Remove IndexedMatrix as unused

12 files changed, 18097 insertions, 18179 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index f1dd8334..84799853 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,10 @@
 2013-05-10  Gabriel Dos Reis  <gdr@integrable-solutions.net>
 
+	* algebra/matrix.spad.pamphlet (IndexedMatrix): Remove as unused.
+	* algebra/Makefile.am (oa_algebra_layer_12): Remove IMATRIX.
+
+2013-05-10  Gabriel Dos Reis  <gdr@integrable-solutions.net>
+
 	* interp/g-opt.boot (optEmptyArray): New expander.  Register.
 	(optSimpleArray): Likewise.
 	(optList2Array): Likewise.
diff --git a/src/algebra/Makefile.am b/src/algebra/Makefile.am
index 340aab63..ed6f127b 100644
--- a/src/algebra/Makefile.am
+++ b/src/algebra/Makefile.am
@@ -1817,7 +1817,7 @@ oa_algebra_layer_11_objects = \
 	$(addprefix $(OUT)/, \
 	   $(addsuffix .$(FASLEXT),$(oa_algebra_layer_11)))
 oa_algebra_layer_12 = \
-  ULSCAT                           BITS     DIRPROD2 IMATRIX \
+  ULSCAT                           BITS     DIRPROD2 \
            LPOLY   LSMP    LSMP1   MATCAT2           TRIMAT  \
                    SYSTEM  HOSTNAME PORTNUM
 
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 9e523fb7..fbf8cc9c 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -950,7 +950,7 @@ oa_algebra_layer_11_objects = \
 	   $(addsuffix .$(FASLEXT),$(oa_algebra_layer_11)))
 
 oa_algebra_layer_12 = \
-  ULSCAT                           BITS     DIRPROD2 IMATRIX \
+  ULSCAT                           BITS     DIRPROD2 \
            LPOLY   LSMP    LSMP1   MATCAT2           TRIMAT  \
                    SYSTEM  HOSTNAME PORTNUM
 
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index 85f460f4..e20f1fa1 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -822,7 +822,6 @@
   (|IndexedDirectProductOrderedAbelianMonoidSup| . IDPOAMS)
   (|IndexedExponents| . INDE)
   (|IndexedFlexibleArray| . IFARRAY)
-  (|IndexedMatrix| . IMATRIX)
   (|IndexedOneDimensionalArray| . IARRAY1)
   (|IndexedTwoDimensionalArray| . IARRAY2)
   (|IndexedVector| . IVECTOR)
diff --git a/src/algebra/matfuns.spad.pamphlet b/src/algebra/matfuns.spad.pamphlet
index 1fdf3cc9..cba5b7f5 100644
--- a/src/algebra/matfuns.spad.pamphlet
+++ b/src/algebra/matfuns.spad.pamphlet
@@ -16,8 +16,7 @@
 ++ Date Created: 13 November 1989
 ++ Date Last Updated: September 1993
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix(R,minRow,minCol), Matrix(R),
-++    RectangularMatrix(n,m,R), SquareMatrix(n,R)
+++ Related Domains: Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, canonical forms, linear algebra
@@ -243,8 +242,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_
 ++ Date Created: 21 November 1989
 ++ Date Last Updated: 21 March 1994
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix(R,minRow,minCol), Matrix(R),
-++    RectangularMatrix(n,m,R), SquareMatrix(n,R)
+++ Related Domains: Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords:
@@ -310,8 +308,7 @@ MatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2):_
 ++ Date Created: 21 November 1989
 ++ Date Last Updated: 12 June 1991
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix(R,minRow,minCol), Matrix(R),
-++    RectangularMatrix(n,m,R), SquareMatrix(n,R)
+++ Related Domains: Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords:
@@ -370,7 +367,7 @@ RectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2):_
 ++ Date Created: 22 November 1989
 ++ Date Last Updated: 22 November 1989
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix(R,minRow,minCol), Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
+++ Related Domains: Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, inverse, integral domain
@@ -430,8 +427,7 @@ InnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2):_
 ++ Date Created: 13 November 1989
 ++ Date Last Updated: December 1992
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix(R,minRow,minCol), Matrix(R),
-++    RectangularMatrix(n,m,R), SquareMatrix(n,R)
+++ Related Domains: Matrix(R), RectangularMatrix(n,m,R), SquareMatrix(n,R)
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, canonical forms, linear algebra
diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet
index 04bbb1fe..8d9242e5 100644
--- a/src/algebra/matrix.spad.pamphlet
+++ b/src/algebra/matrix.spad.pamphlet
@@ -9,74 +9,7 @@
 \eject
 \tableofcontents
 \eject
-\section{domain IMATRIX IndexedMatrix}
-<<domain IMATRIX IndexedMatrix>>=
-)abbrev domain IMATRIX IndