1634561 1634688 "LODOCAT-" 1634693 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631471 1634326 1634444 "LODO2" 1634449 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1628578 1631408 1631453 "LODO1" 1631458 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1625673 1628494 1628560 "LODO" 1628565 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1624542 1624719 1625024 "LODEEF" 1625496 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1622719 1623636 1623889 "LO" 1624374 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617691 1620885 1620926 "LNAGG" 1621788 NIL LNAGG (NIL T) -9 NIL 1622223 NIL) (-672 1616784 1617052 1617394 "LNAGG-" 1617399 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1612764 1613709 1614348 "LMOPS" 1616199 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612063 1612541 1612582 "LMODULE" 1612587 NIL LMODULE (NIL T) -9 NIL 1612613 NIL) (-669 1609018 1611708 1611831 "LMDICT" 1611973 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608594 1608808 1608849 "LLINSET" 1608910 NIL LLINSET (NIL T) -9 NIL 1608954 NIL) (-667 1608239 1608502 1608562 "LITERAL" 1608567 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1607758 1607838 1607977 "LIST3" 1608159 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1605856 1606204 1606603 "LIST2MAP" 1607405 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1604845 1605041 1605269 "LIST2" 1605674 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597299 1603779 1604083 "LIST" 1604574 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1596882 1597118 1597159 "LINSET" 1597164 NIL LINSET (NIL T) -9 NIL 1597198 NIL) (-661 1595696 1596390 1596557 "LINFORM" 1596767 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1593995 1594723 1594764 "LINEXP" 1595254 NIL LINEXP (NIL T) -9 NIL 1595527 NIL) (-659 1592571 1593475 1593656 "LINELT" 1593866 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591128 1591408 1591719 "LINDEP" 1592323 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590264 1590860 1590970 "LINBASIS" 1591058 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587001 1587750 1588527 "LIMITRF" 1589519 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585286 1585600 1586009 "LIMITPS" 1586696 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584114 1584689 1584729 "LIECAT" 1584869 NIL LIECAT (NIL T) -9 NIL 1585020 NIL) (-653 1583949 1583982 1584070 "LIECAT-" 1584075 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1577969 1583460 1583688 "LIE" 1583770 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570154 1577509 1577665 "LIB" 1577833 T LIB (NIL) -8 NIL NIL NIL) (-650 1565723 1566672 1567607 "LGROBP" 1569271 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564347 1565255 1565283 "LFCAT" 1565490 T LFCAT (NIL) -9 NIL 1565629 NIL) (-648 1562285 1562619 1562969 "LF" 1564068 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559145 1559817 1560505 "LEXTRIPK" 1561649 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1555733 1556715 1557218 "LEXP" 1558725 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555149 1555454 1555546 "LETAST" 1555661 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553535 1553860 1554261 "LEADCDET" 1554831 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552713 1552799 1553028 "LAZM3PK" 1553456 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547238 1550790 1551328 "LAUPOL" 1552225 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1546811 1546861 1547022 "LAPLACE" 1547188 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545659 1546375 1546416 "LALG" 1546478 NIL LALG (NIL T) -9 NIL 1546537 NIL) (-639 1545355 1545432 1545568 "LALG-" 1545573 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543092 1544456 1544707 "LA" 1545188 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1542921 1542951 1542992 "KVTFROM" 1543054 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541678 1542288 1542473 "KTVLOGIC" 1542756 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541507 1541537 1541578 "KRCFROM" 1541640 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540399 1540598 1540897 "KOVACIC" 1541307 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540228 1540258 1540299 "KONVERT" 1540361 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540057 1540087 1540128 "KOERCE" 1540190 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539541 1539634 1539766 "KERNEL2" 1539971 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537228 1538134 1538511 "KERNEL" 1539197 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530699 1535705 1535759 "KDAGG" 1536136 NIL KDAGG (NIL T T) -9 NIL 1536342 NIL) (-628 1530210 1530352 1530557 "KDAGG-" 1530562 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1522910 1529871 1530026 "KAFILE" 1530088 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522514 1522799 1522862 "JVMOP" 1522867 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521250 1521754 1522003 "JVMMDACC" 1522285 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520186 1520640 1520845 "JVMFDACC" 1521065 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1518767 1519262 1519562 "JVMCSTTG" 1519906 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1517903 1518307 1518468 "JVMCFACC" 1518626 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517581 1517820 1517869 "JVMBCODE" 1517874 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511600 1517092 1517320 "JORDAN" 1517402 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1510913 1511249 1511370 "JOINAST" 1511499 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1506948 1509090 1509144 "IXAGG" 1510073 NIL IXAGG (NIL T T) -9 NIL 1510532 NIL) (-617 1505801 1506173 1506592 "IXAGG-" 1506597 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1500890 1505723 1505782 "IVECTOR" 1505787 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499615 1499893 1500159 "ITUPLE" 1500657 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498087 1498294 1498589 "ITRIGMNP" 1499437 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1496814 1497036 1497319 "ITFUN3" 1497863 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496412 1496475 1496598 "ITFUN2" 1496737 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495517 1495892 1496066 "ITFORM" 1496258 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493286 1494537 1494815 "ITAYLOR" 1495272 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481690 1487423 1488586 "ISUPS" 1492156 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1480782 1480934 1481170 "ISUMP" 1481537 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475632 1480727 1480768 "ISTRING" 1480773 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475048 1475353 1475445 "ISAST" 1475560 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474245 1474339 1474555 "IRURPK" 1474962 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473157 1473382 1473622 "IRSN" 1474025 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471202 1471583 1472012 "IRRF2F" 1472795 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1470943 1470987 1471063 "IRREDFFX" 1471158 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469516 1469817 1470116 "IROOT" 1470676 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468655 1469009 1469160 "IRFORM" 1469385 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1467737 1467868 1468082 "IR2F" 1468538 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465326 1465845 1466411 "IR2" 1467215 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1461766 1463010 1463702 "IR" 1464666 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461551 1461591 1461651 "IPRNTPK" 1461726 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457525 1461440 1461509 "IPF" 1461514 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455553 1457450 1457507 "IPADIC" 1457512 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1454811 1455113 1455243 "IP4ADDR" 1455443 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454149 1454440 1454572 "IOMODE" 1454699 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453120 1453746 1453873 "IOBFILE" 1454042 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452530 1453024 1453052 "IOBCON" 1453057 T IOBCON (NIL) -9 NIL 1453078 NIL) (-589 1452035 1452099 1452282 "INVLAPLA" 1452466 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441605 1444037 1446423 "INTTR" 1449699 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1437898 1438682 1439547 "INTTOOLS" 1440790 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437478 1437575 1437692 "INTSLPE" 1437801 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1434945 1437401 1437460 "INTRVL" 1437465 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432523 1433059 1433634 "INTRF" 1434430 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1431916 1432031 1432173 "INTRET" 1432421 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1429889 1430302 1430772 "INTRAT" 1431524 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427134 1427735 1428354 "INTPM" 1429374 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1423851 1424478 1425216 "INTPAF" 1426520 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1418952 1419992 1421043 "INTPACK" 1422820 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418198 1418356 1418564 "INTHERTR" 1418794 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417631 1417717 1417905 "INTHERAL" 1418112 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415399 1415920 1416377 "INTHEORY" 1417194 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1406731 1408426 1410198 "INTG0" 1413751 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387256 1392094 1396904 "INTFTBL" 1401941 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386481 1386643 1386816 "INTFACT" 1387115 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1383878 1384354 1384911 "INTEF" 1386035 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382075 1382970 1382998 "INTDOM" 1383299 T INTDOM (NIL) -9 NIL 1383506 NIL) (-570 1381414 1381618 1381860 "INTDOM-" 1381865 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377282 1379703 1379757 "INTCAT" 1380556 NIL INTCAT (NIL T) -9 NIL 1380877 NIL) (-568 1376736 1376857 1376985 "INTBIT" 1377174 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375417 1375589 1375896 "INTALG" 1376581 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1374894 1374990 1375147 "INTAF" 1375321 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1367861 1374704 1374844 "INTABL" 1374849 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367102 1367664 1367729 "INT8" 1367763 T INT8 (NIL) -8 NIL NIL 1367808) (-563 1366342 1366904 1366969 "INT64" 1367003 T INT64 (NIL) -8 NIL NIL 1367048) (-562 1365582 1366144 1366209 "INT32" 1366243 T INT32 (NIL) -8 NIL NIL 1366288) (-561 1364822 1365384 1365449 "INT16" 1365483 T INT16 (NIL) -8 NIL NIL 1365528) (-560 1361024 1364619 1364728 "INT" 1364733 T INT (NIL) -8 NIL NIL NIL) (-559 1355133 1358572 1358600 "INS" 1359534 T INS (NIL) -9 NIL 1360199 NIL) (-558 1352208 1353158 1354125 "INS-" 1354198 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1350965 1351210 1351508 "INPSIGN" 1351961 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350059 1350200 1350397 "INPRODPF" 1350845 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1348929 1349070 1349307 "INPRODFF" 1349939 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1347917 1348081 1348341 "INNMFACT" 1348765 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347096 1347211 1347399 "INMODGCD" 1347816 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345580 1345849 1346173 "INFSP" 1346841 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1344740 1344881 1345064 "INFPROD0" 1345460 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344338 1344410 1344508 "INFORM1" 1344675 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1340905 1342403 1342918 "INFORM" 1343831 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340410 1340517 1340631 "INFINITY" 1340811 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339484 1340130 1340231 "INETCLTS" 1340329 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338082 1338350 1338671 "INEP" 1339232 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337143 1337979 1338044 "INDE" 1338049 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1336695 1336775 1336892 "INCRMAPS" 1337070 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335417 1335964 1336170 "INBFILE" 1336509 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330596 1331653 1332597 "INBFF" 1334505 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329450 1329773 1329801 "INBCON" 1330314 T INBCON (NIL) -9 NIL 1330580 NIL) (-540 1328660 1328925 1329201 "INBCON-" 1329206 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328079 1328384 1328475 "INAST" 1328589 T INAST (NIL) -8 NIL NIL NIL) (-538 1327446 1327758 1327864 "IMPTAST" 1327993 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323367 1327290 1327394 "IMATRIX" 1327399 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322059 1322198 1322514 "IMATQF" 1323223 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320239 1320506 1320843 "IMATLIN" 1321815 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314154 1320163 1320221 "ILIST" 1320226 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1311820 1314014 1314127 "IIARRAY2" 1314132 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306641 1311731 1311795 "IFF" 1311800 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1305922 1306258 1306374 "IFAST" 1306545 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300434 1305214 1305402 "IFARRAY" 1305779 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299472 1300338 1300411 "IFAMON" 1300416 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299044 1299121 1299175 "IEVALAB" 1299382 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1298707 1298787 1298947 "IEVALAB-" 1298952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1297771 1298596 1298671 "IDPOAMS" 1298676 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1296904 1297660 1297735 "IDPOAM" 1297740 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296285 1296819 1296881 "IDPO" 1296886 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1294765 1295292 1295344 "IDPC" 1295856 NIL IDPC (NIL T T) -9 NIL 1296137 NIL) (-522 1294097 1294657 1294730 "IDPAM" 1294735 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293312 1293989 1294062 "IDPAG" 1294067 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1292856 1293118 1293208 "IDENT" 1293242 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289075 1289959 1290854 "IDECOMP" 1292013 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281710 1282998 1284045 "IDEAL" 1288111 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1280852 1280982 1281182 "ICDEN" 1281594 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1279827 1280332 1280479 "ICARD" 1280725 T ICARD (NIL) -8 NIL NIL NIL) (-515 1277857 1278200 1278605 "IBPTOOLS" 1279504 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1272972 1277477 1277590 "IBITS" 1277776 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269647 1270271 1270966 "IBATOOL" 1272389 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267408 1267888 1268421 "IBACHIN" 1269182 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1264998 1267254 1267357 "IARRAY2" 1267362 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260711 1264924 1264981 "IARRAY1" 1264986 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1253728 1259123 1259604 "IAN" 1260250 T IAN (NIL) -8 NIL NIL NIL) (-508 1253233 1253296 1253469 "IALGFACT" 1253665 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1252725 1252874 1252902 "HYPCAT" 1253109 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252227 1252380 1252566 "HYPCAT-" 1252571 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1251774 1252022 1252105 "HOSTNAME" 1252164 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251607 1251656 1251697 "HOMOTOP" 1251702 NIL HOMOTOP (NIL T) -9 NIL 1251735 NIL) (-503 1248040 1249539 1249580 "HOAGG" 1250561 NIL HOAGG (NIL T) -9 NIL 1251290 NIL) (-502 1246556 1247033 1247559 "HOAGG-" 1247564 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239613 1246149 1246299 "HEXADEC" 1246426 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238325 1238583 1238846 "HEUGCD" 1239390 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237257 1238162 1238292 "HELLFDIV" 1238297 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235267 1237034 1237122 "HEAP" 1237201 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234464 1234819 1234953 "HEADAST" 1235153 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1227851 1234379 1234441 "HDP" 1234446 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1220870 1227486 1227638 "HDMP" 1227752 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220176 1220334 1220498 "HB" 1220726 T HB (NIL) -7 NIL NIL NIL) (-493 1213186 1220022 1220126 "HASHTBL" 1220131 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212602 1212907 1212999 "HASAST" 1213114 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210015 1212224 1212406 "HACKPI" 1212440 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205187 1209868 1209981 "GTSET" 1209986 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198226 1205065 1205163 "GSTBL" 1205168 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1189989 1197391 1197647 "GSERIES" 1198026 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189020 1189533 1189561 "GROUP" 1189764 T GROUP (NIL) -9 NIL 1189898 NIL) (-486 1188344 1188545 1188796 "GROUP-" 1188801 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186693 1187032 1187419 "GROEBSOL" 1188021 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185521 1185881 1185932 "GRMOD" 1186461 NIL GRMOD (NIL T T) -9 NIL 1186629 NIL) (-483 1185277 1185325 1185453 "GRMOD-" 1185458 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180417 1181631 1182631 "GRIMAGE" 1184297 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1178811 1179144 1179468 "GRDEF" 1180113 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178243 1178371 1178512 "GRAY" 1178690 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177320 1177822 1177873 "GRALG" 1178026 NIL GRALG (NIL T T) -9 NIL 1178119 NIL) (-478 1176957 1177054 1177217 "GRALG-" 1177222 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173438 1176540 1176719 "GPOLSET" 1176863 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1172786 1172849 1173107 "GOSPER" 1173375 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168356 1169224 1169750 "GMODPOL" 1172485 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167343 1167545 1167783 "GHENSEL" 1168168 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161415 1162342 1163362 "GENUPS" 1166427 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161106 1161163 1161252 "GENUFACT" 1161358 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160506 1160595 1160760 "GENPGCD" 1161024 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1159974 1160015 1160228 "GENMFACT" 1160465 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158510 1158797 1159104 "GENEEZ" 1159717 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151689 1158121 1158283 "GDMP" 1158433 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140427 1145460 1146566 "GCNAALG" 1150672 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138554 1139602 1139630 "GCDDOM" 1139885 T GCDDOM (NIL) -9 NIL 1140042 NIL) (-465 1137994 1138151 1138366 "GCDDOM-" 1138371 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126466 1128940 1131332 "GBINTERN" 1135685 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124267 1124595 1125016 "GBF" 1126141 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123024 1123213 1123480 "GBEUCLID" 1124083 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121674 1121881 1122185 "GB" 1122803 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121005 1121148 1121297 "GAUSSFAC" 1121545 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119326 1119674 1119988 "GALUTIL" 1120724 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117586 1117908 1118232 "GALPOLYU" 1119053 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1114885 1115241 1115648 "GALFACTU" 1117283 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106499 1108190 1109798 "GALFACT" 1113317 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1103785 1104545 1104573 "FVFUN" 1105729 T FVFUN (NIL) -9 NIL 1106449 NIL) (-454 1103015 1103233 1103261 "FVC" 1103552 T FVC (NIL) -9 NIL 1103735 NIL) (-453 1102616 1102840 1102908 "FUNDESC" 1102967 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102189 1102413 1102494 "FUNCTION" 1102568 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100866 1101490 1101693 "FTEM" 1102006 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098496 1099188 1099654 "FT" 1100420 T FT (NIL) -8 NIL NIL NIL) (-449 1096765 1097076 1097473 "FSUPFACT" 1098187 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095084 1095451 1095783 "FST" 1096453 T FST (NIL) -8 NIL NIL NIL) (-447 1094265 1094389 1094577 "FSRED" 1094966 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1092954 1093220 1093567 "FSPRMELT" 1093980 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090164 1090698 1091184 "FSPECF" 1092517 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089686 1089746 1089916 "FSINT" 1090105 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1087822 1088679 1088982 "FSERIES" 1089465 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1086846 1086980 1087204 "FSCINT" 1087702 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1085870 1086031 1086258 "FSAGG2" 1086699 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081734 1084814 1084855 "FSAGG" 1085225 NIL FSAGG (NIL T) -9 NIL 1085484 NIL) (-439 1079334 1080097 1080893 "FSAGG-" 1080988 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1076994 1077292 1077840 "FS2UPS" 1079052 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1075860 1076043 1076345 "FS2EXPXP" 1076819 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075488 1075537 1075666 "FS2" 1075811 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055726 1065262 1065303 "FS" 1069187 NIL FS (NIL T) -9 NIL 1071476 NIL) (-434 1043787 1047362 1051419 "FS-" 1051719 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043201 1043328 1043480 "FRUTIL" 1043667 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037712 1040890 1040930 "FRNAALG" 1042250 NIL FRNAALG (NIL T) -9 NIL 1042848 NIL) (-431 1033193 1034461 1035736 "FRNAALG-" 1036486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1032825 1032874 1033001 "FRNAAF2" 1033144 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031112 1031674 1031970 "FRMOD" 1032637 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030297 1030390 1030681 "FRIDEAL2" 1031019 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1027902 1028672 1028990 "FRIDEAL" 1030088 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1026993 1027449 1027490 "FRETRCT" 1027495 NIL FRETRCT (NIL T) -9 NIL 1027671 NIL) (-425 1026051 1026336 1026687 "FRETRCT-" 1026692 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1022872 1024335 1024394 "FRAMALG" 1025276 NIL FRAMALG (NIL T T) -9 NIL 1025568 NIL) (-423 1020910 1021461 1022091 "FRAMALG-" 1022314 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020540 1020603 1020710 "FRAC2" 1020847 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013532 1020013 1020290 "FRAC" 1020295 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013162 1013225 1013332 "FR2" 1013469 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004079 1008657 1010015 "FR" 1011836 NIL FR (NIL T) -8 NIL NIL NIL) (-418 997998 1001458 1001486 "FPS" 1002605 T FPS (NIL) -9 NIL 1003162 NIL) (-417 997423 997556 997720 "FPS-" 997866 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994389 996380 996408 "FPC" 996633 T FPC (NIL) -9 NIL 996775 NIL) (-415 994170 994222 994319 "FPC-" 994324 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 992928 993658 993699 "FPATMAB" 993704 NIL FPATMAB (NIL T) -9 NIL 993856 NIL) (-413 991071 991670 992017 "FPARFRAC" 992644 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986363 986963 987645 "FORTRAN" 990503 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 983937 984601 984629 "FORTFN" 985689 T FORTFN (NIL) -9 NIL 986313 NIL) (-410 983689 983751 983779 "FORTCAT" 983838 T FORTCAT (NIL) -9 NIL 983900 NIL) (-409 981375 981905 982444 "FORT" 983170 T FORT (NIL) -7 NIL NIL NIL) (-408 981157 981193 981262 "FORMULA1" 981339 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979161 979773 980163 "FORMULA" 980787 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978678 978736 978909 "FORDER" 979103 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977738 977938 978131 "FOP" 978505 T FOP (NIL) -7 NIL NIL NIL) (-404 976151 977018 977192 "FNLA" 977620 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974770 975281 975309 "FNCAT" 975769 T FNCAT (NIL) -9 NIL 976029 NIL) (-402 974213 974729 974757 "FNAME" 974762 T FNAME (NIL) -8 NIL NIL NIL) (-401 972539 973712 973740 "FMTC" 973745 T FMTC (NIL) -9 NIL 973781 NIL) (-400 971088 972475 972521 "FMONOID" 972526 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967677 969043 969084 "FMONCAT" 970301 NIL FMONCAT (NIL T) -9 NIL 970906 NIL) (-398 964999 965747 965775 "FMFUN" 966919 T FMFUN (NIL) -9 NIL 967627 NIL) (-397 961872 962924 962978 "FMCAT" 964173 NIL FMCAT (NIL T T) -9 NIL 964668 NIL) (-396 961105 961322 961350 "FMC" 961640 T FMC (NIL) -9 NIL 961822 NIL) (-395 959773 960871 960971 "FM1" 961050 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 958791 959515 959664 "FM" 959669 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956529 956981 957475 "FLOATRP" 958342 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 953931 954467 955045 "FLOATCP" 955996 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946594 951660 952281 "FLOAT" 953330 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945112 946186 946227 "FLINEXP" 946232 NIL FLINEXP (NIL T) -9 NIL 946325 NIL) (-389 944242 944501 944829 "FLINEXP-" 944834 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943300 943462 943686 "FLASORT" 944094 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940218 941270 941322 "FLALG" 942549 NIL FLALG (NIL T T) -9 NIL 943016 NIL) (-386 939242 939403 939630 "FLAGG2" 940071 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932497 936651 936692 "FLAGG" 937954 NIL FLAGG (NIL T) -9 NIL 938606 NIL) (-384 931151 931562 932052 "FLAGG-" 932057 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 927789 928996 929055 "FINRALG" 930183 NIL FINRALG (NIL T T) -9 NIL 930691 NIL) (-382 926913 927178 927517 "FINRALG-" 927522 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926219 926518 926546 "FINITE" 926742 T FINITE (NIL) -9 NIL 926849 NIL) (-380 918170 920749 920789 "FINAALG" 924456 NIL FINAALG (NIL T) -9 NIL 925909 NIL) (-379 913286 914552 915696 "FINAALG-" 917075 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 911846 912268 912322 "FILECAT" 913006 NIL FILECAT (NIL T T) -9 NIL 913222 NIL) (-377 911124 911601 911704 "FILE" 911776 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908527 910354 910382 "FIELD" 910422 T FIELD (NIL) -9 NIL 910502 NIL) (-375 907069 907532 908043 "FIELD-" 908048 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904752 905704 906051 "FGROUP" 906755 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 903824 904006 904226 "FGLMICPK" 904584 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899079 903749 903806 "FFX" 903811 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898674 898741 898876 "FFSLPE" 899012 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898172 898214 898423 "FFPOLY2" 898632 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894048 894944 895740 "FFPOLY" 897408 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889317 893967 894030 "FFP" 894035 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 883848 888660 888850 "FFNBX" 889171 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878181 882983 883241 "FFNBP" 883702 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872219 877465 877676 "FFNB" 878014 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871039 871249 871564 "FFINTBAS" 872016 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866632 869286 869314 "FFIELDC" 869934 T FFIELDC (NIL) -9 NIL 870310 NIL) (-362 865252 865693 866176 "FFIELDC-" 866181 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 864809 864867 864991 "FFHOM" 865194 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862468 862991 863508 "FFF" 864324 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857503 862210 862311 "FFCGX" 862411 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852542 857235 857342 "FFCGP" 857446 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847142 852269 852377 "FFCG" 852478 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846547 846596 846831 "FFCAT2" 847093 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825229 836279 836365 "FFCAT" 841530 NIL FFCAT (NIL T T T) -9 NIL 842981 NIL) (-354 820240 821474 822788 "FFCAT-" 824018 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815061 820151 820215 "FF" 820220 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803714 808033 809253 "FEXPR" 813913 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802642 803111 803152 "FEVALAB" 803236 NIL FEVALAB (NIL T) -9 NIL 803497 NIL) (-350 801759 802011 802349 "FEVALAB-" 802354 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798621 799506 799621 "FDIVCAT" 801189 NIL FDIVCAT (NIL T T T T) -9 NIL 801626 NIL) (-348 798377 798410 798580 "FDIVCAT-" 798585 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797591 797684 797961 "FDIV2" 798284 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796001 796974 797177 "FDIV" 797490 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 794909 795296 795498 "FCTRDATA" 795819 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793565 793854 794143 "FCPAK1" 794640 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792568 793065 793206 "FCOMP" 793456 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 775882 779718 783256 "FC" 789050 T FC (NIL) -8 NIL NIL NIL) (-341 767591 772203 772243 "FAXF" 774045 NIL FAXF (NIL T) -9 NIL 774737 NIL) (-340 764732 765539 766357 "FAXF-" 766822 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759301 764108 764284 "FARRAY" 764589 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753866 756248 756301 "FAMR" 757324 NIL FAMR (NIL T T) -9 NIL 757784 NIL) (-337 752690 753058 753493 "FAMR-" 753498 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751717 752612 752665 "FAMONOID" 752670 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749347 750199 750252 "FAMONC" 751193 NIL FAMONC (NIL T T) -9 NIL 751579 NIL) (-334 747821 749101 749238 "FAGROUP" 749243 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745574 745935 746338 "FACUTIL" 747502 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744661 744858 745080 "FACTFUNC" 745384 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736433 743964 744163 "EXPUPXS" 744517 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 733886 734456 735042 "EXPRTUBE" 735867 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730097 730749 731479 "EXPRODE" 733225 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724531 725238 726044 "EXPR2UPS" 729395 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724157 724220 724329 "EXPR2" 724468 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708465 722806 723235 "EXPR" 723761 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698803 707616 707907 "EXPEXPAN" 708301 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698223 698527 698618 "EXITAST" 698732 T EXITAST (NIL) -8 NIL NIL NIL) (-323 697987 698180 698209 "EXIT" 698214 T EXIT (NIL) -8 NIL NIL NIL) (-322 697608 697676 697789 "EVALCYC" 697919 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697125 697267 697308 "EVALAB" 697478 NIL EVALAB (NIL T) -9 NIL 697582 NIL) (-320 696582 696728 696949 "EVALAB-" 696954 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693697 695238 695266 "EUCDOM" 695821 T EUCDOM (NIL) -9 NIL 696171 NIL) (-318 692057 692558 693141 "EUCDOM-" 693146 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691683 691746 691855 "ESTOOLS2" 691994 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691428 691476 691556 "ESTOOLS1" 691635 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678745 681726 684476 "ESTOOLS" 688698 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678484 678522 678604 "ESCONT1" 678707 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674792 675619 676399 "ESCONT" 677724 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674461 674517 674617 "ES2" 674736 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674085 674149 674258 "ES1" 674397 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667786 669716 669744 "ES" 672512 T ES (NIL) -9 NIL 673922 NIL) (-309 662463 664020 665837 "ES-" 666001 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661655 661808 661984 "ERROR" 662307 T ERROR (NIL) -7 NIL NIL NIL) (-307 654671 661514 661605 "EQTBL" 661610 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654297 654360 654469 "EQ2" 654608 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646556 649611 651060 "EQ" 652881 NIL -1500 (NIL T) -8 NIL NIL NIL) (-304 641799 642894 643987 "EP" 645495 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640339 640690 640996 "ENV" 641513 T ENV (NIL) -8 NIL NIL NIL) (-302 639299 639973 640001 "ENTIRER" 640006 T ENTIRER (NIL) -9 NIL 640052 NIL) (-301 635718 637481 637842 "EMR" 639107 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634822 635033 635087 "ELTAGG" 635467 NIL ELTAGG (NIL T T) -9 NIL 635678 NIL) (-299 634529 634603 634744 "ELTAGG-" 634749 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634287 634322 634376 "ELTAB" 634460 NIL ELTAB (NIL T T) -9 NIL 634512 NIL) (-297 633389 633559 633758 "ELFUTS" 634138 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633113 633187 633215 "ELEMFUN" 633320 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 632977 633004 633072 "ELEMFUN-" 633077 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627388 631019 631060 "ELAGG" 632000 NIL ELAGG (NIL T) -9 NIL 632463 NIL) (-293 625565 626107 626770 "ELAGG-" 626775 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624847 625014 625170 "ELABOR" 625429 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623453 623787 624081 "ELABEXPR" 624573 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 615965 618090 618919 "EFUPXS" 622728 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609091 611214 612025 "EFULS" 615240 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606528 606934 607406 "EFSTRUC" 608723 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 595965 597885 599433 "EF" 605043 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 594943 595450 595599 "EAB" 595836 T EAB (NIL) -8 NIL NIL NIL) (-285 594065 594902 594930 "E04UCFA" 594935 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593187 594024 594052 "E04NAFA" 594057 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592309 593146 593174 "E04MBFA" 593179 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591431 592268 592296 "E04JAFA" 592301 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590555 591390 591418 "E04GCFA" 591423 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589679 590514 590542 "E04FDFA" 590547 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588801 589638 589666 "E04DGFA" 589671 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582878 584326 585690 "E04AGNT" 587457 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581498 582179 582219 "DVARCAT" 582560 NIL DVARCAT (NIL T) -9 NIL 582723 NIL) (-276 580648 580914 581228 "DVARCAT-" 581233 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572616 580447 580576 "DSMP" 580581 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 570967 571758 571799 "DSEXT" 572162 NIL DSEXT (NIL T) -9 NIL 572456 NIL) (-273 569156 569680 570346 "DSEXT-" 570351 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568815 568880 568978 "DROPT1" 569091 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563834 565056 566193 "DROPT0" 567698 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558417 559779 560847 "DROPT" 562786 T DROPT (NIL) -8 NIL NIL NIL) (-269 556726 557087 557473 "DRAWPT" 558051 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556353 556412 556530 "DRAWHACK" 556667 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555054 555353 555644 "DRAWCX" 556082 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554563 554638 554789 "DRAWCURV" 554980 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 544881 546993 549108 "DRAWCFUN" 552468 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539372 540391 541470 "DRAW" 543855 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535843 538037 538078 "DQAGG" 538707 NIL DQAGG (NIL T) -9 NIL 538981 NIL) (-262 522426 530054 530137 "DPOLCAT" 531989 NIL DPOLCAT (NIL T T T T) -9 NIL 532534 NIL) (-261 516945 518611 520569 "DPOLCAT-" 520574 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509802 516806 516904 "DPMO" 516909 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502556 509582 509749 "DPMM" 509754 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502078 502340 502429 "DOMTMPLT" 502487 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501427 501880 501960 "DOMCTOR" 502018 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500579 500907 501058 "DOMAIN" 501296 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493598 500214 500366 "DMP" 500480 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491375 492665 492706 "DMEXT" 492711 NIL DMEXT (NIL T) -9 NIL 492887 NIL) (-253 490969 491031 491175 "DLP" 491313 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484092 490296 490486 "DLIST" 490811 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480630 482917 482958 "DLAGG" 483508 NIL DLAGG (NIL T) -9 NIL 483738 NIL) (-250 479142 479956 479984 "DIVRING" 480076 T DIVRING (NIL) -9 NIL 480159 NIL) (-249 478325 478569 478869 "DIVRING-" 478874 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476367 476784 477190 "DISPLAY" 477939 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475197 475418 475683 "DIRPROD2" 476160 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468604 475111 475174 "DIRPROD" 475179 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456816 463315 463368 "DIRPCAT" 463626 NIL DIRPCAT (NIL NIL T) -9 NIL 464501 NIL) (-244 454016 454784 455665 "DIRPCAT-" 456002 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453297 453463 453649 "DIOSP" 453850 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449711 452181 452222 "DIOPS" 452656 NIL DIOPS (NIL T) -9 NIL 452885 NIL) (-241 449230 449374 449565 "DIOPS-" 449570 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448137 448909 448937 "DIFRING" 448942 T DIFRING (NIL) -9 NIL 448964 NIL) (-239 447785 447883 447911 "DIFFSPC" 448030 T DIFFSPC (NIL) -9 NIL 448105 NIL) (-238 447406 447508 447660 "DIFFSPC-" 447665 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446342 446940 446981 "DIFFMOD" 446986 NIL DIFFMOD (NIL T) -9 NIL 447084 NIL) (-236 446038 446095 446136 "DIFFDOM" 446257 NIL DIFFDOM (NIL T) -9 NIL 446325 NIL) (-235 445885 445915 445999 "DIFFDOM-" 446004 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443625 445089 445130 "DIFEXT" 445135 NIL DIFEXT (NIL T) -9 NIL 445288 NIL) (-233 440659 443129 443170 "DIAGG" 443175 NIL DIAGG (NIL T) -9 NIL 443195 NIL) (-232 440007 440200 440452 "DIAGG-" 440457 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434857 438966 439243 "DHMATRIX" 439776 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430325 431378 432388 "DFSFUN" 433867 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424566 429256 429568 "DFLOAT" 430033 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422805 423110 423499 "DFINTTLS" 424274 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419624 420826 421226 "DERHAM" 422471 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417160 419399 419488 "DEQUEUE" 419568 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416402 416547 416730 "DEGRED" 417022 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412808 413577 414423 "DEFINTRF" 415630 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410345 410832 411424 "DEFINTEF" 412327 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409629 409965 410080 "DEFAST" 410250 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402686 409222 409372 "DECIMAL" 409499 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400144 400656 401162 "DDFACT" 402230 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399734 399783 399934 "DBLRESP" 400095 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398935 399504 399595 "DBASIS" 399683 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396719 397165 397526 "DBASE" 398701 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395907 396199 396345 "DATAARY" 396618 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394965 395866 395894 "D03FAFA" 395899 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394024 394924 394952 "D03EEFA" 394957 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391950 392440 392929 "D03AGNT" 393555 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391191 391909 391937 "D02EJFA" 391942 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390432 391150 391178 "D02CJFA" 391183 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389673 390391 390419 "D02BHFA" 390424 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388914 389632 389660 "D02BBFA" 389665 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382045 383700 385306 "D02AGNT" 387328 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379795 380336 380882 "D01WGTS" 381519 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378802 379754 379782 "D01TRNS" 379787 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377810 378761 378789 "D01GBFA" 378794 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376818 377769 377797 "D01FCFA" 377802 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375826 376777 376805 "D01ASFA" 376810 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374834 375785 375813 "D01AQFA" 375818 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373842 374793 374821 "D01APFA" 374826 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372850 373801 373829 "D01ANFA" 373834 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371858 372809 372837 "D01AMFA" 372842 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370866 371817 371845 "D01ALFA" 371850 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369874 370825 370853 "D01AKFA" 370858 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368882 369833 369861 "D01AJFA" 369866 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362105 363730 365291 "D01AGNT" 367341 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361424 361570 361722 "CYCLOTOM" 361973 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358079 358872 359599 "CYCLES" 360717 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357379 357525 357696 "CVMP" 357940 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355166 355478 355847 "CTRIGMNP" 357107 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354639 354897 354998 "CTORKIND" 355085 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353844 354232 354260 "CTORCAT" 354442 T CTORCAT (NIL) -9 NIL 354555 NIL) (-188 353418 353553 353712 "CTORCAT-" 353717 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352832 353092 353200 "CTORCALL" 353342 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352190 352626 352699 "CTOR" 352779 T CTOR (NIL) -8 NIL NIL NIL) (-185 351546 351663 351816 "CSTTOOLS" 352087 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347243 348002 348760 "CRFP" 350858 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346658 346964 347056 "CRCEAST" 347171 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345681 345890 346118 "CRAPACK" 346462 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345061 345166 345370 "CPMATCH" 345557 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344780 344814 344920 "CPIMA" 345027 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341038 341800 342519 "COORDSYS" 344115 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340426 340571 340713 "CONTOUR" 340916 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335898 338429 338921 "CONTFRAC" 339966 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335772 335799 335827 "CONDUIT" 335864 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334726 335400 335428 "COMRING" 335433 T COMRING (NIL) -9 NIL 335485 NIL) (-174 333708 334084 334268 "COMPPROP" 334562 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333363 333404 333532 "COMPLPAT" 333667 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332993 333056 333163 "COMPLEX2" 333300 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321397 332802 332911 "COMPLEX" 332916 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320718 320857 321017 "COMPILER" 321257 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320430 320471 320569 "COMPFACT" 320677 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301824 314134 314174 "COMPCAT" 315178 NIL COMPCAT (NIL T) -9 NIL 316526 NIL) (-167 290712 294263 297890 "COMPCAT-" 298246 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290435 290469 290572 "COMMUPC" 290678 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290223 290263 290322 "COMMONOP" 290396 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289745 290027 290102 "COMMAAST" 290168 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289252 289496 289583 "COMM" 289678 T COMM (NIL) -8 NIL NIL NIL) (-162 288447 288695 288723 "COMBOPC" 289061 T COMBOPC (NIL) -9 NIL 289236 NIL) (-161 287301 287553 287795 "COMBINAT" 288237 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283644 284332 284959 "COMBF" 286723 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282306 282760 282995 "COLOR" 283429 T COLOR (NIL) -8 NIL NIL NIL) (-158 281722 282027 282119 "COLONAST" 282234 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281356 281409 281534 "CMPLXRT" 281669 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280744 281056 281155 "CLLCTAST" 281277 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276203 277274 278354 "CLIP" 279684 T CLIP (NIL) -7 NIL NIL NIL) (-154 274376 275304 275544 "CLIF" 276030 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270358 272494 272535 "CLAGG" 273464 NIL CLAGG (NIL T) -9 NIL 274000 NIL) (-152 268702 269237 269820 "CLAGG-" 269825 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268240 268331 268471 "CINTSLPE" 268611 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265705 266212 266760 "CHVAR" 267768 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264745 265419 265447 "CHARZ" 265452 T CHARZ (NIL) -9 NIL 265467 NIL) (-148 264493 264539 264617 "CHARPOL" 264699 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263411 264117 264145 "CHARNZ" 264206 T CHARNZ (NIL) -9 NIL 264255 NIL) (-146 260355 261465 261994 "CHAR" 262902 T CHAR (NIL) -8 NIL NIL NIL) (-145 260063 260142 260170 "CFCAT" 260281 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259286 259415 259598 "CDEN" 259947 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254883 258439 258719 "CCLASS" 259026 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254104 254291 254468 "CATEGORY" 254726 T -10 (NIL) -8 NIL NIL NIL) (-141 253599 254023 254071 "CATCTOR" 254076 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252990 253302 253400 "CATAST" 253521 T CATAST (NIL) -8 NIL NIL NIL) (-139 252406 252711 252803 "CASEAST" 252918 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251502 251662 251883 "CARTEN2" 252253 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247659 248403 "CARTEN" 250814 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -2309 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2309 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2309 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . 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+(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2309 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2309 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -2309 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2309 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) 
+((-1793 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) 
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+((-1793 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) 
+(-10 -7 (-15 -1793 (|#4| (-1 |#3| |#1|) |#2|))) 
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+NIL 
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+NIL 
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(-12 (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) (-5 *2 (-663 (-2 (|:| -3527 (-1203 *5)) (|:| -3084 (-663 (-976 *5)))))) (-5 *1 (-1327 *5 *6 *7)) (-5 *3 (-663 (-976 *5))) (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209))))) (-2618 (*1 *2 *3) (-12 (-5 *3 (-1078 *4 *5)) (-4 *4 (-13 (-871) (-319) (-149) (-1052))) (-14 *5 (-663 (-1209))) (-5 *2 (-663 (-2 (|:| -3527 (-1203 *4)) (|:| -3084 (-663 (-976 *4)))))) (-5 *1 (-1327 *4 *5 *6)) (-14 *6 (-663 (-1209))))) (-1460 (*1 *2 *3) (-12 (-5 *3 (-663 (-976 *4))) (-4 *4 (-13 (-871) (-319) (-149) (-1052))) (-5 *2 (-663 (-1078 *4 *5))) (-5 *1 (-1327 *4 *5 *6)) (-14 *5 (-663 (-1209))) (-14 *6 (-663 (-1209))))) (-1460 (*1 *2 *3 *4) (-12 (-5 *3 (-663 (-976 *5))) (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) (-5 *2 (-663 (-1078 *5 *6))) (-5 *1 (-1327 *5 *6 *7)) (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209))))) (-1460 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-663 (-976 *5))) (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) (-5 *2 (-663 (-1078 *5 *6))) (-5 *1 (-1327 *5 *6 *7)) (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209)))))) 
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+((-2194 (((-3 (-1299 (-421 (-560))) "failed") (-1299 |#1|) |#1|) 21 T ELT)) (-2957 (((-114) (-1299 |#1|)) 12 T ELT)) (-1576 (((-3 (-1299 (-560)) "failed") (-1299 |#1|)) 16 T ELT))) 
+(((-1328 |#1|) (-10 -7 (-15 -2957 ((-114) (-1299 |#1|))) (-15 -1576 ((-3 (-1299 (-560)) "failed") (-1299 |#1|))) (-15 -2194 ((-3 (-1299 (-421 (-560))) "failed") (-1299 |#1|) |#1|))) (-13 (-1081) (-660 (-560)))) (T -1328)) 
+((-2194 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1299 *4)) (-4 *4 (-13 (-1081) (-660 (-560)))) (-5 *2 (-1299 (-421 (-560)))) (-5 *1 (-1328 *4)))) (-1576 (*1 *2 *3) (|partial| -12 (-5 *3 (-1299 *4)) (-4 *4 (-13 (-1081) (-660 (-560)))) (-5 *2 (-1299 (-560))) (-5 *1 (-1328 *4)))) (-2957 (*1 *2 *3) (-12 (-5 *3 (-1299 *4)) (-4 *4 (-13 (-1081) (-660 (-560)))) (-5 *2 (-114)) (-5 *1 (-1328 *4))))) 
+(-10 -7 (-15 -2957 ((-114) (-1299 |#1|))) (-15 -1576 ((-3 (-1299 (-560)) "failed") (-1299 |#1|))) (-15 -2194 ((-3 (-1299 (-421 (-560))) "failed") (-1299 |#1|) |#1|))) 
+((-3808 (((-114) $ $) NIL T ELT)) (-3136 (((-114) $) 12 T ELT)) (-1469 (((-3 $ "failed") $ $) NIL T ELT)) (-2233 (((-793)) 9 T ELT)) (-4489 (($) NIL T CONST)) (-2167 (((-3 $ "failed") $) 57 T ELT)) (-2150 (($) 46 T ELT)) (-3363 (((-114) $) 38 T ELT)) (-3851 (((-713 $) $) 36 T ELT)) (-3862 (((-949) $) 14 T ELT)) (-2128 (((-1191) $) NIL T ELT)) (-2689 (($) 26 T CONST)) (-2081 (($ (-949)) 47 T ELT)) (-1473 (((-1152) $) NIL T ELT)) (-1830 (((-560) $) 16 T ELT)) (-3834 (((-888) $) 21 T ELT) (($ (-560)) 18 T ELT)) (-3103 (((-793)) 10 T CONST)) (-1519 (((-114) $ $) 59 T ELT)) (-2971 (($) 23 T CONST)) (-2983 (($) 25 T CONST)) (-2478 (((-114) $ $) 31 T ELT)) (-2581 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-2571 (($ $ $) 29 T ELT)) (** (($ $ (-949)) NIL T ELT) (($ $ (-793)) 52 T ELT)) (* (($ (-949) $) NIL T ELT) (($ (-793) $) NIL T ELT) (($ (-560) $) 41 T ELT) (($ $ $) 40 T ELT))) 
+(((-1329 |#1|) (-13 (-175) (-381) (-633 (-560)) (-1184)) (-949)) (T -1329)) 
+NIL 
+(-13 (-175) (-381) (-633 (-560)) (-1184)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
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XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3443186 3445757 3446145 "XPBWPOLY" 3446898 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3438078 3439657 3439712 "XFALG" 3441884 NIL XFALG (NIL T T) -9 NIL 3442673 NIL) (-1318 3433354 3436054 3436096 "XF" 3436717 NIL XF (NIL T) -9 NIL 3437117 NIL) (-1317 3432951 3433063 3433232 "XF-" 3433237 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3432066 3432188 3432393 "XEXPPKG" 3432843 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3429807 3431916 3432012 "XDPOLY" 3432017 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3428462 3429200 3429243 "XALG" 3429248 NIL XALG (NIL T) -9 NIL 3429359 NIL) (-1313 3421372 3426439 3426933 "WUTSET" 3428054 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3419474 3420424 3420747 "WP" 3421183 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3419022 3419296 3419366 "WHILEAST" 3419426 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418434 3418739 3418833 "WHEREAST" 3418950 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417308 3417518 3417813 "WFFINTBS" 3418231 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415176 3415639 3416101 "WEIER" 3416880 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3414100 3414658 3414700 "VSPACE" 3414836 NIL VSPACE (NIL T) -9 NIL 3414910 NIL) (-1306 3413932 3413965 3414056 "VSPACE-" 3414061 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413729 3413783 3413851 "VOID" 3413886 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409997 3410792 3411529 "VIEWDEF" 3413014 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398941 3401545 3403718 "VIEW3D" 3407846 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390958 3392852 3394431 "VIEW2D" 3397384 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3389058 3389453 3389859 "VIEW" 3390574 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387611 3387894 3388212 "VECTOR2" 3388788 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382517 3387381 3387473 "VECTOR" 3387554 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375462 3380221 3380264 "VECTCAT" 3381259 NIL VECTCAT (NIL T) -9 NIL 3381846 NIL) (-1297 3374404 3374730 3375120 "VECTCAT-" 3375125 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373810 3374055 3374175 "VARIABLE" 3374319 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373743 3373748 3373778 "UTYPE" 3373783 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372551 3372727 3372989 "UTSODETL" 3373569 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369943 3370451 3370975 "UTSODE" 3372092 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359953 3365876 3365919 "UTSCAT" 3367031 NIL UTSCAT (NIL T) -9 NIL 3367789 NIL) (-1291 3357079 3358023 3359012 "UTSCAT-" 3359017 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356700 3356749 3356882 "UTS2" 3357030 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3348017 3354461 3354941 "UTS" 3356278 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341884 3344827 3344870 "URAGG" 3346940 NIL URAGG (NIL T) -9 NIL 3347663 NIL) (-1287 3338607 3339686 3340809 "URAGG-" 3340814 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333983 3337242 3337707 "UPXSSING" 3338271 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326412 3333887 3333959 "UPXSCONS" 3333964 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315170 3322614 3322676 "UPXSCCA" 3323250 NIL UPXSCCA (NIL T T) -9 NIL 3323483 NIL) (-1283 3314790 3314893 3315067 "UPXSCCA-" 3315072 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303448 3310617 3310660 "UPXSCAT" 3311308 NIL UPXSCAT (NIL T) -9 NIL 3311917 NIL) (-1281 3302872 3302957 3303136 "UPXS2" 3303363 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294364 3302254 3302518 "UPXS" 3302666 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3293000 3293271 3293622 "UPSQFREE" 3294107 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285831 3289266 3289321 "UPSCAT" 3290401 NIL UPSCAT (NIL T T) -9 NIL 3291167 NIL) (-1277 3284987 3285242 3285569 "UPSCAT-" 3285574 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284608 3284657 3284790 "UPOLYC2" 3284938 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268756 3277735 3277778 "UPOLYC" 3279879 NIL UPOLYC (NIL T) -9 NIL 3281100 NIL) (-1274 3259625 3262524 3265664 "UPOLYC-" 3265669 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258946 3259071 3259235 "UPMP" 3259514 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258493 3258580 3258719 "UPDIVP" 3258859 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3257031 3257310 3257626 "UPDECOMP" 3258242 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256244 3256374 3256560 "UPCDEN" 3256915 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255757 3255832 3255981 "UP2" 3256169 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246353 3255440 3255569 "UP" 3255676 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245558 3245695 3245900 "UNISEG2" 3246196 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243911 3244762 3245039 "UNISEG" 3245316 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242953 3243151 3243377 "UNIFACT" 3243727 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229684 3242857 3242929 "ULSCONS" 3242934 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209501 3222764 3222826 "ULSCCAT" 3223464 NIL ULSCCAT (NIL T T) -9 NIL 3223753 NIL) (-1262 3208497 3208796 3209184 "ULSCCAT-" 3209189 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196952 3204043 3204086 "ULSCAT" 3204949 NIL ULSCAT (NIL T) -9 NIL 3205680 NIL) (-1260 3196376 3196461 3196640 "ULS2" 3196867 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178207 3195688 3195930 "ULS" 3196192 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3177126 3177826 3177940 "UINT8" 3178051 T UINT8 (NIL) -8 NIL NIL 3178143) (-1257 3176044 3176744 3176858 "UINT64" 3176969 T UINT64 (NIL) -8 NIL NIL 3177061) (-1256 3174962 3175662 3175776 "UINT32" 3175887 T UINT32 (NIL) -8 NIL NIL 3175979) (-1255 3173880 3174580 3174694 "UINT16" 3174805 T UINT16 (NIL) -8 NIL NIL 3174897) (-1254 3171959 3173126 3173156 "UFD" 3173368 T UFD (NIL) -9 NIL 3173482 NIL) (-1253 3171741 3171799 3171894 "UFD-" 3171899 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170799 3171006 3171222 "UDVO" 3171547 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168565 3169024 3169495 "UDPO" 3170363 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168277 3168520 3168551 "TYPEAST" 3168556 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168210 3168215 3168245 "TYPE" 3168250 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167163 3167383 3167623 "TWOFACT" 3168004 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3166138 3166572 3166807 "TUPLE" 3166963 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163775 3164348 3164887 "TUBETOOL" 3165621 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162581 3162822 3163064 "TUBE" 3163568 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150716 3155338 3155435 "TSETCAT" 3160704 NIL TSETCAT (NIL T T T T) -9 NIL 3162236 NIL) (-1243 3145184 3147048 3148939 "TSETCAT-" 3148944 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139370 3144156 3144439 "TS" 3144936 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133843 3134856 3135785 "TRMANIP" 3138506 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133272 3133347 3133510 "TRIMAT" 3133775 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3131084 3131375 3131732 "TRIGMNIP" 3133021 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130568 3130717 3130747 "TRIGCAT" 3130960 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130213 3130316 3130457 "TRIGCAT-" 3130462 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126827 3129071 3129352 "TREE" 3129967 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125933 3126629 3126659 "TRANFUN" 3126694 T TRANFUN (NIL) -9 NIL 3126760 NIL) (-1234 3125152 3125403 3125683 "TRANFUN-" 3125688 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124950 3124988 3125049 "TOPSP" 3125113 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124280 3124413 3124567 "TOOLSIGN" 3124831 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122794 3123457 3123696 "TEXTFILE" 3124063 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122569 3122606 3122678 "TEX1" 3122757 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120373 3121022 3121451 "TEX" 3122162 T TEX (NIL) -8 NIL NIL NIL) (-1228 3120009 3120084 3120174 "TEMUTL" 3120305 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3118103 3118443 3118768 "TBCMPPK" 3119732 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109423 3116189 3116245 "TBAGG" 3116645 NIL TBAGG (NIL T T) -9 NIL 3116856 NIL) (-1225 3104307 3105981 3107735 "TBAGG-" 3107740 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103673 3103798 3103943 "TANEXP" 3104196 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103124 3103448 3103538 "TALGOP" 3103618 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102518 3102635 3102773 "TABLEAU" 3103021 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095532 3102375 3102468 "TABLE" 3102473 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3090062 3091360 3092608 "TABLBUMP" 3094318 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089272 3089431 3089612 "SYSTEM" 3089903 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085677 3086430 3087213 "SYSSOLP" 3088523 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085439 3085632 3085663 "SYSPTR" 3085668 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084278 3084970 3085096 "SYSNNI" 3085282 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085374) (-1215 3083485 3084040 3084119 "SYSINT" 3084179 NIL SYSINT (NIL NIL) -8 NIL NIL 3084224) (-1214 3079583 3080763 3081473 "SYNTAX" 3082797 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076663 3077343 3077975 "SYMTAB" 3078973 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071762 3072814 3073797 "SYMS" 3075702 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068668 3071213 3071446 "SYMPOLY" 3071564 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068173 3068260 3068383 "SYMFUNC" 3068580 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063971 3065485 3066298 "SYMBOL" 3067382 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057444 3059199 3060919 "SWITCH" 3062273 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050205 3056400 3056694 "SUTS" 3057208 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041697 3049587 3049851 "SUPXS" 3049999 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040844 3040983 3041200 "SUPFRACF" 3041565 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040459 3040524 3040637 "SUP2" 3040779 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3031003 3040077 3040203 "SUP" 3040368 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029427 3029725 3030081 "SUMRF" 3030702 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028750 3028828 3029020 "SUMFS" 3029348 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010616 3028062 3028304 "SULS" 3028566 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010164 3010438 3010508 "SUCHTAST" 3010568 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009405 3009689 3009829 "SUCH" 3010072 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3003044 3004311 3005270 "SUBSPACE" 3008493 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002464 3002564 3002728 "SUBRESP" 3002932 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996475 2997757 2998904 "STTFNC" 3001364 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989669 2991140 2992451 "STTF" 2995211 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980786 2982851 2984645 "STTAYLOR" 2987910 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973540 2980650 2980733 "STRTBL" 2980738 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967937 2973249 2973348 "STRING" 2973463 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967441 2967524 2967668 "STREAM3" 2967854 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966405 2966606 2966841 "STREAM2" 2967254 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2966087 2966145 2966238 "STREAM1" 2966347 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958201 2963706 2964317 "STREAM" 2965511 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957193 2957398 2957629 "STINPROD" 2958017 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956308 2956682 2956830 "STEPAST" 2957067 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955804 2956049 2956079 "STEP" 2956173 T STEP (NIL) -9 NIL 2956244 NIL) (-1183 2948860 2955703 2955780 "STBL" 2955785 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943410 2948023 2948066 "STAGG" 2948219 NIL STAGG (NIL T) -9 NIL 2948308 NIL) (-1181 2940962 2941714 2942586 "STAGG-" 2942591 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938934 2940732 2940824 "STACK" 2940905 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938251 2938764 2938794 "SRING" 2938799 T SRING (NIL) -9 NIL 2938819 NIL) (-1178 2930258 2936392 2936848 "SREGSET" 2937881 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922605 2924052 2925565 "SRDCMPK" 2928864 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914905 2919964 2919994 "SRAGG" 2921297 T SRAGG (NIL) -9 NIL 2921905 NIL) (-1175 2913856 2914177 2914556 "SRAGG-" 2914561 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907440 2912803 2913224 "SQMATRIX" 2913482 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900852 2904158 2904885 "SPLTREE" 2906785 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896677 2897508 2898154 "SPLNODE" 2900278 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895652 2895957 2895987 "SPFCAT" 2896431 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894347 2894599 2894863 "SPECOUT" 2895410 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884993 2887311 2887341 "SPADXPT" 2892019 T SPADXPT (NIL) -9 NIL 2894185 NIL) (-1168 2884748 2884794 2884863 "SPADPRSR" 2884946 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882351 2884703 2884734 "SPADAST" 2884739 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873952 2876055 2876098 "SPACEC" 2880471 NIL SPACEC (NIL T) -9 NIL 2882287 NIL) (-1165 2871752 2873884 2873933 "SPACE3" 2873938 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870484 2870675 2870966 "SORTPAK" 2871557 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868546 2868879 2869291 "SOLVETRA" 2870148 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867584 2867818 2868079 "SOLVESER" 2868319 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862816 2863776 2864771 "SOLVERAD" 2866636 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858541 2859240 2859969 "SOLVEFOR" 2862183 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852145 2857889 2857986 "SNTSCAT" 2857991 NIL SNTSCAT (NIL T T T T) -9 NIL 2858061 NIL) (-1158 2845696 2850468 2850859 "SMTS" 2851835 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839418 2845584 2845661 "SMP" 2845666 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837547 2837878 2838276 "SMITH" 2839115 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2829072 2834126 2834229 "SMATCAT" 2835580 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836130 NIL) (-1154 2825844 2826835 2828013 "SMATCAT-" 2828018 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823313 2825052 2825095 "SKAGG" 2825356 NIL SKAGG (NIL T) -9 NIL 2825491 NIL) (-1152 2818831 2822796 2822973 "SINT" 2823125 T SINT (NIL) -8 NIL NIL 2823280) (-1151 2818597 2818641 2818707 "SIMPAN" 2818787 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817417 2817656 2817931 "SIGNRF" 2818356 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816232 2816401 2816685 "SIGNEF" 2817246 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815472 2815815 2815939 "SIGAST" 2816130 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814697 2815007 2815147 "SIG" 2815354 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812349 2812841 2813347 "SHP" 2814238 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805673 2812250 2812326 "SHDP" 2812331 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805184 2805424 2805454 "SGROUP" 2805547 T SGROUP (NIL) -9 NIL 2805609 NIL) (-1143 2805036 2805068 2805141 "SGROUP-" 2805146 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801755 2802525 2803248 "SGCF" 2804335 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795457 2801201 2801298 "SFRTCAT" 2801303 NIL SFRTCAT (NIL T T T T) -9 NIL 2801342 NIL) (-1140 2788776 2789896 2791032 "SFRGCD" 2794440 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781794 2782975 2784161 "SFQCMPK" 2787709 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781396 2781503 2781614 "SFORT" 2781735 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780322 2781236 2781357 "SEXOF" 2781362 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775911 2776818 2776913 "SEXCAT" 2779535 NIL SEXCAT (NIL T T T T T) -9 NIL 2780095 NIL) (-1135 2774826 2775792 2775860 "SEX" 2775865 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772948 2773539 2773844 "SETMN" 2774567 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772478 2772666 2772696 "SETCAT" 2772813 T SETCAT (NIL) -9 NIL 2772898 NIL) (-1132 2772246 2772310 2772409 "SETCAT-" 2772414 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768349 2770707 2770750 "SETAGG" 2771620 NIL SETAGG (NIL T) -9 NIL 2771960 NIL) (-1130 2767771 2767923 2768160 "SETAGG-" 2768165 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764580 2767705 2767753 "SET" 2767758 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763963 2764276 2764377 "SEQAST" 2764501 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763090 2763456 2763517 "SEGXCAT" 2763803 NIL SEGXCAT (NIL T T) -9 NIL 2763923 NIL) (-1126 2762015 2762283 2762326 "SEGCAT" 2762848 NIL SEGCAT (NIL T) -9 NIL 2763069 NIL) (-1125 2761630 2761695 2761808 "SEGBIND2" 2761950 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760520 2760993 2761201 "SEGBIND" 2761457 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2760039 2760321 2760398 "SEGAST" 2760465 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759248 2759384 2759588 "SEG2" 2759883 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758164 2758914 2759096 "SEG" 2759101 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757397 2758099 2758146 "SDVAR" 2758151 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748755 2757167 2757297 "SDPOL" 2757302 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747324 2747614 2747933 "SCPKG" 2748470 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746446 2746660 2746852 "SCOPE" 2747154 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745642 2745800 2745979 "SCACHE" 2746301 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745226 2745460 2745490 "SASTCAT" 2745495 T SASTCAT (NIL) -9 NIL 2745508 NIL) (-1114 2744629 2745061 2745137 "SAOS" 2745172 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744188 2744229 2744402 "SAERFFC" 2744588 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743775 2743816 2743975 "SAEFACT" 2744147 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736823 2743672 2743752 "SAE" 2743757 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735126 2735458 2735859 "RURPK" 2736489 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733703 2734069 2734374 "RULESET" 2734960 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733273 2733497 2733580 "RULECOLD" 2733655 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730388 2731026 2731484 "RULE" 2732954 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730172 2730206 2730277 "RTVALUE" 2730339 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729583 2729889 2729983 "RSTRCAST" 2730100 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724353 2725226 2726146 "RSETGCD" 2728782 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712917 2718661 2718758 "RSETCAT" 2722877 NIL RSETCAT (NIL T T T T) -9 NIL 2723974 NIL) (-1102 2710736 2711383 2712207 "RSETCAT-" 2712212 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2703044 2704498 2706018 "RSDCMPK" 2709335 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700913 2701476 2701550 "RRCC" 2702636 NIL RRCC (NIL T T) -9 NIL 2702980 NIL) (-1099 2700234 2700438 2700717 "RRCC-" 2700722 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699617 2699930 2700031 "RPTAST" 2700155 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2672003 2682729 2682796 "RPOLCAT" 2693462 NIL RPOLCAT (NIL T T T) -9 NIL 2696622 NIL) (-1096 2662973 2665841 2668963 "RPOLCAT-" 2668968 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653426 2661184 2661666 "ROUTINE" 2662513 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649489 2653052 2653192 "ROMAN" 2653308 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647601 2648349 2648609 "ROIRC" 2649294 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643321 2646090 2646120 "RNS" 2646424 T RNS (NIL) -9 NIL 2646698 NIL) (-1091 2641728 2642213 2642747 "RNS-" 2642822 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640689 2641093 2641295 "RNGBIND" 2641579 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639982 2640486 2640516 "RNG" 2640521 T RNG (NIL) -9 NIL 2640542 NIL) (-1088 2639277 2639755 2639798 "RMODULE" 2639803 NIL RMODULE (NIL T) -9 NIL 2639830 NIL) (-1087 2638101 2638207 2638543 "RMCAT2" 2639178 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634603 2637447 2637744 "RMATRIX" 2637863 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627102 2629690 2629805 "RMATCAT" 2633164 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634146 NIL) (-1084 2626441 2626624 2626931 "RMATCAT-" 2626936 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2626014 2626228 2626271 "RLINSET" 2626333 NIL RLINSET (NIL T) -9 NIL 2626377 NIL) (-1082 2625575 2625656 2625784 "RINTERP" 2625933 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624499 2625173 2625203 "RING" 2625259 T RING (NIL) -9 NIL 2625351 NIL) (-1080 2624279 2624335 2624432 "RING-" 2624437 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623090 2623357 2623615 "RIDIST" 2624043 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613715 2622558 2622764 "RGCHAIN" 2622938 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612973 2613457 2613498 "RGBCSPC" 2613556 NIL RGBCSPC (NIL T) -9 NIL 2613608 NIL) (-1076 2612039 2612498 2612539 "RGBCMDL" 2612771 NIL RGBCMDL (NIL T) -9 NIL 2612885 NIL) (-1075 2611679 2611748 2611851 "RFFACTOR" 2611970 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611398 2611439 2611536 "RFFACT" 2611638 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609449 2609879 2610261 "RFDIST" 2611038 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606389 2607057 2607727 "RF" 2608813 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605836 2605934 2606097 "RETSOL" 2606291 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605454 2605552 2605595 "RETRACT" 2605728 NIL RETRACT (NIL T) -9 NIL 2605815 NIL) (-1069 2605297 2605328 2605415 "RETRACT-" 2605420 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604845 2605119 2605189 "RETAST" 2605249 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597195 2604498 2604625 "RESULT" 2604740 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595630 2596464 2596663 "RESRING" 2597098 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595254 2595315 2595413 "RESLATC" 2595567 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594953 2594994 2595101 "REPSQ" 2595213 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594644 2594685 2594796 "REPDB" 2594912 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588476 2589933 2591156 "REP2" 2593456 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584779 2585534 2586342 "REP1" 2587703 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582159 2582781 2583383 "REP" 2584199 T REP (NIL) -7 NIL NIL NIL) (-1059 2574167 2580300 2580756 "REGSET" 2581789 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572876 2573315 2573565 "REF" 2573952 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572241 2572356 2572523 "REDORDER" 2572760 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567612 2571454 2571681 "RECLOS" 2572069 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566646 2566845 2567060 "REALSOLV" 2567419 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563093 2563931 2564815 "REAL0Q" 2565811 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558646 2559682 2560743 "REAL0" 2562074 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558480 2558533 2558563 "REAL" 2558568 T REAL (NIL) -9 NIL 2558603 NIL) (-1051 2557891 2558197 2558291 "RDUCEAST" 2558408 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557290 2557368 2557575 "RDIV" 2557813 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556340 2556532 2556745 "RDIST" 2557112 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554925 2555224 2555596 "RDETRS" 2556048 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552719 2553191 2553729 "RDETR" 2554467 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551338 2551622 2552019 "RDEEFS" 2552435 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549841 2550153 2550578 "RDEEF" 2551026 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543320 2546795 2546825 "RCFIELD" 2548120 T RCFIELD (NIL) -9 NIL 2548851 NIL) (-1043 2541276 2541888 2542584 "RCFIELD-" 2542659 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537328 2539349 2539392 "RCAGG" 2540476 NIL RCAGG (NIL T) -9 NIL 2540941 NIL) (-1041 2536938 2537050 2537213 "RCAGG-" 2537218 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536255 2536385 2536550 "RATRET" 2536822 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535796 2535875 2535996 "RATFACT" 2536183 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2535074 2535224 2535376 "RANDSRC" 2535666 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534802 2534852 2534925 "RADUTIL" 2535023 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526947 2533633 2533944 "RADIX" 2534525 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516562 2526789 2526919 "RADFF" 2526924 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516191 2516284 2516314 "RADCAT" 2516474 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515961 2516021 2516121 "RADCAT-" 2516126 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513872 2515731 2515823 "QUEUE" 2515904 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513497 2513546 2513677 "QUATCT2" 2513823 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505875 2509920 2509962 "QUATCAT" 2510753 NIL QUATCAT (NIL T) -9 NIL 2511519 NIL) (-1029 2501756 2503051 2504441 "QUATCAT-" 2504537 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497602 2501689 2501737 "QUAT" 2501742 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494858 2496650 2496693 "QUAGG" 2497074 NIL QUAGG (NIL T) -9 NIL 2497249 NIL) (-1026 2494406 2494680 2494750 "QQUTAST" 2494810 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493317 2493919 2494084 "QFORM" 2494287 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492942 2492991 2493122 "QFCAT2" 2493268 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482639 2488789 2488831 "QFCAT" 2489499 NIL QFCAT (NIL T) -9 NIL 2490500 NIL) (-1022 2477973 2479421 2481008 "QFCAT-" 2481104 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477404 2477538 2477670 "QEQUAT" 2477863 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470422 2471603 2472789 "QCMPACK" 2476337 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469651 2469833 2470069 "QALGSET2" 2470240 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467101 2467637 2468067 "QALGSET" 2469306 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465768 2466010 2466329 "PWFFINTB" 2466874 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463913 2464111 2464467 "PUSHVAR" 2465582 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459640 2460856 2460899 "PTRANFN" 2462810 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457977 2458322 2458646 "PTPACK" 2459351 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457600 2457663 2457774 "PTFUNC2" 2457914 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451516 2456389 2456432 "PTCAT" 2456732 NIL PTCAT (NIL T) -9 NIL 2456885 NIL) (-1011 2451165 2451206 2451332 "PSQFR" 2451475 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449737 2450053 2450389 "PSEUDLIN" 2450863 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436257 2438832 2441158 "PSETPK" 2447497 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428965 2431993 2432091 "PSETCAT" 2435132 NIL PSETCAT (NIL T T T T) -9 NIL 2435946 NIL) (-1007 2426690 2427432 2428256 "PSETCAT-" 2428261 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2426003 2426198 2426228 "PSCURVE" 2426500 T PSCURVE (NIL) -9 NIL 2426667 NIL) (-1005 2421726 2423493 2423560 "PSCAT" 2424412 NIL PSCAT (NIL T T T) -9 NIL 2424652 NIL) (-1004 2420720 2421002 2421405 "PSCAT-" 2421410 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418888 2419779 2420044 "PRTITION" 2420477 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418299 2418605 2418699 "PRTDAST" 2418816 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407143 2409565 2411755 "PRS" 2416161 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404758 2406460 2406502 "PRQAGG" 2406688 NIL PRQAGG (NIL T) -9 NIL 2406790 NIL) (-999 2403937 2404386 2404414 "PROPLOG" 2404553 T PROPLOG (NIL) -9 NIL 2404668 NIL) (-998 2403535 2403598 2403721 "PROPFUN2" 2403860 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402832 2402971 2403143 "PROPFUN1" 2403396 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400813 2401579 2401876 "PROPFRML" 2402568 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400258 2400389 2400517 "PROPERTY" 2400705 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2394071 2398424 2399244 "PRODUCT" 2399484 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393861 2393899 2393958 "PRINT" 2394032 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393177 2393318 2393470 "PRIMES" 2393741 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391224 2391643 2392109 "PRIMELT" 2392756 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390941 2391002 2391030 "PRIMCAT" 2391154 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389930 2390126 2390354 "PRIMARR2" 2390759 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385652 2389868 2389913 "PRIMARR" 2389918 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385289 2385351 2385462 "PREASSOC" 2385590 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382254 2384747 2384981 "PR" 2385100 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381705 2381862 2381890 "PPCURVE" 2382095 T PPCURVE (NIL) -9 NIL 2382231 NIL) (-984 2381252 2381500 2381583 "PORTNUM" 2381642 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378589 2379010 2379602 "POLYROOT" 2380833 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377966 2378030 2378264 "POLYLIFT" 2378525 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374187 2374690 2375319 "POLYCATQ" 2377511 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359835 2365934 2365999 "POLYCAT" 2369513 NIL POLYCAT (NIL T T T) -9 NIL 2371391 NIL) (-979 2352975 2355160 2357537 "POLYCAT-" 2357542 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352556 2352630 2352750 "POLY2UP" 2352901 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352182 2352245 2352354 "POLY2" 2352493 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345397 2351786 2351946 "POLY" 2352055 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2344058 2344321 2344597 "POLUTIL" 2345171 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342377 2342690 2343021 "POLTOPOL" 2343780 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337373 2342311 2342358 "POINT" 2342363 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335506 2335917 2336292 "PNTHEORY" 2337018 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333952 2334261 2334660 "PMTOOLS" 2335204 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333539 2333623 2333740 "PMSYM" 2333868 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2333041 2333116 2333291 "PMQFCAT" 2333464 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332422 2332520 2332682 "PMPREDFS" 2332942 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331765 2331887 2332043 "PMPRED" 2332299 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330419 2330637 2331015 "PMPLCAT" 2331527 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329945 2330030 2330182 "PMLSAGG" 2330334 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329412 2329494 2329676 "PMKERNEL" 2329863 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2329023 2329104 2329217 "PMINS" 2329331 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328459 2328534 2328743 "PMFS" 2328948 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327675 2327805 2328010 "PMDOWN" 2328336 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326924 2327058 2327221 "PMASSFS" 2327562 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2326067 2326249 2326430 "PMASS" 2326763 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325716 2325790 2325884 "PLOTTOOL" 2325993 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321368 2322562 2323484 "PLOT3D" 2324814 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320256 2320457 2320692 "PLOT1" 2321172 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314677 2316067 2317215 "PLOT" 2319128 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289852 2294743 2299594 "PLEQN" 2309943 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289539 2289592 2289695 "PINTERPA" 2289799 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288845 2288979 2289159 "PINTERP" 2289404 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286929 2288095 2288123 "PID" 2288320 T PID (NIL) -9 NIL 2288447 NIL) (-950 2286674 2286717 2286792 "PICOERCE" 2286886 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285770 2286438 2286525 "PI" 2286565 T PI (NIL) -8 NIL NIL 2286632) (-948 2285078 2285229 2285405 "PGROEB" 2285626 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280517 2281476 2282382 "PGE" 2284192 T PGE (NIL) -7 NIL NIL NIL) (-946 2278598 2278887 2279253 "PGCD" 2280234 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277924 2278039 2278200 "PFRPAC" 2278482 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274182 2276472 2276825 "PFR" 2277603 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272535 2272815 2273140 "PFOTOOLS" 2273929 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2271050 2271307 2271658 "PFOQ" 2272292 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269533 2269763 2270119 "PFO" 2270834 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266617 2268123 2268151 "PFECAT" 2268744 T PFECAT (NIL) -9 NIL 2269121 NIL) (-939 2266065 2266230 2266437 "PFECAT-" 2266442 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264638 2264920 2265221 "PFBRU" 2265814 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262467 2262856 2263288 "PFBR" 2264289 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258413 2262356 2262425 "PF" 2262430 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253467 2254620 2255490 "PERMGRP" 2257576 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251379 2252491 2252532 "PERMCAT" 2252932 NIL PERMCAT (NIL T) -9 NIL 2253230 NIL) (-933 2251026 2251073 2251197 "PERMAN" 2251332 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246828 2248535 2249183 "PERM" 2250411 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2244069 2246493 2246615 "PENDTREE" 2246739 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242950 2243213 2243254 "PDSPC" 2243787 NIL PDSPC (NIL T) -9 NIL 2244032 NIL) (-929 2242005 2242271 2242633 "PDSPC-" 2242638 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240719 2241655 2241696 "PDRING" 2241701 NIL PDRING (NIL T) -9 NIL 2241729 NIL) (-927 2239462 2240224 2240278 "PDMOD" 2240283 NIL PDMOD (NIL T T) -9 NIL 2240387 NIL) (-926 2236629 2237455 2238123 "PDEPROB" 2238814 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234138 2234678 2235233 "PDEPACK" 2236094 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2233026 2233240 2233491 "PDECOMP" 2233937 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230543 2231434 2231462 "PDECAT" 2232249 T PDECAT (NIL) -9 NIL 2232962 NIL) (-922 2230160 2230227 2230281 "PDDOM" 2230446 NIL PDDOM (NIL T T) -9 NIL 2230526 NIL) (-921 2229973 2230009 2230116 "PDDOM-" 2230121 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229718 2229757 2229847 "PCOMP" 2229934 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227758 2228519 2228816 "PBWLB" 2229447 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227384 2227447 2227556 "PATTERN2" 2227695 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225093 2225529 2225986 "PATTERN1" 2226973 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217272 2219166 2220504 "PATTERN" 2223776 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216830 2216903 2217035 "PATRES2" 2217199 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214096 2214779 2215260 "PATRES" 2216395 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211949 2212384 2212791 "PATMATCH" 2213763 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211403 2211654 2211695 "PATMAB" 2211802 NIL PATMAB (NIL T) -9 NIL 2211885 NIL) (-911 2209849 2210257 2210515 "PATLRES" 2211208 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209387 2209518 2209559 "PATAB" 2209564 NIL PATAB (NIL T) -9 NIL 2209736 NIL) (-909 2207527 2207964 2208387 "PARTPERM" 2208984 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207136 2207211 2207313 "PARSURF" 2207458 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206762 2206825 2206934 "PARSU2" 2207073 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206520 2206566 2206633 "PARSER" 2206715 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206129 2206204 2206306 "PARSCURV" 2206451 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205755 2205818 2205927 "PARSC2" 2206066 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205382 2205452 2205549 "PARPCURV" 2205691 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2205008 2205071 2205180 "PARPC2" 2205319 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203997 2204381 2204563 "PARAMAST" 2204846 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203505 2203603 2203722 "PAN2EXPR" 2203898 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202198 2202626 2202854 "PALETTE" 2203297 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200543 2201203 2201563 "PAIR" 2201884 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193476 2199800 2199995 "PADICRC" 2200397 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185733 2192820 2193005 "PADICRAT" 2193323 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182530 2184393 2184433 "PADICCT" 2185014 NIL PADICCT (NIL NIL) -9 NIL 2185296 NIL) (-894 2180546 2182467 2182512 "PADIC" 2182517 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179491 2179703 2179971 "PADEPAC" 2180333 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178691 2178836 2179042 "PADE" 2179353 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176924 2177899 2178179 "OWP" 2178495 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176369 2176630 2176727 "OVERSET" 2176847 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175289 2175974 2176146 "OVAR" 2176237 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163525 2166398 2168598 "OUTFORM" 2173109 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162807 2163122 2163249 "OUTBFILE" 2163418 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2162084 2162279 2162307 "OUTBCON" 2162625 T OUTBCON (NIL) -9 NIL 2162791 NIL) (-885 2161667 2161797 2161954 "OUTBCON-" 2161959 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160907 2161052 2161213 "OUT" 2161526 T OUT (NIL) -7 NIL NIL NIL) (-883 2160203 2160636 2160725 "OSI" 2160838 T OSI (NIL) -8 NIL NIL NIL) (-882 2159622 2160044 2160072 "OSGROUP" 2160077 T OSGROUP (NIL) -9 NIL 2160099 NIL) (-881 2158333 2158594 2158879 "ORTHPOL" 2159369 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155584 2158168 2158289 "OREUP" 2158294 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152687 2155275 2155402 "ORESUP" 2155526 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150187 2150715 2151276 "OREPCTO" 2152176 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143565 2146060 2146101 "OREPCAT" 2148449 NIL OREPCAT (NIL T) -9 NIL 2149553 NIL) (-876 2140538 2141494 2142552 "OREPCAT-" 2142557 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139730 2140008 2140036 "ORDTYPE" 2140345 T ORDTYPE (NIL) -9 NIL 2140508 NIL) (-874 2139031 2139247 2139502 "ORDTYPE-" 2139507 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138387 2138770 2138928 "ORDSTRCT" 2138933 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137885 2138255 2138283 "ORDSET" 2138288 T ORDSET (NIL) -9 NIL 2138310 NIL) (-871 2136536 2137507 2137535 "ORDRING" 2137540 T ORDRING (NIL) -9 NIL 2137569 NIL) (-870 2135787 2136352 2136380 "ORDMON" 2136385 T ORDMON (NIL) -9 NIL 2136406 NIL) (-869 2134931 2135096 2135291 "ORDFUNS" 2135636 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134146 2134661 2134689 "ORDFIN" 2134754 T ORDFIN (NIL) -9 NIL 2134828 NIL) (-867 2133400 2133539 2133725 "ORDCOMP2" 2134006 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129747 2131986 2132395 "ORDCOMP" 2133024 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126268 2127238 2128052 "OPTPROB" 2128953 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2123010 2123709 2124413 "OPTPACK" 2125584 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120623 2121449 2121477 "OPTCAT" 2122296 T OPTCAT (NIL) -9 NIL 2122946 NIL) (-862 2119941 2120300 2120405 "OPSIG" 2120538 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119703 2119748 2119814 "OPQUERY" 2119895 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2119009 2119289 2119330 "OPERCAT" 2119542 NIL OPERCAT (NIL T) -9 NIL 2119639 NIL) (-859 2118752 2118820 2118937 "OPERCAT-" 2118942 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115668 2117063 2117567 "OP" 2118281 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114961 2115088 2115262 "ONECOMP2" 2115540 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111574 2113758 2114127 "ONECOMP" 2114625 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110975 2111099 2111229 "OMSERVER" 2111464 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107487 2110413 2110453 "OMSAGG" 2110514 NIL OMSAGG (NIL T) -9 NIL 2110579 NIL) (-853 2106062 2106373 2106655 "OMPKG" 2107225 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104409 2105611 2105780 "OMLO" 2105943 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103345 2103516 2103736 "OMEXPR" 2104235 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102430 2102766 2102926 "OMERRK" 2103205 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101667 2101976 2102112 "OMERR" 2102314 T OMERR (NIL) -8 NIL NIL NIL) (-848 2101058 2101344 2101452 "OMENC" 2101579 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094695 2096138 2097309 "OMDEV" 2099907 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093728 2093935 2094129 "OMCONN" 2094521 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093134 2093261 2093289 "OM" 2093588 T OM (NIL) -9 NIL NIL NIL) (-844 2091412 2092604 2092632 "OINTDOM" 2092637 T OINTDOM (NIL) -9 NIL 2092658 NIL) (-843 2088487 2090100 2090437 "OFMONOID" 2091107 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087721 2088424 2088469 "ODVAR" 2088474 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084865 2087466 2087621 "ODR" 2087626 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076277 2084641 2084767 "ODPOL" 2084772 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069571 2076149 2076254 "ODP" 2076259 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068313 2068552 2068827 "ODETOOLS" 2069345 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065256 2065938 2066654 "ODESYS" 2067646 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2060086 2061046 2062071 "ODERTRIC" 2064331 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059506 2059594 2059788 "ODERED" 2059998 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056358 2056942 2057619 "ODERAT" 2058929 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053274 2053782 2054379 "ODEPRRIC" 2055887 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051169 2051813 2052299 "ODEPROB" 2052808 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047635 2048174 2048821 "ODEPRIM" 2050648 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046878 2046986 2047246 "ODEPAL" 2047527 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042980 2043831 2044695 "ODEPACK" 2046034 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2042023 2042148 2042370 "ODEINT" 2042869 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036088 2037549 2038996 "ODEIFTBL" 2040596 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031438 2032272 2033224 "ODEEF" 2035247 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030781 2030876 2031099 "ODECONST" 2031343 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028844 2029553 2029581 "ODECAT" 2030186 T ODECAT (NIL) -9 NIL 2030717 NIL) (-823 2028476 2028525 2028652 "OCTCT2" 2028795 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024976 2028181 2028303 "OCT" 2028386 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024169 2024769 2024797 "OCAMON" 2024802 T OCAMON (NIL) -9 NIL 2024823 NIL) (-820 2018440 2021212 2021252 "OC" 2022349 NIL OC (NIL T) -9 NIL 2023207 NIL) (-819 2015475 2016415 2017405 "OC-" 2017499 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014895 2015320 2015348 "OASGP" 2015353 T OASGP (NIL) -9 NIL 2015373 NIL) (-817 2013991 2014618 2014646 "OAMONS" 2014686 T OAMONS (NIL) -9 NIL 2014729 NIL) (-816 2013167 2013726 2013754 "OAMON" 2013812 T OAMON (NIL) -9 NIL 2013864 NIL) (-815 2013025 2013058 2013126 "OAMON-" 2013131 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011806 2012559 2012587 "OAGROUP" 2012734 T OAGROUP (NIL) -9 NIL 2012827 NIL) (-813 2011509 2011597 2011715 "OAGROUP-" 2011720 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011191 2011247 2011336 "NUMTUBE" 2011453 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004710 2006282 2007818 "NUMQUAD" 2009675 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000390 2001424 2002459 "NUMODE" 2003695 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997671 1998611 1998639 "NUMINT" 1999562 T NUMINT (NIL) -9 NIL 2000326 NIL) (-808 1996583 1996816 1997034 "NUMFMT" 1997473 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982766 1985887 1988419 "NUMERIC" 1994090 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976470 1982214 1982309 "NTSCAT" 1982314 NIL NTSCAT (NIL T T T T) -9 NIL 1982353 NIL) (-805 1975650 1975829 1976022 "NTPOLFN" 1976309 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975276 1975339 1975448 "NSUP2" 1975587 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962058 1972101 1972913 "NSUP" 1974497 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950901 1961832 1961965 "NSMP" 1961970 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949309 1949634 1949991 "NREP" 1950589 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947888 1948152 1948510 "NPCOEF" 1949052 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946936 1947069 1947285 "NORMRETR" 1947769 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944947 1945267 1945676 "NORMPK" 1946644 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944626 1944660 1944784 "NORMMA" 1944913 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944409 1944444 1944513 "NONE1" 1944590 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944173 1944366 1944395 "NONE" 1944400 T NONE (NIL) -8 NIL NIL NIL) (-794 1943664 1943732 1943911 "NODE1" 1944105 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941725 1942787 1943042 "NNI" 1943389 T NNI (NIL) -8 NIL NIL 1943624) (-792 1940121 1940458 1940822 "NLINSOL" 1941393 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936302 1937357 1938256 "NIPROB" 1939242 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935041 1935293 1935595 "NFINTBAS" 1936064 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934125 1934691 1934732 "NETCLT" 1934904 NIL NETCLT (NIL T) -9 NIL 1934986 NIL) (-788 1932797 1933064 1933345 "NCODIV" 1933893 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932553 1932596 1932671 "NCNTFRAC" 1932754 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930709 1931097 1931517 "NCEP" 1932178 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929372 1930319 1930347 "NASRING" 1930457 T NASRING (NIL) -9 NIL 1930537 NIL) (-784 1929155 1929211 1929305 "NASRING-" 1929310 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928122 1928773 1928801 "NARNG" 1928918 T NARNG (NIL) -9 NIL 1929009 NIL) (-782 1927796 1927881 1928015 "NARNG-" 1928020 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926633 1926882 1927117 "NAGSP" 1927581 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917677 1919589 1921262 "NAGS" 1924980 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916201 1916533 1916864 "NAGF07" 1917366 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910673 1912030 1913337 "NAGF04" 1914914 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903545 1905255 1906888 "NAGF02" 1909060 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898709 1899869 1900986 "NAGF01" 1902448 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892289 1893903 1895488 "NAGE04" 1897144 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883350 1885579 1887709 "NAGE02" 1890179 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879243 1880250 1881214 "NAGE01" 1882406 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877020 1877572 1878130 "NAGD03" 1878705 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868716 1870698 1872652 "NAGD02" 1875086 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862455 1863952 1865392 "NAGD01" 1867296 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858592 1859486 1860323 "NAGC06" 1861638 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857039 1857389 1857745 "NAGC05" 1858256 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856403 1856534 1856678 "NAGC02" 1856915 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855204 1855931 1855971 "NAALG" 1856050 NIL NAALG (NIL T) -9 NIL 1856111 NIL) (-765 1855033 1855068 1855158 "NAALG-" 1855163 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848905 1850091 1851278 "MULTSQFR" 1853929 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848212 1848299 1848483 "MULTFACT" 1848817 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840357 1844795 1844848 "MTSCAT" 1845918 NIL MTSCAT (NIL T T) -9 NIL 1846434 NIL) (-761 1840063 1840123 1840215 "MTHING" 1840297 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839849 1839888 1839948 "MSYSCMD" 1840023 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836594 1839410 1839451 "MSETAGG" 1839456 NIL MSETAGG (NIL T) -9 NIL 1839490 NIL) (-758 1832308 1835349 1835669 "MSET" 1836307 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827907 1829687 1830432 "MRING" 1831608 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827467 1827540 1827671 "MRF2" 1827834 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827079 1827120 1827264 "MRATFAC" 1827426 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824649 1824986 1825417 "MPRFF" 1826784 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817983 1824503 1824600 "MPOLY" 1824605 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817467 1817508 1817716 "MPCPF" 1817942 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816975 1817024 1817208 "MPC3" 1817418 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816158 1816251 1816472 "MPC2" 1816890 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814435 1814796 1815186 "MONOTOOL" 1815818 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813580 1813963 1813991 "MONOID" 1814210 T MONOID (NIL) -9 NIL 1814357 NIL) (-747 1813096 1813245 1813426 "MONOID-" 1813431 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802069 1808916 1808975 "MONOGEN" 1809649 NIL MONOGEN (NIL T T) -9 NIL 1810105 NIL) (-745 1799119 1800022 1801022 "MONOGEN-" 1801141 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797836 1798384 1798412 "MONADWU" 1798804 T MONADWU (NIL) -9 NIL 1799042 NIL) (-743 1797166 1797367 1797615 "MONADWU-" 1797620 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796451 1796755 1796783 "MONAD" 1796990 T MONAD (NIL) -9 NIL 1797102 NIL) (-741 1796118 1796214 1796346 "MONAD-" 1796351 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794257 1795031 1795310 "MOEBIUS" 1795871 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793425 1793925 1793965 "MODULE" 1793970 NIL MODULE (NIL T) -9 NIL 1794009 NIL) (-738 1792963 1793089 1793279 "MODULE-" 1793284 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790493 1791327 1791654 "MODRING" 1792787 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787222 1788598 1789119 "MODOP" 1790022 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785708 1786289 1786566 "MODMONOM" 1787085 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774469 1783999 1784413 "MODMON" 1785345 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771302 1773313 1773589 "MODFIELD" 1774344 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770213 1770583 1770773 "MMLFORM" 1771132 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769733 1769782 1769961 "MMAP" 1770164 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767626 1768565 1768606 "MLO" 1769029 NIL MLO (NIL T) -9 NIL 1769271 NIL) (-729 1764974 1765508 1766110 "MLIFT" 1767107 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764353 1764449 1764603 "MKUCFUNC" 1764885 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763946 1764022 1764145 "MKRECORD" 1764276 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762969 1763155 1763383 "MKFUNC" 1763757 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762345 1762461 1762617 "MKFLCFN" 1762852 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761610 1761724 1761909 "MKBCFUNC" 1762238 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757607 1761164 1761300 "MINT" 1761494 T MINT (NIL) -8 NIL NIL NIL) (-722 1756389 1756662 1756939 "MHROWRED" 1757362 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751140 1754924 1755329 "MFLOAT" 1756004 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750485 1750573 1750744 "MFINFACT" 1751052 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746764 1747648 1748532 "MESH" 1749621 T MESH (NIL) -7 NIL NIL NIL) (-718 1745118 1745466 1745819 "MDDFACT" 1746451 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741654 1744249 1744290 "MDAGG" 1744545 NIL MDAGG (NIL T) -9 NIL 1744688 NIL) (-716 1729377 1740947 1741154 "MCMPLX" 1741467 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728496 1728660 1728861 "MCDEN" 1729226 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726344 1726656 1727036 "MCALCFN" 1728226 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725221 1725509 1725742 "MAYBE" 1726150 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722779 1723356 1723918 "MATSTOR" 1724692 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718201 1722151 1722399 "MATRIX" 1722564 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713901 1714674 1715410 "MATLIN" 1717558 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712477 1712648 1712981 "MATCAT2" 1713736 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701816 1705534 1705611 "MATCAT" 1710643 NIL MATCAT (NIL T T T) -9 NIL 1712115 NIL) (-707 1697769 1699079 1700492 "MATCAT-" 1700497 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695845 1696205 1696589 "MAPPKG3" 1697444 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694802 1694999 1695221 "MAPPKG2" 1695669 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693259 1693585 1693912 "MAPPKG1" 1694508 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692260 1692665 1692842 "MAPPAST" 1693102 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691865 1691929 1692052 "MAPHACK3" 1692196 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691445 1691518 1691632 "MAPHACK2" 1691797 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690871 1690986 1691128 "MAPHACK1" 1691336 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688794 1689571 1689875 "MAGMA" 1690599 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688213 1688518 1688609 "MACROAST" 1688723 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684456 1686452 1686913 "M3D" 1687785 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677928 1682767 1682808 "LZSTAGG" 1683590 NIL LZSTAGG (NIL T) -9 NIL 1683885 NIL) (-695 1673610 1675059 1676516 "LZSTAGG-" 1676521 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670523 1671501 1671988 "LWORD" 1673155 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670045 1670327 1670402 "LSTAST" 1670468 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661973 1669816 1669950 "LSQM" 1669955 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661191 1661336 1661564 "LSPP" 1661828 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657928 1658644 1659374 "LSMP1" 1660493 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655710 1656041 1656497 "LSMP" 1657617 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648838 1654800 1654841 "LSAGG" 1654903 NIL LSAGG (NIL T) -9 NIL 1654981 NIL) (-687 1645347 1646457 1647670 "LSAGG-" 1647675 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642642 1644491 1644740 "LPOLY" 1645142 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642218 1642309 1642432 "LPEFRAC" 1642551 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641901 1641980 1642008 "LOGIC" 1642119 T LOGIC (NIL) -9 NIL 1642201 NIL) (-683 1641757 1641786 1641857 "LOGIC-" 1641862 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640932 1641090 1641283 "LODOOPS" 1641613 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639456 1639705 1640058 "LODOF" 1640679 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635332 1638091 1638132 "LODOCAT" 1638570 NIL LODOCAT (NIL T) -9 NIL 1638781 NIL) (-679 1635047 1635123 1635250 "LODOCAT-" 1635255 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632033 1634888 1635006 "LODO2" 1635011 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629140 1631970 1632015 "LODO1" 1632020 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626235 1629056 1629122 "LODO" 1629127 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625104 1625281 1625586 "LODEEF" 1626058 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623090 1624198 1624451 "LO" 1624936 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618062 1621256 1621297 "LNAGG" 1622159 NIL LNAGG (NIL T) -9 NIL 1622594 NIL) (-672 1617155 1617423 1617765 "LNAGG-" 1617770 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613135 1614080 1614719 "LMOPS" 1616570 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612434 1612912 1612953 "LMODULE" 1612958 NIL LMODULE (NIL T) -9 NIL 1612984 NIL) (-669 1609389 1612079 1612202 "LMDICT" 1612344 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608965 1609179 1609220 "LLINSET" 1609281 NIL LLINSET (NIL T) -9 NIL 1609325 NIL) (-667 1608610 1608873 1608933 "LITERAL" 1608938 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608129 1608209 1608348 "LIST3" 1608530 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606227 1606575 1606974 "LIST2MAP" 1607776 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605216 1605412 1605640 "LIST2" 1606045 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597670 1604150 1604454 "LIST" 1604945 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597253 1597489 1597530 "LINSET" 1597535 NIL LINSET (NIL T) -9 NIL 1597569 NIL) (-661 1596067 1596761 1596928 "LINFORM" 1597138 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594366 1595094 1595135 "LINEXP" 1595625 NIL LINEXP (NIL T) -9 NIL 1595898 NIL) (-659 1592942 1593846 1594027 "LINELT" 1594237 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591499 1591779 1592090 "LINDEP" 1592694 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590635 1591231 1591341 "LINBASIS" 1591429 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587372 1588121 1588898 "LIMITRF" 1589890 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585657 1585971 1586380 "LIMITPS" 1587067 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584485 1585060 1585100 "LIECAT" 1585240 NIL LIECAT (NIL T) -9 NIL 1585391 NIL) (-653 1584320 1584353 1584441 "LIECAT-" 1584446 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578340 1583831 1584059 "LIE" 1584141 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570525 1577880 1578036 "LIB" 1578204 T LIB (NIL) -8 NIL NIL NIL) (-650 1566094 1567043 1567978 "LGROBP" 1569642 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564718 1565626 1565654 "LFCAT" 1565861 T LFCAT (NIL) -9 NIL 1566000 NIL) (-648 1562656 1562990 1563340 "LF" 1564439 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559516 1560188 1560876 "LEXTRIPK" 1562020 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556104 1557086 1557589 "LEXP" 1559096 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555520 1555825 1555917 "LETAST" 1556032 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553906 1554231 1554632 "LEADCDET" 1555202 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553084 1553170 1553399 "LAZM3PK" 1553827 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547609 1551161 1551699 "LAUPOL" 1552596 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547182 1547232 1547393 "LAPLACE" 1547559 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546030 1546746 1546787 "LALG" 1546849 NIL LALG (NIL T) -9 NIL 1546908 NIL) (-639 1545726 1545803 1545939 "LALG-" 1545944 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543463 1544827 1545078 "LA" 1545559 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543292 1543322 1543363 "KVTFROM" 1543425 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542049 1542659 1542844 "KTVLOGIC" 1543127 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541878 1541908 1541949 "KRCFROM" 1542011 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540770 1540969 1541268 "KOVACIC" 1541678 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540599 1540629 1540670 "KONVERT" 1540732 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540428 1540458 1540499 "KOERCE" 1540561 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539912 1540005 1540137 "KERNEL2" 1540342 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537599 1538505 1538882 "KERNEL" 1539568 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531070 1536076 1536130 "KDAGG" 1536507 NIL KDAGG (NIL T T) -9 NIL 1536713 NIL) (-628 1530581 1530723 1530928 "KDAGG-" 1530933 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523281 1530242 1530397 "KAFILE" 1530459 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522885 1523170 1523233 "JVMOP" 1523238 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521621 1522125 1522374 "JVMMDACC" 1522656 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520557 1521011 1521216 "JVMFDACC" 1521436 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519138 1519633 1519933 "JVMCSTTG" 1520277 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518274 1518678 1518839 "JVMCFACC" 1518997 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517952 1518191 1518240 "JVMBCODE" 1518245 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511971 1517463 1517691 "JORDAN" 1517773 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511284 1511620 1511741 "JOINAST" 1511870 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507319 1509461 1509515 "IXAGG" 1510444 NIL IXAGG (NIL T T) -9 NIL 1510903 NIL) (-617 1506172 1506544 1506963 "IXAGG-" 1506968 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501261 1506094 1506153 "IVECTOR" 1506158 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499986 1500264 1500530 "ITUPLE" 1501028 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498458 1498665 1498960 "ITRIGMNP" 1499808 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497185 1497407 1497690 "ITFUN3" 1498234 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496783 1496846 1496969 "ITFUN2" 1497108 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495888 1496263 1496437 "ITFORM" 1496629 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493657 1494908 1495186 "ITAYLOR" 1495643 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482061 1487794 1488957 "ISUPS" 1492527 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481153 1481305 1481541 "ISUMP" 1481908 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476003 1481098 1481139 "ISTRING" 1481144 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475419 1475724 1475816 "ISAST" 1475931 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474616 1474710 1474926 "IRURPK" 1475333 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473528 1473753 1473993 "IRSN" 1474396 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471573 1471954 1472383 "IRRF2F" 1473166 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471314 1471358 1471434 "IRREDFFX" 1471529 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469887 1470188 1470487 "IROOT" 1471047 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469026 1469380 1469531 "IRFORM" 1469756 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468108 1468239 1468453 "IR2F" 1468909 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465697 1466216 1466782 "IR2" 1467586 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462137 1463381 1464073 "IR" 1465037 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461922 1461962 1462022 "IPRNTPK" 1462097 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457896 1461811 1461880 "IPF" 1461885 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455924 1457821 1457878 "IPADIC" 1457883 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455182 1455484 1455614 "IP4ADDR" 1455814 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454520 1454811 1454943 "IOMODE" 1455070 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453491 1454117 1454244 "IOBFILE" 1454413 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452901 1453395 1453423 "IOBCON" 1453428 T IOBCON (NIL) -9 NIL 1453449 NIL) (-589 1452406 1452470 1452653 "INVLAPLA" 1452837 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441976 1444408 1446794 "INTTR" 1450070 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438269 1439053 1439918 "INTTOOLS" 1441161 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437849 1437946 1438063 "INTSLPE" 1438172 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435316 1437772 1437831 "INTRVL" 1437836 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432894 1433430 1434005 "INTRF" 1434801 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432287 1432402 1432544 "INTRET" 1432792 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430260 1430673 1431143 "INTRAT" 1431895 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427505 1428106 1428725 "INTPM" 1429745 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424222 1424849 1425587 "INTPAF" 1426891 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419323 1420363 1421414 "INTPACK" 1423191 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418569 1418727 1418935 "INTHERTR" 1419165 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418002 1418088 1418276 "INTHERAL" 1418483 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415770 1416291 1416748 "INTHEORY" 1417565 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407102 1408797 1410569 "INTG0" 1414122 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387627 1392465 1397275 "INTFTBL" 1402312 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386852 1387014 1387187 "INTFACT" 1387486 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384249 1384725 1385282 "INTEF" 1386406 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382446 1383341 1383369 "INTDOM" 1383670 T INTDOM (NIL) -9 NIL 1383877 NIL) (-570 1381785 1381989 1382231 "INTDOM-" 1382236 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377653 1380074 1380128 "INTCAT" 1380927 NIL INTCAT (NIL T) -9 NIL 1381248 NIL) (-568 1377107 1377228 1377356 "INTBIT" 1377545 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375788 1375960 1376267 "INTALG" 1376952 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375265 1375361 1375518 "INTAF" 1375692 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368232 1375075 1375215 "INTABL" 1375220 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367473 1368035 1368100 "INT8" 1368134 T INT8 (NIL) -8 NIL NIL 1368179) (-563 1366713 1367275 1367340 "INT64" 1367374 T INT64 (NIL) -8 NIL NIL 1367419) (-562 1365953 1366515 1366580 "INT32" 1366614 T INT32 (NIL) -8 NIL NIL 1366659) (-561 1365193 1365755 1365820 "INT16" 1365854 T INT16 (NIL) -8 NIL NIL 1365899) (-560 1361395 1364990 1365099 "INT" 1365104 T INT (NIL) -8 NIL NIL NIL) (-559 1355504 1358943 1358971 "INS" 1359905 T INS (NIL) -9 NIL 1360570 NIL) (-558 1352579 1353529 1354496 "INS-" 1354569 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330936 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329790 1330113 1330141 "INBCON" 1330654 T INBCON (NIL) -9 NIL 1330920 NIL) (-540 1329000 1329265 1329541 "INBCON-" 1329546 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328419 1328724 1328815 "INAST" 1328929 T INAST (NIL) -8 NIL NIL NIL) (-538 1327786 1328098 1328204 "IMPTAST" 1328333 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323707 1327630 1327734 "IMATRIX" 1327739 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322399 1322538 1322854 "IMATQF" 1323563 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320579 1320846 1321183 "IMATLIN" 1322155 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314494 1320503 1320561 "ILIST" 1320566 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312160 1314354 1314467 "IIARRAY2" 1314472 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306981 1312071 1312135 "IFF" 1312140 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306262 1306598 1306714 "IFAST" 1306885 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300774 1305554 1305742 "IFARRAY" 1306119 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299812 1300678 1300751 "IFAMON" 1300756 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299384 1299461 1299515 "IEVALAB" 1299722 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299047 1299127 1299287 "IEVALAB-" 1299292 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298080 1298936 1299011 "IDPOAMS" 1299016 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297182 1297969 1298044 "IDPOAM" 1298049 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296563 1297097 1297159 "IDPO" 1297164 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295043 1295570 1295622 "IDPC" 1296134 NIL IDPC (NIL T T) -9 NIL 1296415 NIL) (-522 1294375 1294935 1295008 "IDPAM" 1295013 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293590 1294267 1294340 "IDPAG" 1294345 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293134 1293396 1293486 "IDENT" 1293520 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289353 1290237 1291132 "IDECOMP" 1292291 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281988 1283276 1284323 "IDEAL" 1288389 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281130 1281260 1281460 "ICDEN" 1281872 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280105 1280610 1280757 "ICARD" 1281003 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278135 1278478 1278883 "IBPTOOLS" 1279782 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273250 1277755 1277868 "IBITS" 1278054 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269925 1270549 1271244 "IBATOOL" 1272667 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267686 1268166 1268699 "IBACHIN" 1269460 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265276 1267532 1267635 "IARRAY2" 1267640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260989 1265202 1265259 "IARRAY1" 1265264 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254006 1259401 1259882 "IAN" 1260528 T IAN (NIL) -8 NIL NIL NIL) (-508 1253511 1253574 1253747 "IALGFACT" 1253943 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253003 1253152 1253180 "HYPCAT" 1253387 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252505 1252658 1252844 "HYPCAT-" 1252849 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252052 1252300 1252383 "HOSTNAME" 1252442 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251885 1251934 1251975 "HOMOTOP" 1251980 NIL HOMOTOP (NIL T) -9 NIL 1252013 NIL) (-503 1248318 1249817 1249858 "HOAGG" 1250839 NIL HOAGG (NIL T) -9 NIL 1251568 NIL) (-502 1246834 1247311 1247837 "HOAGG-" 1247842 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239891 1246427 1246577 "HEXADEC" 1246704 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238603 1238861 1239124 "HEUGCD" 1239668 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237535 1238440 1238570 "HELLFDIV" 1238575 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235543 1237310 1237399 "HEAP" 1237478 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234740 1235095 1235229 "HEADAST" 1235429 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228078 1234655 1234717 "HDP" 1234722 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221097 1227713 1227865 "HDMP" 1227979 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220403 1220561 1220725 "HB" 1220953 T HB (NIL) -7 NIL NIL NIL) (-493 1213413 1220249 1220353 "HASHTBL" 1220358 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212829 1213134 1213226 "HASAST" 1213341 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210242 1212451 1212633 "HACKPI" 1212667 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205414 1210095 1210208 "GTSET" 1210213 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198453 1205292 1205390 "GSTBL" 1205395 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190216 1197618 1197874 "GSERIES" 1198253 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189247 1189760 1189788 "GROUP" 1189991 T GROUP (NIL) -9 NIL 1190125 NIL) (-486 1188571 1188772 1189023 "GROUP-" 1189028 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186920 1187259 1187646 "GROEBSOL" 1188248 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185748 1186108 1186159 "GRMOD" 1186688 NIL GRMOD (NIL T T) -9 NIL 1186856 NIL) (-483 1185504 1185552 1185680 "GRMOD-" 1185685 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180644 1181858 1182858 "GRIMAGE" 1184524 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179038 1179371 1179695 "GRDEF" 1180340 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178470 1178598 1178739 "GRAY" 1178917 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177547 1178049 1178100 "GRALG" 1178253 NIL GRALG (NIL T T) -9 NIL 1178346 NIL) (-478 1177184 1177281 1177444 "GRALG-" 1177449 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173665 1176767 1176946 "GPOLSET" 1177090 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173013 1173076 1173334 "GOSPER" 1173602 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168583 1169451 1169977 "GMODPOL" 1172712 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167570 1167772 1168010 "GHENSEL" 1168395 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161642 1162569 1163589 "GENUPS" 1166654 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161333 1161390 1161479 "GENUFACT" 1161585 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160733 1160822 1160987 "GENPGCD" 1161251 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160201 1160242 1160455 "GENMFACT" 1160692 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158737 1159024 1159331 "GENEEZ" 1159944 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151916 1158348 1158510 "GDMP" 1158660 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140654 1145687 1146793 "GCNAALG" 1150899 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138781 1139829 1139857 "GCDDOM" 1140112 T GCDDOM (NIL) -9 NIL 1140269 NIL) (-465 1138221 1138378 1138593 "GCDDOM-" 1138598 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126693 1129167 1131559 "GBINTERN" 1135912 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124494 1124822 1125243 "GBF" 1126368 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123251 1123440 1123707 "GBEUCLID" 1124310 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121901 1122108 1122412 "GB" 1123030 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121232 1121375 1121524 "GAUSSFAC" 1121772 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119553 1119901 1120215 "GALUTIL" 1120951 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117813 1118135 1118459 "GALPOLYU" 1119280 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115112 1115468 1115875 "GALFACTU" 1117510 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106726 1108417 1110025 "GALFACT" 1113544 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104012 1104772 1104800 "FVFUN" 1105956 T FVFUN (NIL) -9 NIL 1106676 NIL) (-454 1103242 1103460 1103488 "FVC" 1103779 T FVC (NIL) -9 NIL 1103962 NIL) (-453 1102843 1103067 1103135 "FUNDESC" 1103194 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102416 1102640 1102721 "FUNCTION" 1102795 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101093 1101717 1101920 "FTEM" 1102233 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098723 1099415 1099881 "FT" 1100647 T FT (NIL) -8 NIL NIL NIL) (-449 1096992 1097303 1097700 "FSUPFACT" 1098414 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095311 1095678 1096010 "FST" 1096680 T FST (NIL) -8 NIL NIL NIL) (-447 1094492 1094616 1094804 "FSRED" 1095193 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093181 1093447 1093794 "FSPRMELT" 1094207 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090391 1090925 1091411 "FSPECF" 1092744 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089913 1089973 1090143 "FSINT" 1090332 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088049 1088906 1089209 "FSERIES" 1089692 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087073 1087207 1087431 "FSCINT" 1087929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086097 1086258 1086485 "FSAGG2" 1086926 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081961 1085041 1085082 "FSAGG" 1085452 NIL FSAGG (NIL T) -9 NIL 1085711 NIL) (-439 1079561 1080324 1081120 "FSAGG-" 1081215 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077221 1077519 1078067 "FS2UPS" 1079279 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076087 1076270 1076572 "FS2EXPXP" 1077046 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075715 1075764 1075893 "FS2" 1076038 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055953 1065489 1065530 "FS" 1069414 NIL FS (NIL T) -9 NIL 1071703 NIL) (-434 1044014 1047589 1051646 "FS-" 1051946 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043428 1043555 1043707 "FRUTIL" 1043894 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037939 1041117 1041157 "FRNAALG" 1042477 NIL FRNAALG (NIL T) -9 NIL 1043075 NIL) (-431 1033420 1034688 1035963 "FRNAALG-" 1036713 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033052 1033101 1033228 "FRNAAF2" 1033371 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031339 1031901 1032197 "FRMOD" 1032864 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030524 1030617 1030908 "FRIDEAL2" 1031246 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028129 1028899 1029217 "FRIDEAL" 1030315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027220 1027676 1027717 "FRETRCT" 1027722 NIL FRETRCT (NIL T) -9 NIL 1027898 NIL) (-425 1026278 1026563 1026914 "FRETRCT-" 1026919 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023099 1024562 1024621 "FRAMALG" 1025503 NIL FRAMALG (NIL T T) -9 NIL 1025795 NIL) (-423 1021137 1021688 1022318 "FRAMALG-" 1022541 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020767 1020830 1020937 "FRAC2" 1021074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013759 1020240 1020517 "FRAC" 1020522 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013389 1013452 1013559 "FR2" 1013696 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004306 1008884 1010242 "FR" 1012063 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998225 1001685 1001713 "FPS" 1002832 T FPS (NIL) -9 NIL 1003389 NIL) (-417 997650 997783 997947 "FPS-" 998093 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994616 996607 996635 "FPC" 996860 T FPC (NIL) -9 NIL 997002 NIL) (-415 994397 994449 994546 "FPC-" 994551 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993155 993885 993926 "FPATMAB" 993931 NIL FPATMAB (NIL T) -9 NIL 994083 NIL) (-413 991298 991897 992244 "FPARFRAC" 992871 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986590 987190 987872 "FORTRAN" 990730 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984164 984828 984856 "FORTFN" 985916 T FORTFN (NIL) -9 NIL 986540 NIL) (-410 983916 983978 984006 "FORTCAT" 984065 T FORTCAT (NIL) -9 NIL 984127 NIL) (-409 981602 982132 982671 "FORT" 983397 T FORT (NIL) -7 NIL NIL NIL) (-408 981384 981420 981489 "FORMULA1" 981566 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979388 980000 980390 "FORMULA" 981014 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978905 978963 979136 "FORDER" 979330 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977965 978165 978358 "FOP" 978732 T FOP (NIL) -7 NIL NIL NIL) (-404 976378 977245 977419 "FNLA" 977847 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974997 975508 975536 "FNCAT" 975996 T FNCAT (NIL) -9 NIL 976256 NIL) (-402 974440 974956 974984 "FNAME" 974989 T FNAME (NIL) -8 NIL NIL NIL) (-401 972766 973939 973967 "FMTC" 973972 T FMTC (NIL) -9 NIL 974008 NIL) (-400 971315 972702 972748 "FMONOID" 972753 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967904 969270 969311 "FMONCAT" 970528 NIL FMONCAT (NIL T) -9 NIL 971133 NIL) (-398 965226 965974 966002 "FMFUN" 967146 T FMFUN (NIL) -9 NIL 967854 NIL) (-397 962099 963151 963205 "FMCAT" 964400 NIL FMCAT (NIL T T) -9 NIL 964895 NIL) (-396 961332 961549 961577 "FMC" 961867 T FMC (NIL) -9 NIL 962049 NIL) (-395 960000 961098 961198 "FM1" 961277 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959018 959742 959891 "FM" 959896 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956756 957208 957702 "FLOATRP" 958569 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954158 954694 955272 "FLOATCP" 956223 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946821 951887 952508 "FLOAT" 953557 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945339 946413 946454 "FLINEXP" 946459 NIL FLINEXP (NIL T) -9 NIL 946552 NIL) (-389 944469 944728 945056 "FLINEXP-" 945061 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943527 943689 943913 "FLASORT" 944321 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940445 941497 941549 "FLALG" 942776 NIL FLALG (NIL T T) -9 NIL 943243 NIL) (-386 939469 939630 939857 "FLAGG2" 940298 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932724 936878 936919 "FLAGG" 938181 NIL FLAGG (NIL T) -9 NIL 938833 NIL) (-384 931378 931789 932279 "FLAGG-" 932284 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928016 929223 929282 "FINRALG" 930410 NIL FINRALG (NIL T T) -9 NIL 930918 NIL) (-382 927140 927405 927744 "FINRALG-" 927749 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926446 926745 926773 "FINITE" 926969 T FINITE (NIL) -9 NIL 927076 NIL) (-380 918397 920976 921016 "FINAALG" 924683 NIL FINAALG (NIL T) -9 NIL 926136 NIL) (-379 913513 914779 915923 "FINAALG-" 917302 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912073 912495 912549 "FILECAT" 913233 NIL FILECAT (NIL T T) -9 NIL 913449 NIL) (-377 911351 911828 911931 "FILE" 912003 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908754 910581 910609 "FIELD" 910649 T FIELD (NIL) -9 NIL 910729 NIL) (-375 907296 907759 908270 "FIELD-" 908275 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904979 905931 906278 "FGROUP" 906982 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904051 904233 904453 "FGLMICPK" 904811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899306 903976 904033 "FFX" 904038 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898901 898968 899103 "FFSLPE" 899239 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898399 898441 898650 "FFPOLY2" 898859 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894275 895171 895967 "FFPOLY" 897635 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889544 894194 894257 "FFP" 894262 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884075 888887 889077 "FFNBX" 889398 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878408 883210 883468 "FFNBP" 883929 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872446 877692 877903 "FFNB" 878241 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871266 871476 871791 "FFINTBAS" 872243 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866859 869513 869541 "FFIELDC" 870161 T FFIELDC (NIL) -9 NIL 870537 NIL) (-362 865479 865920 866403 "FFIELDC-" 866408 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865036 865094 865218 "FFHOM" 865421 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862695 863218 863735 "FFF" 864551 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857730 862437 862538 "FFCGX" 862638 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852769 857462 857569 "FFCGP" 857673 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847369 852496 852604 "FFCG" 852705 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846774 846823 847058 "FFCAT2" 847320 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825456 836506 836592 "FFCAT" 841757 NIL FFCAT (NIL T T T) -9 NIL 843208 NIL) (-354 820467 821701 823015 "FFCAT-" 824245 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815288 820378 820442 "FF" 820447 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803941 808260 809480 "FEXPR" 814140 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802869 803338 803379 "FEVALAB" 803463 NIL FEVALAB (NIL T) -9 NIL 803724 NIL) (-350 801986 802238 802576 "FEVALAB-" 802581 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798848 799733 799848 "FDIVCAT" 801416 NIL FDIVCAT (NIL T T T T) -9 NIL 801853 NIL) (-348 798604 798637 798807 "FDIVCAT-" 798812 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797818 797911 798188 "FDIV2" 798511 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796228 797201 797404 "FDIV" 797717 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795136 795523 795725 "FCTRDATA" 796046 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793792 794081 794370 "FCPAK1" 794867 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792795 793292 793433 "FCOMP" 793683 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776109 779945 783483 "FC" 789277 T FC (NIL) -8 NIL NIL NIL) (-341 767818 772430 772470 "FAXF" 774272 NIL FAXF (NIL T) -9 NIL 774964 NIL) (-340 764959 765766 766584 "FAXF-" 767049 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759528 764335 764511 "FARRAY" 764816 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754093 756475 756528 "FAMR" 757551 NIL FAMR (NIL T T) -9 NIL 758011 NIL) (-337 752917 753285 753720 "FAMR-" 753725 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751944 752839 752892 "FAMONOID" 752897 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749574 750426 750479 "FAMONC" 751420 NIL FAMONC (NIL T T) -9 NIL 751806 NIL) (-334 748048 749328 749465 "FAGROUP" 749470 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745801 746162 746565 "FACUTIL" 747729 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744888 745085 745307 "FACTFUNC" 745611 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736629 744191 744390 "EXPUPXS" 744744 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734082 734652 735238 "EXPRTUBE" 736063 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730293 730945 731675 "EXPRODE" 733421 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724727 725434 726240 "EXPR2UPS" 729591 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724353 724416 724525 "EXPR2" 724664 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708661 723002 723431 "EXPR" 723957 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698999 707812 708103 "EXPEXPAN" 708497 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698419 698723 698814 "EXITAST" 698928 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698183 698376 698405 "EXIT" 698410 T EXIT (NIL) -8 NIL NIL NIL) (-322 697804 697872 697985 "EVALCYC" 698115 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697321 697463 697504 "EVALAB" 697674 NIL EVALAB (NIL T) -9 NIL 697778 NIL) (-320 696778 696924 697145 "EVALAB-" 697150 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693893 695434 695462 "EUCDOM" 696017 T EUCDOM (NIL) -9 NIL 696367 NIL) (-318 692253 692754 693337 "EUCDOM-" 693342 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691879 691942 692051 "ESTOOLS2" 692190 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691624 691672 691752 "ESTOOLS1" 691831 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678941 681922 684672 "ESTOOLS" 688894 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678680 678718 678800 "ESCONT1" 678903 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674988 675815 676595 "ESCONT" 677920 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674657 674713 674813 "ES2" 674932 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674281 674345 674454 "ES1" 674593 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667982 669912 669940 "ES" 672708 T ES (NIL) -9 NIL 674118 NIL) (-309 662659 664216 666033 "ES-" 666197 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661851 662004 662180 "ERROR" 662503 T ERROR (NIL) -7 NIL NIL NIL) (-307 654867 661710 661801 "EQTBL" 661806 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654493 654556 654665 "EQ2" 654804 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646752 649807 651256 "EQ" 653077 NIL -1539 (NIL T) -8 NIL NIL NIL) (-304 641995 643090 644183 "EP" 645691 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640535 640886 641192 "ENV" 641709 T ENV (NIL) -8 NIL NIL NIL) (-302 639495 640169 640197 "ENTIRER" 640202 T ENTIRER (NIL) -9 NIL 640248 NIL) (-301 635914 637677 638038 "EMR" 639303 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635018 635229 635283 "ELTAGG" 635663 NIL ELTAGG (NIL T T) -9 NIL 635874 NIL) (-299 634725 634799 634940 "ELTAGG-" 634945 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634483 634518 634572 "ELTAB" 634656 NIL ELTAB (NIL T T) -9 NIL 634708 NIL) (-297 633585 633755 633954 "ELFUTS" 634334 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633309 633383 633411 "ELEMFUN" 633516 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633173 633200 633268 "ELEMFUN-" 633273 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627584 631215 631256 "ELAGG" 632196 NIL ELAGG (NIL T) -9 NIL 632659 NIL) (-293 625761 626303 626966 "ELAGG-" 626971 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625043 625210 625366 "ELABOR" 625625 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623649 623983 624277 "ELABEXPR" 624769 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616161 618286 619115 "EFUPXS" 622924 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609287 611410 612221 "EFULS" 615436 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606724 607130 607602 "EFSTRUC" 608919 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596161 598081 599629 "EF" 605239 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595139 595646 595795 "EAB" 596032 T EAB (NIL) -8 NIL NIL NIL) (-285 594261 595098 595126 "E04UCFA" 595131 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593383 594220 594248 "E04NAFA" 594253 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592505 593342 593370 "E04MBFA" 593375 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591627 592464 592492 "E04JAFA" 592497 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590751 591586 591614 "E04GCFA" 591619 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589875 590710 590738 "E04FDFA" 590743 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588997 589834 589862 "E04DGFA" 589867 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583074 584522 585886 "E04AGNT" 587653 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581694 582375 582415 "DVARCAT" 582756 NIL DVARCAT (NIL T) -9 NIL 582919 NIL) (-276 580844 581110 581424 "DVARCAT-" 581429 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572812 580643 580772 "DSMP" 580777 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571163 571954 571995 "DSEXT" 572358 NIL DSEXT (NIL T) -9 NIL 572652 NIL) (-273 569352 569876 570542 "DSEXT-" 570547 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569011 569076 569174 "DROPT1" 569287 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564030 565252 566389 "DROPT0" 567894 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558613 559975 561043 "DROPT" 562982 T DROPT (NIL) -8 NIL NIL NIL) (-269 556922 557283 557669 "DRAWPT" 558247 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556549 556608 556726 "DRAWHACK" 556863 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555250 555549 555840 "DRAWCX" 556278 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554759 554834 554985 "DRAWCURV" 555176 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545077 547189 549304 "DRAWCFUN" 552664 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539568 540587 541666 "DRAW" 544051 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536039 538233 538274 "DQAGG" 538903 NIL DQAGG (NIL T) -9 NIL 539177 NIL) (-262 522622 530250 530333 "DPOLCAT" 532185 NIL DPOLCAT (NIL T T T T) -9 NIL 532730 NIL) (-261 517141 518807 520765 "DPOLCAT-" 520770 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509949 517002 517100 "DPMO" 517105 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502654 509729 509896 "DPMM" 509901 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502176 502438 502527 "DOMTMPLT" 502585 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501525 501978 502058 "DOMCTOR" 502116 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500677 501005 501156 "DOMAIN" 501394 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493696 500312 500464 "DMP" 500578 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491473 492763 492804 "DMEXT" 492809 NIL DMEXT (NIL T) -9 NIL 492985 NIL) (-253 491067 491129 491273 "DLP" 491411 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484190 490394 490584 "DLIST" 490909 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480728 483015 483056 "DLAGG" 483606 NIL DLAGG (NIL T) -9 NIL 483836 NIL) (-250 479240 480054 480082 "DIVRING" 480174 T DIVRING (NIL) -9 NIL 480257 NIL) (-249 478423 478667 478967 "DIVRING-" 478972 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476465 476882 477288 "DISPLAY" 478037 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475295 475516 475781 "DIRPROD2" 476258 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468653 475209 475272 "DIRPROD" 475277 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456816 463364 463417 "DIRPCAT" 463675 NIL DIRPCAT (NIL NIL T) -9 NIL 464550 NIL) (-244 454016 454784 455665 "DIRPCAT-" 456002 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453297 453463 453649 "DIOSP" 453850 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449711 452181 452222 "DIOPS" 452656 NIL DIOPS (NIL T) -9 NIL 452885 NIL) (-241 449230 449374 449565 "DIOPS-" 449570 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448137 448909 448937 "DIFRING" 448942 T DIFRING (NIL) -9 NIL 448964 NIL) (-239 447785 447883 447911 "DIFFSPC" 448030 T DIFFSPC (NIL) -9 NIL 448105 NIL) (-238 447406 447508 447660 "DIFFSPC-" 447665 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446342 446940 446981 "DIFFMOD" 446986 NIL DIFFMOD (NIL T) -9 NIL 447084 NIL) (-236 446038 446095 446136 "DIFFDOM" 446257 NIL DIFFDOM (NIL T) -9 NIL 446325 NIL) (-235 445885 445915 445999 "DIFFDOM-" 446004 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443625 445089 445130 "DIFEXT" 445135 NIL DIFEXT (NIL T) -9 NIL 445288 NIL) (-233 440659 443129 443170 "DIAGG" 443175 NIL DIAGG (NIL T) -9 NIL 443195 NIL) (-232 440007 440200 440452 "DIAGG-" 440457 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434857 438966 439243 "DHMATRIX" 439776 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430325 431378 432388 "DFSFUN" 433867 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424566 429256 429568 "DFLOAT" 430033 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422805 423110 423499 "DFINTTLS" 424274 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419624 420826 421226 "DERHAM" 422471 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417160 419399 419488 "DEQUEUE" 419568 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416402 416547 416730 "DEGRED" 417022 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412808 413577 414423 "DEFINTRF" 415630 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410345 410832 411424 "DEFINTEF" 412327 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409629 409965 410080 "DEFAST" 410250 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402686 409222 409372 "DECIMAL" 409499 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400144 400656 401162 "DDFACT" 402230 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399734 399783 399934 "DBLRESP" 400095 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398935 399504 399595 "DBASIS" 399683 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396719 397165 397526 "DBASE" 398701 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395907 396199 396345 "DATAARY" 396618 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394965 395866 395894 "D03FAFA" 395899 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394024 394924 394952 "D03EEFA" 394957 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391950 392440 392929 "D03AGNT" 393555 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391191 391909 391937 "D02EJFA" 391942 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390432 391150 391178 "D02CJFA" 391183 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389673 390391 390419 "D02BHFA" 390424 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388914 389632 389660 "D02BBFA" 389665 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382045 383700 385306 "D02AGNT" 387328 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379795 380336 380882 "D01WGTS" 381519 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378802 379754 379782 "D01TRNS" 379787 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377810 378761 378789 "D01GBFA" 378794 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376818 377769 377797 "D01FCFA" 377802 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375826 376777 376805 "D01ASFA" 376810 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374834 375785 375813 "D01AQFA" 375818 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373842 374793 374821 "D01APFA" 374826 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372850 373801 373829 "D01ANFA" 373834 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371858 372809 372837 "D01AMFA" 372842 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370866 371817 371845 "D01ALFA" 371850 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369874 370825 370853 "D01AKFA" 370858 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368882 369833 369861 "D01AJFA" 369866 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362105 363730 365291 "D01AGNT" 367341 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361424 361570 361722 "CYCLOTOM" 361973 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358079 358872 359599 "CYCLES" 360717 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357379 357525 357696 "CVMP" 357940 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355166 355478 355847 "CTRIGMNP" 357107 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354639 354897 354998 "CTORKIND" 355085 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353844 354232 354260 "CTORCAT" 354442 T CTORCAT (NIL) -9 NIL 354555 NIL) (-188 353418 353553 353712 "CTORCAT-" 353717 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352832 353092 353200 "CTORCALL" 353342 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352190 352626 352699 "CTOR" 352779 T CTOR (NIL) -8 NIL NIL NIL) (-185 351546 351663 351816 "CSTTOOLS" 352087 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347243 348002 348760 "CRFP" 350858 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346658 346964 347056 "CRCEAST" 347171 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345681 345890 346118 "CRAPACK" 346462 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345061 345166 345370 "CPMATCH" 345557 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344780 344814 344920 "CPIMA" 345027 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341038 341800 342519 "COORDSYS" 344115 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340426 340571 340713 "CONTOUR" 340916 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335898 338429 338921 "CONTFRAC" 339966 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335772 335799 335827 "CONDUIT" 335864 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334726 335400 335428 "COMRING" 335433 T COMRING (NIL) -9 NIL 335485 NIL) (-174 333708 334084 334268 "COMPPROP" 334562 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333363 333404 333532 "COMPLPAT" 333667 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332993 333056 333163 "COMPLEX2" 333300 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321397 332802 332911 "COMPLEX" 332916 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320718 320857 321017 "COMPILER" 321257 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320430 320471 320569 "COMPFACT" 320677 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301824 314134 314174 "COMPCAT" 315178 NIL COMPCAT (NIL T) -9 NIL 316526 NIL) (-167 290712 294263 297890 "COMPCAT-" 298246 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290435 290469 290572 "COMMUPC" 290678 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290223 290263 290322 "COMMONOP" 290396 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289745 290027 290102 "COMMAAST" 290168 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289252 289496 289583 "COMM" 289678 T COMM (NIL) -8 NIL NIL NIL) (-162 288447 288695 288723 "COMBOPC" 289061 T COMBOPC (NIL) -9 NIL 289236 NIL) (-161 287301 287553 287795 "COMBINAT" 288237 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283644 284332 284959 "COMBF" 286723 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282306 282760 282995 "COLOR" 283429 T COLOR (NIL) -8 NIL NIL NIL) (-158 281722 282027 282119 "COLONAST" 282234 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281356 281409 281534 "CMPLXRT" 281669 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280744 281056 281155 "CLLCTAST" 281277 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276203 277274 278354 "CLIP" 279684 T CLIP (NIL) -7 NIL NIL NIL) (-154 274376 275304 275544 "CLIF" 276030 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270358 272494 272535 "CLAGG" 273464 NIL CLAGG (NIL T) -9 NIL 274000 NIL) (-152 268702 269237 269820 "CLAGG-" 269825 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268240 268331 268471 "CINTSLPE" 268611 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265705 266212 266760 "CHVAR" 267768 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264745 265419 265447 "CHARZ" 265452 T CHARZ (NIL) -9 NIL 265467 NIL) (-148 264493 264539 264617 "CHARPOL" 264699 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263411 264117 264145 "CHARNZ" 264206 T CHARNZ (NIL) -9 NIL 264255 NIL) (-146 260355 261465 261994 "CHAR" 262902 T CHAR (NIL) -8 NIL NIL NIL) (-145 260063 260142 260170 "CFCAT" 260281 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259286 259415 259598 "CDEN" 259947 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254883 258439 258719 "CCLASS" 259026 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254104 254291 254468 "CATEGORY" 254726 T -10 (NIL) -8 NIL NIL NIL) (-141 253599 254023 254071 "CATCTOR" 254076 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252990 253302 253400 "CATAST" 253521 T CATAST (NIL) -8 NIL NIL NIL) (-139 252406 252711 252803 "CASEAST" 252918 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251502 251662 251883 "CARTEN2" 252253 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247659 248403 "CARTEN" 250814 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 4b97b17e..be34c5b1 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,6663 +1,1999 @@
 
-(733414 . 3508766237)        
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 (((*1 *2 *3)
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-      (-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|
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-              (|:| |notEvaluated|
-                   "Internal singularities not yet evaluated")))
-        (|:| -2132
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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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 (((*1 *2 *3)
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 (((*1 *2 *3 *4 *4 *5 *6 *7)
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@@ -6667,1083 +2003,494 @@
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      (|:| |mdnia|
           (-2 (|:| |fn| (-326 (-229)))
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            (|:| |cf| (-663 (-326 (-229))))
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@@ -7753,446 +2500,461 @@
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             (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229))))))
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      (|:| |tol| (-229))))
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 (((*1 *2 *3)
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+ ((*1 *2 *3 *2)
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+  (-12 (-5 *2 (-1299 (-352 (-3845) (-3845 'X) (-721))))
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-  (-12 (-5 *2 (-1298 (-352 (-2548 'X) (-2548 '-3790) (-721))))
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+  (-12 (-5 *2 (-1299 (-352 (-3845 'X) (-3845 '-2050) (-721))))
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-  (-12 (-5 *2 (-1298 (-352 (-2548 'X '-3790) (-2548) (-721))))
-   (-5 *1 (-83 *3)) (-14 *3 (-1208))))
+  (-12 (-5 *2 (-1299 (-352 (-3845 'X '-2050) (-3845) (-721))))
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-  (-12 (-5 *2 (-711 (-352 (-2548 'X '-3790) (-2548) (-721))))
-   (-5 *1 (-84 *3)) (-14 *3 (-1208))))
+  (-12 (-5 *2 (-711 (-352 (-3845 'X '-2050) (-3845) (-721))))
+   (-5 *1 (-84 *3)) (-14 *3 (-1209))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-711 (-352 (-2548 'X) (-2548) (-721)))) (-5 *1 (-85 *3))
-   (-14 *3 (-1208))))
+  (-12 (-5 *2 (-711 (-352 (-3845 'X) (-3845) (-721)))) (-5 *1 (-85 *3))
+   (-14 *3 (-1209))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1298 (-352 (-2548 'X) (-2548) (-721))))
-   (-5 *1 (-86 *3)) (-14 *3 (-1208))))
+  (-12 (-5 *2 (-1299 (-352 (-3845 'X) (-3845) (-721))))
+   (-5 *1 (-86 *3)) (-14 *3 (-1209))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-711 (-352 (-2548 'XL 'XR 'ELAM) (-2548) (-721))))
-   (-5 *1 (-88 *3)) (-14 *3 (-1208))))
+  (-12 (-5 *2 (-711 (-352 (-3845 'XL 'XR 'ELAM) (-3845) (-721))))
+   (-5 *1 (-88 *3)) (-14 *3 (-1209))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-2548 'X) (-2548 '-3790) (-721))) (-5 *1 (-89 *3))
-   (-14 *3 (-1208))))
+  (-12 (-5 *2 (-352 (-3845 'X) (-3845 '-2050) (-721))) (-5 *1 (-89 *3))
+   (-14 *3 (-1209))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-663 (-137 *3 *4 *5))) (-5 *1 (-137 *3 *4 *5))
    (-14 *3 (-560)) (-14 *4 (-793)) (-4 *5 (-175))))
@@ -10508,33 +3838,33 @@
   (-12 (-5 *2 (-663 *5)) (-4 *5 (-175)) (-5 *1 (-137 *3 *4 *5))
    (-14 *3 (-560)) (-14 *4 (-793))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1173 *4 *5)) (-14 *4 (-793)) (-4 *5 (-175))
+  (-12 (-5 *2 (-1174 *4 *5)) (-14 *4 (-793)) (-4 *5 (-175))
    (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-560))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-246 *4 *5)) (-14 *4 (-793)) (-4 *5 (-175))
    (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-560))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1298 (-711 *4))) (-4 *4 (-175))
-   (-5 *2 (-1298 (-711 (-421 (-975 *4))))) (-5 *1 (-192 *4))))
+  (-12 (-5 *3 (-1299 (-711 *4))) (-4 *4 (-175))
+   (-5 *2 (-1299 (-711 (-421 (-976 *4))))) (-5 *1 (-192 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1123 (-326 *4)))
-   (-4 *4 (-13 (-871) (-571) (-633 (-391)))) (-5 *2 (-1123 (-391)))
+  (-12 (-5 *3 (-1124 (-326 *4)))
+   (-4 *4 (-13 (-872) (-571) (-633 (-391)))) (-5 *2 (-1124 (-391)))
    (-5 *1 (-268 *4))))
- ((*1 *1 *2) (-12 (-4 *1 (-277 *2)) (-4 *2 (-871))))
+ ((*1 *1 *2) (-12 (-4 *1 (-277 *2)) (-4 *2 (-872))))
  ((*1 *1 *2) (-12 (-5 *2 (-663 (-560))) (-5 *1 (-286))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-1274 *3)) (-5 *1 (-301 *3 *2 *4 *5 *6 *7))
+  (-12 (-4 *2 (-1275 *3)) (-5 *1 (-301 *3 *2 *4 *5 *6 *7))
    (-4 *3 (-175)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4))
    (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1279 *4 *5 *6)) (-4 *4 (-13 (-27) (-1234) (-435 *3)))
-   (-14 *5 (-1208)) (-14 *6 *4)
-   (-4 *3 (-13 (-1069 (-560)) (-660 (-560)) (-466)))
+  (-12 (-5 *2 (-1280 *4 *5 *6)) (-4 *4 (-13 (-27) (-1235) (-435 *3)))
+   (-14 *5 (-1209)) (-14 *6 *4)
+   (-4 *3 (-13 (-1070 (-560)) (-660 (-560)) (-466)))
    (-5 *1 (-325 *3 *4 *5 *6))))
  ((*1 *2 *1)
   (-12 (-5 *2 (-326 *5)) (-5 *1 (-352 *3 *4 *5))
-   (-14 *3 (-663 (-1208))) (-14 *4 (-663 (-1208))) (-4 *5 (-401))))
+   (-14 *3 (-663 (-1209))) (-14 *4 (-663 (-1209))) (-4 *5 (-401))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-363)) (-4 *2 (-341 *4)) (-5 *1 (-361 *3 *4 *2))
    (-4 *3 (-341 *4))))
@@ -10542,175 +3872,175 @@
   (-12 (-4 *4 (-363)) (-4 *2 (-341 *4)) (-5 *1 (-361 *2 *4 *3))
    (-4 *3 (-341 *4))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-871)) (-4 *4 (-175))
-   (-5 *2 (-1323 *3 *4))))
+  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175))
+   (-5 *2 (-1324 *3 *4))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-871)) (-4 *4 (-175))
-   (-5 *2 (-1314 *3 *4))))
- ((*1 *1 *2) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-871)) (-4 *3 (-175))))
+  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175))
+   (-5 *2 (-1315 *3 *4))))
+ ((*1 *1 *2) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-872)) (-4 *3 (-175))))
  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
    (-4 *1 (-396))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-396))))
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  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
    (-4 *1 (-398))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-398))))
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- ((*1 *2 *3) (-12 (-5 *2 (-407)) (-5 *1 (-408 *3)) (-4 *3 (-1132))))
+ ((*1 *2 *3) (-12 (-5 *2 (-407)) (-5 *1 (-408 *3)) (-4 *3 (-1133))))
  ((*1 *1 *2)
   (-12
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+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
    (-4 *1 (-411))))
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   (-12 (-5 *2 (-305 (-326 (-171 (-391))))) (-5 *1 (-412 *3 *4 *5 *6))
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-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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   (-12 (-5 *2 (-305 (-326 (-391)))) (-5 *1 (-412 *3 *4 *5 *6))
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-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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   (-12 (-5 *2 (-305 (-326 (-560)))) (-5 *1 (-412 *3 *4 *5 *6))
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  ((*1 *1 *2)
   (-12 (-5 *2 (-326 (-171 (-391)))) (-5 *1 (-412 *3 *4 *5 *6))
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-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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  ((*1 *1 *2)
   (-12 (-5 *2 (-326 (-560))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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  ((*1 *1 *2)
   (-12 (-5 *2 (-305 (-326 (-716)))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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  ((*1 *1 *2)
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-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+   (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-305 (-326 (-723)))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-326 (-716))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+   (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-326 (-721))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
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+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-326 (-723))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+   (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12
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-   (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
+   (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209))
+   (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-663 (-342))) (-5 *1 (-412 *3 *4 *5 *6))
-   (-14 *3 (-1208)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+   (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-342)) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1208))
-   (-14 *4 (-3 (|:| |fst| (-448)) (|:| -2565 "void")))
-   (-14 *5 (-663 (-1208))) (-14 *6 (-1212))))
+  (-12 (-5 *2 (-342)) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209))
+   (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4056 "void")))
+   (-14 *5 (-663 (-1209))) (-14 *6 (-1213))))
  ((*1 *1 *2)
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+  (-12 (-5 *2 (-421 (-976 (-421 *3)))) (-4 *3 (-571)) (-4 *3 (-1133))
    (-4 *1 (-435 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-975 (-421 *3))) (-4 *3 (-571)) (-4 *3 (-1132))
+  (-12 (-5 *2 (-976 (-421 *3))) (-4 *3 (-571)) (-4 *3 (-1133))
    (-4 *1 (-435 *3))))
  ((*1 *1 *2)
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+  (-12 (-5 *2 (-421 *3)) (-4 *3 (-571)) (-4 *3 (-1133))
    (-4 *1 (-435 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1156 *3 (-630 *1))) (-4 *3 (-1080)) (-4 *3 (-1132))
+  (-12 (-5 *2 (-1157 *3 (-630 *1))) (-4 *3 (-1081)) (-4 *3 (-1133))
    (-4 *1 (-435 *3))))
  ((*1 *1 *2)
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+  (-12 (-5 *2 (-343 *4)) (-4 *4 (-13 (-872) (-21)))
    (-5 *1 (-443 *3 *4)) (-4 *3 (-13 (-175) (-38 (-421 (-560)))))))
  ((*1 *1 *2)
   (-12 (-5 *1 (-443 *2 *3)) (-4 *2 (-13 (-175) (-38 (-421 (-560)))))
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- ((*1 *2 *1) (-12 (-5 *2 (-1134)) (-5 *1 (-448))))
- ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-448))))
- ((*1 *1 *2) (-12 (-5 *2 (-1208)) (-5 *1 (-448))))
- ((*1 *1 *2) (-12 (-5 *2 (-1190)) (-5 *1 (-448))))
+   (-4 *3 (-13 (-872) (-21)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1135)) (-5 *1 (-448))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1209)) (-5 *1 (-448))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-448))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-448))))
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  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
    (-4 *1 (-454))))
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  ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454))))
- ((*1 *1 *2) (-12 (-5 *2 (-1298 (-721))) (-4 *1 (-454))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1299 (-721))) (-4 *1 (-454))))
  ((*1 *1 *2)
   (-12
-   (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342)))))
+   (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2154 (-663 (-342)))))
    (-4 *1 (-455))))
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- ((*1 *1 *2) (-12 (-5 *2 (-663 (-663 (-972 (-229))))) (-5 *1 (-482))))
- ((*1 *2 *1) (-12 (-5 *2 (-887)) (-5 *1 (-482))))
+  (-12 (-5 *2 (-1299 (-421 (-976 *3)))) (-4 *3 (-175))
+   (-14 *6 (-1299 (-711 *3))) (-5 *1 (-467 *3 *4 *5 *6))
+   (-14 *4 (-949)) (-14 *5 (-663 (-1209)))))
+ ((*1 *1 *2) (-12 (-5 *2 (-663 (-663 (-973 (-229))))) (-5 *1 (-482))))
+ ((*1 *2 *1) (-12 (-5 *2 (-888)) (-5 *1 (-482))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1279 *3 *4 *5)) (-4 *3 (-1080)) (-14 *4 (-1208))
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+   (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-538))))
+ ((*1 *1 *2) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-619))))
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   (-12 (-4 *3 (-175)) (-5 *1 (-620 *3 *2)) (-4 *2 (-766 *3))))
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- ((*1 *1 *2) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1248))))
- ((*1 *1 *2) (-12 (-4 *1 (-640 *2)) (-4 *2 (-1080))))
+ ((*1 *2 *1) (-12 (-4 *1 (-632 *2)) (-4 *2 (-1249))))
+ ((*1 *1 *2) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1249))))
+ ((*1 *1 *2) (-12 (-4 *1 (-640 *2)) (-4 *2 (-1081))))
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-   (-4 *4 (-13 (-175) (-739 (-421 (-560))))) (-14 *5 (-948))))
+  (-12 (-5 *2 (-1320 *3 *4)) (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-872))
+   (-4 *4 (-13 (-175) (-739 (-421 (-560))))) (-14 *5 (-949))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1314 *3 *4)) (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-871))
-   (-4 *4 (-13 (-175) (-739 (-421 (-560))))) (-14 *5 (-948))))
+  (-12 (-5 *2 (-1315 *3 *4)) (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-872))
+   (-4 *4 (-13 (-175) (-739 (-421 (-560))))) (-14 *5 (-949))))
  ((*1 *1 *2)
   (-12 (-4 *3 (-175)) (-5 *1 (-652 *3 *2)) (-4 *2 (-766 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-699 *3)) (-5 *1 (-694 *3)) (-4 *3 (-871))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-694 *3)) (-4 *3 (-871))))
+ ((*1 *2 *1) (-12 (-5 *2 (-699 *3)) (-5 *1 (-694 *3)) (-4 *3 (-872))))
+ ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-694 *3)) (-4 *3 (-872))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-987 (-987 (-987 *3)))) (-5 *1 (-697 *3))
-   (-4 *3 (-1132))))
+  (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-5 *1 (-697 *3))
+   (-4 *3 (-1133))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-987 (-987 (-987 *3)))) (-4 *3 (-1132))
+  (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-4 *3 (-1133))
    (-5 *1 (-697 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-699 *3)) (-4 *3 (-871))))
- ((*1 *1 *2) (-12 (-5 *2 (-1146)) (-5 *1 (-703))))
- ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-704 *3)) (-4 *3 (-1132))))
+ ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-699 *3)) (-4 *3 (-872))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1147)) (-5 *1 (-703))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-704 *3)) (-4 *3 (-1133))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-1080)) (-4 *1 (-708 *3 *4 *2)) (-4 *4 (-385 *3))
+  (-12 (-4 *3 (-1081)) (-4 *1 (-708 *3 *4 *2)) (-4 *4 (-385 *3))
    (-4 *2 (-385 *3))))
  ((*1 *2 *1) (-12 (-5 *2 (-171 (-391))) (-5 *1 (-716))))
  ((*1 *1 *2) (-12 (-5 *2 (-171 (-723))) (-5 *1 (-716))))
@@ -10721,7 +4051,7 @@
  ((*1 *2 *1) (-12 (-5 *2 (-391)) (-5 *1 (-721))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-326 (-560))) (-5 *2 (-326 (-723))) (-5 *1 (-723))))
- ((*1 *2 *3) (-12 (-5 *3 (-887)) (-5 *2 (-1190)) (-5 *1 (-732))))
+ ((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1191)) (-5 *1 (-732))))
  ((*1 *2 *1)
   (-12 (-4 *2 (-175)) (-5 *1 (-733 *2 *3 *4 *5 *6)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
@@ -10731,80 +4061,80 @@
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-663 (-2 (|:| -1398 *3) (|:| -4002 *4))))
-   (-4 *3 (-1080)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4))))
+  (-12 (-5 *2 (-663 (-2 (|:| -3265 *3) (|:| -2724 *4))))
+   (-4 *3 (-1081)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4))))
  ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-3
      (|:| |nia|
-          (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229)))
-           (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229))
+          (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229)))
+           (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229))
            (|:| |relerr| (-229))))
      (|:| |mdnia|
           (-2 (|:| |fn| (-326 (-229)))
-           (|:| -2132 (-663 (-1120 (-864 (-229)))))
+           (|:| -3423 (-663 (-1121 (-866 (-229)))))
            (|:| |abserr| (-229)) (|:| |relerr| (-229))))))
    (-5 *1 (-791))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |fn| (-326 (-229)))
-     (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229))
+     (|:| -3423 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *1 (-791))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229)))
-     (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229)))
+     (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *1 (-791))))
- ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1248))))
+ ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1298 (-326 (-229)))) (|:| |yinit| (-663 (-229)))
+     (|:| |fn| (-1299 (-326 (-229)))) (|:| |yinit| (-663 (-229)))
      (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
-   (-5 *1 (-830))))
- ((*1 *1 *2) (-12 (-5 *2 (-1208)) (-5 *1 (-848))))
+   (-5 *1 (-832))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-850))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -2814 (-663 (-229)))
-           (|:| |lb| (-663 (-864 (-229))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -2689 (-663 (-229)))
+           (|:| |lb| (-663 (-866 (-229))))
            (|:| |cf| (-663 (-326 (-229))))
-           (|:| |ub| (-663 (-864 (-229))))))
+           (|:| |ub| (-663 (-866 (-229))))))
      (|:| |lsa|
           (-2 (|:| |lfn| (-663 (-326 (-229))))
-           (|:| -2814 (-663 (-229)))))))
-   (-5 *1 (-863))))
+           (|:| -2689 (-663 (-229)))))))
+   (-5 *1 (-865))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2814 (-663 (-229)))))
-   (-5 *1 (-863))))
+    (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2689 (-663 (-229)))))
+   (-5 *1 (-865))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |fn| (-326 (-229))) (|:| -2814 (-663 (-229)))
-     (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229))))
-     (|:| |ub| (-663 (-864 (-229))))))
-   (-5 *1 (-863))))
- ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-882))))
- ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-898))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-975 (-48))) (-5 *2 (-326 (-560))) (-5 *1 (-899))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-421 (-975 (-48)))) (-5 *2 (-326 (-560)))
-   (-5 *1 (-899))))
- ((*1 *1 *2) (-12 (-5 *1 (-918 *2)) (-4 *2 (-871))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-918 *3)) (-4 *3 (-871))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -2689 (-663 (-229)))
+     (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229))))
+     (|:| |ub| (-663 (-866 (-229))))))
+   (-5 *1 (-865))))
+ ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-883))))
+ ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-899))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-976 (-48))) (-5 *2 (-326 (-560))) (-5 *1 (-900))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-421 (-976 (-48)))) (-5 *2 (-326 (-560)))
+   (-5 *1 (-900))))
+ ((*1 *1 *2) (-12 (-5 *1 (-919 *2)) (-4 *2 (-872))))
+ ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-919 *3)) (-4 *3 (-872))))
  ((*1 *1 *2)
   (-12
    (-5 *2
@@ -10814,700 +4144,6584 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229))
             (|:| |grid| (-793)) (|:| |boundaryType| (-560))
             (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229))))))
-     (|:| |f| (-663 (-663 (-326 (-229))))) (|:| |st| (-1190))
+     (|:| |f| (-663 (-663 (-326 (-229))))) (|:| |st| (-1191))
      (|:| |tol| (-229))))
-   (-5 *1 (-925))))
- ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1132)) (-5 *1 (-931 *3))))
+   (-5 *1 (-926))))
+ ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-932 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1132)) (-5 *1 (-931 *3))))
+  (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1133)) (-5 *1 (-932 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-663 (-931 *3))) (-4 *3 (-1132)) (-5 *1 (-934 *3))))
+  (-12 (-5 *2 (-663 (-932 *3))) (-4 *3 (-1133)) (-5 *1 (-935 *3))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-663 (-931 *3))) (-5 *1 (-934 *3)) (-4 *3 (-1132))))
+  (-12 (-5 *2 (-663 (-932 *3))) (-5 *1 (-935 *3)) (-4 *3 (-1133))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-421 (-419 *3))) (-4 *3 (-319)) (-5 *1 (-943 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-421 *3)) (-5 *1 (-943 *3)) (-4 *3 (-319))))
+  (-12 (-5 *2 (-421 (-419 *3))) (-4 *3 (-319)) (-5 *1 (-944 *3))))
+ ((*1 *2 *1) (-12 (-5 *2 (-421 *3)) (-5 *1 (-944 *3)) (-4 *3 (-319))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-491)) (-5 *2 (-326 *4)) (-5 *1 (-949 *4))
+  (-12 (-5 *3 (-491)) (-5 *2 (-326 *4)) (-5 *1 (-950 *4))
    (-4 *4 (-571))))
- ((*1 *2 *3) (-12 (-5 *2 (-1304)) (-5 *1 (-1064 *3)) (-4 *3 (-1248))))
- ((*1 *2 *3) (-12 (-5 *3 (-323)) (-5 *1 (-1064 *2)) (-4 *2 (-1248))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1305)) (-5 *1 (-1065 *3)) (-4 *3 (-1249))))
+ ((*1 *2 *3) (-12 (-5 *3 (-323)) (-5 *1 (-1065 *2)) (-4 *2 (-1249))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871))
-   (-5 *1 (-1065 *3 *4 *5 *2 *6)) (-4 *2 (-979 *3 *4 *5))
+  (-12 (-4 *3 (-376)) (-4 *4 (-817)) (-4 *5 (-872))
+   (-5 *1 (-1066 *3 *4 *5 *2 *6)) (-4 *2 (-980 *3 *4 *5))
    (-14 *6 (-663 *2))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-421 (-975 *3))) (-5 *1 (-1071 *3)) (-4 *3 (-571))))
+  (-12 (-5 *2 (-421 (-976 *3))) (-5 *1 (-1072 *3)) (-4 *3 (-571))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-1080)) (-4 *4 (-871)) (-5 *1 (-1157 *3 *4 *2))
-   (-4 *2 (-979 *3 (-545 *4) *4))))
+  (-12 (-4 *3 (-1081)) (-4 *4 (-872)) (-5 *1 (-1158 *3 *4 *2))
+   (-4 *2 (-980 *3 (-545 *4) *4))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-1080)) (-4 *2 (-871)) (-5 *1 (-1157 *3 *2 *4))
-   (-4 *4 (-979 *3 (-545 *2) *2))))
- ((*1 *2 *1) (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-887))))
- ((*1 *1 *2) (-12 (-5 *2 (-146)) (-4 *1 (-1175))))
+  (-12 (-4 *3 (-1081)) (-4 *2 (-872)) (-5 *1 (-1158 *3 *2 *4))
+   (-4 *4 (-980 *3 (-545 *2) *2))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1081)) (-5 *2 (-888))))
+ ((*1 *1 *2) (-12 (-5 *2 (-146)) (-4 *1 (-1176))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-1186 *3)) (-5 *1 (-1192 *3)) (-4 *3 (-1080))))
+  (-12 (-5 *2 (-1187 *3)) (-5 *1 (-1193 *3)) (-4 *3 (-1081))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1295 *4)) (-14 *4 (-1208)) (-5 *1 (-1199 *3 *4 *5))
-   (-4 *3 (-1080)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1200 *3 *4 *5))
+   (-4 *3 (-1081)) (-14 *5 *3)))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1295 *4)) (-14 *4 (-1208)) (-5 *1 (-1206 *3 *4 *5))
-   (-4 *3 (-1080)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1207 *3 *4 *5))
+   (-4 *3 (-1081)) (-14 *5 *3)))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1267 *4 *3)) (-4 *3 (-1080)) (-14 *4 (-1208))
-   (-14 *5 *3) (-5 *1 (-1206 *3 *4 *5))))
- ((*1 *1 *2) (-12 (-5 *2 (-1208)) (-5 *1 (-1207))))
- ((*1 *2 *1) (-12 (-5 *2 (-1220 (-1208) (-450))) (-5 *1 (-1212))))
- ((*1 *2 *1) (-12 (-5 *2 (-1190)) (-5 *1 (-1213))))
- ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-1213))))
- ((*1 *2 *1) (-12 (-5 *2 (-229)) (-5 *1 (-1213))))
- ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-1213))))
- ((*1 *2 *1) (-12 (-5 *2 (-887)) (-5 *1 (-1221 *3)) (-4 *3 (-1132))))
- ((*1 *2 *3) (-12 (-5 *2 (-1228)) (-5 *1 (-1229 *3)) (-4 *3 (-1132))))
+  (-12 (-5 *2 (-1268 *4 *3)) (-4 *3 (-1081)) (-14 *4 (-1209))
+   (-14 *5 *3) (-5 *1 (-1207 *3 *4 *5))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-1208))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1221 (-1209) (-450))) (-5 *1 (-1213))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1214))))
+ ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-1214))))
+ ((*1 *2 *1) (-12 (-5 *2 (-229)) (-5 *1 (-1214))))
+ ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-1214))))
+ ((*1 *2 *1) (-12 (-5 *2 (-888)) (-5 *1 (-1222 *3)) (-4 *3 (-1133))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1229)) (-5 *1 (-1230 *3)) (-4 *3 (-1133))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-975 *3)) (-4 *3 (-1080)) (-5 *1 (-1241 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1208)) (-5 *1 (-1241 *3)) (-4 *3 (-1080))))
+  (-12 (-5 *2 (-976 *3)) (-4 *3 (-1081)) (-5 *1 (-1242 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-1242 *3)) (-4 *3 (-1081))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1295 *4)) (-14 *4 (-1208)) (-5 *1 (-1258 *3 *4 *5))
-   (-4 *3 (-1080)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1259 *3 *4 *5))
+   (-4 *3 (-1081)) (-14 *5 *3)))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1120 *3)) (-4 *3 (-1248)) (-5 *1 (-1265 *3))))
+  (-12 (-5 *2 (-1121 *3)) (-4 *3 (-1249)) (-5 *1 (-1266 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1295 *4)) (-14 *4 (-1208)) (-5 *1 (-1288 *3 *4 *5))
-   (-4 *3 (-1080)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1289 *3 *4 *5))
+   (-4 *3 (-1081)) (-14 *5 *3)))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1267 *4 *3)) (-4 *3 (-1080)) (-14 *4 (-1208))
-   (-14 *5 *3) (-5 *1 (-1288 *3 *4 *5))))
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+           (|:| |upperInfinite| "The top of range is infinite")
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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|
+                (-3 (|:| |str| (-1187 (-229)))
+                 (|:| |notEvaluated|
+                      "Internal singularities not yet evaluated")))
+           (|:| -3423
+                (-3 (|:| |finite| "The range is finite")
+                 (|:| |lowerInfinite|
+                      "The bottom of range is infinite")
+                 (|:| |upperInfinite| "The top of range is infinite")
+                 (|:| |bothInfinite|
+                      "Both top and bottom points are infinite")
+                 (|:| |notEvaluated| "Range not yet evaluated")))))))
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+(((*1 *2 *3)
+  (-12
+   (-5 *3
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+     (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229))
+     (|:| |relerr| (-229))))
+   (-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| (-1187 (-229)))
+           (|:| |notEvaluated|
+                "Internal singularities not yet evaluated")))
+     (|:| -3423
+          (-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 (-574))))) 
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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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+              (|:| |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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+           (-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| (-1187 (-229)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3423
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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@@ -11523,1684 +10737,3535 @@
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@@ -13209,253 +14274,957 @@
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+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1249))
+   (-4 *6 (-1249)) (-5 *2 (-58 *6)) (-5 *1 (-59 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-560))
    (-14 *6 (-793)) (-4 *7 (-175)) (-4 *8 (-175))
@@ -13464,51 +15233,51 @@
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-171 *5)) (-4 *5 (-175))
    (-4 *6 (-175)) (-5 *2 (-171 *6)) (-5 *1 (-172 *5 *6))))
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-   (-5 *1 (-227 *3 *4)) (-14 *4 (-663 (-1208)))))
+  (-12 (-5 *2 (-1 (-326 *3) (-326 *3))) (-4 *3 (-13 (-1081) (-872)))
+   (-5 *1 (-227 *3 *4)) (-14 *4 (-663 (-1209)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-793))
-   (-4 *6 (-1248)) (-4 *7 (-1248)) (-5 *2 (-246 *5 *7))
+   (-4 *6 (-1249)) (-4 *7 (-1249)) (-5 *2 (-246 *5 *7))
    (-5 *1 (-247 *5 *6 *7))))
  ((*1 *1 *2 *1)
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+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1249)) (-5 *1 (-305 *3))))
  ((*1 *2 *3 *4)
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-   (-4 *6 (-1248)) (-5 *2 (-305 *6)) (-5 *1 (-306 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-305 *5)) (-4 *5 (-1249))
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  ((*1 *1 *2 *3)
   (-12 (-5 *2 (-1 *1 *1)) (-5 *3 (-630 *1)) (-4 *1 (-310))))
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+  (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1191)) (-5 *5 (-630 *6))
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    (-5 *2 (-346 *9 *10 *11 *12))
    (-5 *1 (-347 *5 *6 *7 *8 *9 *10 *11 *12))
    (-4 *12 (-355 *9 *10 *11))))
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+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-351 *3)) (-4 *3 (-1133))))
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-   (-4 *6 (-1274 *5)) (-4 *7 (-1274 (-421 *6))) (-4 *9 (-1274 *8))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1254)) (-4 *8 (-1254))
+   (-4 *6 (-1275 *5)) (-4 *7 (-1275 (-421 *6))) (-4 *9 (-1275 *8))
    (-4 *2 (-355 *8 *9 *10)) (-5 *1 (-356 *5 *6 *7 *4 *8 *9 *10 *2))
-   (-4 *4 (-355 *5 *6 *7)) (-4 *10 (-1274 (-421 *9)))))
+   (-4 *4 (-355 *5 *6 *7)) (-4 *10 (-1275 (-421 *9)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1248)) (-4 *6 (-1248))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1249)) (-4 *6 (-1249))
    (-4 *2 (-385 *6)) (-5 *1 (-386 *5 *4 *6 *2)) (-4 *4 (-385 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-397 *3 *4)) (-4 *3 (-1080))
-   (-4 *4 (-1132))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-397 *3 *4)) (-4 *3 (-1081))
+   (-4 *4 (-1133))))
  ((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-571)) (-5 *1 (-419 *3))))
  ((*1 *2 *3 *4)
@@ -13519,34 +15288,34 @@
    (-4 *6 (-571)) (-5 *2 (-421 *6)) (-5 *1 (-422 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-427 *5 *6 *7 *8)) (-4 *5 (-319))
-   (-4 *6 (-1022 *5)) (-4 *7 (-1274 *6))
-   (-4 *8 (-13 (-424 *6 *7) (-1069 *6))) (-4 *9 (-319))
-   (-4 *10 (-1022 *9)) (-4 *11 (-1274 *10))
+   (-4 *6 (-1023 *5)) (-4 *7 (-1275 *6))
+   (-4 *8 (-13 (-424 *6 *7) (-1070 *6))) (-4 *9 (-319))
+   (-4 *10 (-1023 *9)) (-4 *11 (-1275 *10))
    (-5 *2 (-427 *9 *10 *11 *12))
    (-5 *1 (-428 *5 *6 *7 *8 *9 *10 *11 *12))
-   (-4 *12 (-13 (-424 *10 *11) (-1069 *10)))))
+   (-4 *12 (-13 (-424 *10 *11) (-1070 *10)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175))
    (-4 *2 (-432 *6)) (-5 *1 (-430 *4 *5 *2 *6)) (-4 *4 (-432 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1080)) (-4 *6 (-1080))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081))
    (-4 *2 (-435 *6)) (-5 *1 (-436 *5 *4 *6 *2)) (-4 *4 (-435 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1132)) (-4 *6 (-1132))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1133)) (-4 *6 (-1133))
    (-4 *2 (-440 *6)) (-5 *1 (-441 *5 *4 *6 *2)) (-4 *4 (-440 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-503 *3)) (-4 *3 (-1248))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-503 *3)) (-4 *3 (-1249))))
  ((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-523 *3 *4)) (-4 *3 (-102))
-   (-4 *4 (-874))))
+   (-4 *4 (-875))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-597 *5)) (-4 *5 (-376))
    (-4 *6 (-376)) (-5 *2 (-597 *6)) (-5 *1 (-598 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *6 *5))
-      (-5 *4 (-3 (-2 (|:| -3735 *5) (|:| |coeff| *5)) "failed"))
+      (-5 *4 (-3 (-2 (|:| -2301 *5) (|:| |coeff| *5)) "failed"))
       (-4 *5 (-376)) (-4 *6 (-376))
-      (-5 *2 (-2 (|:| -3735 *6) (|:| |coeff| *6)))
+      (-5 *2 (-2 (|:| -2301 *6) (|:| |coeff| *6)))
       (-5 *1 (-598 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed"))
@@ -13566,4797 +15335,3028 @@
              (-663 (-2 (|:| |coeff| *6) (|:| |logand| *6))))))
       (-5 *1 (-598 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-615 *5)) (-4 *5 (-1248))
-   (-4 *6 (-1248)) (-5 *2 (-615 *6)) (-5 *1 (-612 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-615 *5)) (-4 *5 (-1249))
+   (-4 *6 (-1249)) (-5 *2 (-615 *6)) (-5 *1 (-612 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-615 *6)) (-5 *5 (-615 *7))
-   (-4 *6 (-1248)) (-4 *7 (-1248)) (-4 *8 (-1248)) (-5 *2 (-615 *8))
+   (-4 *6 (-1249)) (-4 *7 (-1249)) (-4 *8 (-1249)) (-5 *2 (-615 *8))
    (-5 *1 (-613 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1186 *6)) (-5 *5 (-615 *7))
-   (-4 *6 (-1248)) (-4 *7 (-1248)) (-4 *8 (-1248)) (-5 *2 (-1186 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1187 *6)) (-5 *5 (-615 *7))
+   (-4 *6 (-1249)) (-4 *7 (-1249)) (-4 *8 (-1249)) (-5 *2 (-1187 *8))
    (-5 *1 (-613 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
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-   (-4 *6 (-1248)) (-4 *7 (-1248)) (-4 *8 (-1248)) (-5 *2 (-1186 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-615 *6)) (-5 *5 (-1187 *7))
+   (-4 *6 (-1249)) (-4 *7 (-1249)) (-4 *8 (-1249)) (-5 *2 (-1187 *8))
    (-5 *1 (-613 *6 *7 *8))))
  ((*1 *1 *2 *1)
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+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1249)) (-5 *1 (-615 *3))))
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-   (-4 *6 (-1248)) (-5 *2 (-663 *6)) (-5 *1 (-664 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-663 *5)) (-4 *5 (-1249))
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  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-663 *6)) (-5 *5 (-663 *7))
-   (-4 *6 (-1248)) (-4 *7 (-1248)) (-4 *8 (-1248)) (-5 *2 (-663 *8))
+   (-4 *6 (-1249)) (-4 *7 (-1249)) (-4 *8 (-1249)) (-5 *2 (-663 *8))
    (-5 *1 (-666 *6 *7 *8))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-673 *3)) (-4 *3 (-1248))))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-673 *3)) (-4 *3 (-1249))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1080)) (-4 *8 (-1080))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1081)) (-4 *8 (-1081))
    (-4 *6 (-385 *5)) (-4 *7 (-385 *5)) (-4 *2 (-708 *8 *9 *10))
    (-5 *1 (-709 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-708 *5 *6 *7))
    (-4 *9 (-385 *8)) (-4 *10 (-385 *8))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1080))
-      (-4 *8 (-1080)) (-4 *6 (-385 *5)) (-4 *7 (-385 *5))
+  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1081))
+      (-4 *8 (-1081)) (-4 *6 (-385 *5)) (-4 *7 (-385 *5))
       (-4 *2 (-708 *8 *9 *10)) (-5 *1 (-709 *5 *6 *7 *4 *8 *9 *10 *2))
       (-4 *4 (-708 *5 *6 *7)) (-4 *9 (-385 *8)) (-4 *10 (-385 *8))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-571)) (-4 *7 (-571))
-   (-4 *6 (-1274 *5)) (-4 *2 (-1274 (-421 *8)))
-   (-5 *1 (-731 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1274 (-421 *6)))
-   (-4 *8 (-1274 *7))))
- ((*1 *2 *3 *4)
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-   (-4 *5 (-871)) (-4 *6 (-815)) (-4 *2 (-979 *9 *7 *5))
-   (-5 *1 (-750 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-815))
-   (-4 *4 (-979 *8 *6 *5))))
- ((*1 *2 *3 *4)
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-   (-4 *9 (-1080)) (-4 *2 (-979 *9 *8 *6))
-   (-5 *1 (-751 *5 *6 *7 *8 *9 *4 *2)) (-4 *8 (-815))
-   (-4 *4 (-979 *9 *7 *5))))
- ((*1 *2 *3 *4)
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-   (-4 *6 (-1080)) (-4 *7 (-748)) (-5 *2 (-757 *6 *7))
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+   (-5 *1 (-731 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1275 (-421 *6)))
+   (-4 *8 (-1275 *7))))
+ ((*1 *2 *3 *4)
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+   (-4 *5 (-872)) (-4 *6 (-817)) (-4 *2 (-980 *9 *7 *5))
+   (-5 *1 (-750 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-817))
+   (-4 *4 (-980 *8 *6 *5))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-872)) (-4 *6 (-872)) (-4 *7 (-817))
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+   (-4 *4 (-980 *9 *7 *5))))
+ ((*1 *2 *3 *4)
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+   (-4 *6 (-1081)) (-4 *7 (-748)) (-5 *2 (-757 *6 *7))
    (-5 *1 (-756 *5 *6 *7))))
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-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-757 *3 *4))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1081)) (-5 *1 (-757 *3 *4))
    (-4 *4 (-748))))
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+   (-4 *2 (-820 *6)) (-5 *1 (-823 *4 *5 *2 *6)) (-4 *4 (-820 *5))))
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-   (-4 *6 (-1132)) (-5 *2 (-854 *6)) (-5 *1 (-855 *5 *6))))
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  ((*1 *2 *3 *4 *2)
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-   (-4 *5 (-1132)) (-4 *6 (-1132)) (-5 *1 (-855 *5 *6))))
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  ((*1 *2 *3 *4 *2 *2)
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-   (-4 *6 (-1248)) (-5 *2 (-902 *6)) (-5 *1 (-901 *5 *6))))
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-   (-4 *6 (-1248)) (-5 *2 (-907 *6)) (-5 *1 (-906 *5 *6))))
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-   (-4 *6 (-1132)) (-4 *7 (-1132)) (-5 *2 (-913 *5 *7))
-   (-5 *1 (-914 *5 *6 *7))))
+  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-914 *5 *6)) (-4 *5 (-1133))
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+   (-5 *1 (-915 *5 *6 *7))))
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-   (-4 *6 (-1132)) (-5 *2 (-915 *6)) (-5 *1 (-917 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-916 *5)) (-4 *5 (-1133))
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-   (-4 *8 (-1080)) (-4 *6 (-815))
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+   (-4 *8 (-1081)) (-4 *6 (-817))
    (-4 *2
-    (-13 (-1132)
-     (-10 -8 (-15 -2413 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793))))))
-   (-5 *1 (-981 *6 *7 *8 *5 *2)) (-4 *5 (-979 *8 *6 *7))))
+    (-13 (-1133)
+     (-10 -8 (-15 -2571 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793))))))
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  ((*1 *2 *3 *4)
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-   (-4 *6 (-1248)) (-5 *2 (-987 *6)) (-5 *1 (-988 *5 *6))))
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  ((*1 *2 *3 *4)
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 (((*1 *1 *2 *3)
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-(((*1 *2)
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- ((*1 *2 *2 *3 *2 *3)
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+(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-114) (-115) (-115))) (-5 *1 (-115))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1209)) (-5 *2 (-1305)) (-5 *1 (-1212))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-1213))))) 
+(((*1 *1 *1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-793))))
+ ((*1 *1 *1) (-4 *1 (-416)))) 
 (((*1 *2 *3)
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-(((*1 *2 *3) (-12 (-5 *3 (-421 (-560))) (-5 *2 (-229)) (-5 *1 (-315))))) 
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- ((*1 *2 *3 *4)
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 (((*1 *2 *3)
-  (-12
-   (-5 *3
-    (-2
-     (|:| |endPointContinuity|
-          (-3 (|:| |continuous| "Continuous at the end points")
-           (|:| |lowerSingular|
-                "There is a singularity at the lower end point")
-           (|:| |upperSingular|
-                "There is a singularity at the upper end point")
-           (|:| |bothSingular|
-                "There are singularities at both end points")
-           (|:| |notEvaluated|
-                "End point continuity not yet evaluated")))
-     (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1186 (-229)))
-           (|:| |notEvaluated|
-                "Internal singularities not yet evaluated")))
-     (|:| -2132
-          (-3 (|:| |finite| "The range is finite")
-           (|:| |lowerInfinite| "The bottom of range is infinite")
-           (|:| |upperInfinite| "The top of range is infinite")
-           (|:| |bothInfinite|
-                "Both top and bottom points are infinite")
-           (|:| |notEvaluated| "Range not yet evaluated")))))
-   (-5 *2 (-1066)) (-5 *1 (-315))))) 
-(((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1190)) (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871))
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- ((*1 *2 *3 *3 *3)
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-   (-5 *1 (-1139 *4 *5 *6 *7 *8)) (-4 *8 (-1102 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-976 (-229))) (-5 *2 (-326 (-391))) (-5 *1 (-315))))) 
+(((*1 *2)
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+   (-4 *4 (-432 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-571) (-1069 (-560)))) (-5 *1 (-191 *3 *2))
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  ((*1 *2 *2)
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- ((*1 *2 *2 *3)
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-(((*1 *2 *3 *4)
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+            (|:| -3423 (-1121 (-866 (-229)))) (|:| |abserr| (-229))
+            (|:| |relerr| (-229))))
+      (|:| -3529
+           (-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| (-1187 (-229)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3423
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+ (-4486 . 899) (-4487 . 789) (-4488 . 652) (-4489 . 118) (-4490 . 30)) 
\ No newline at end of file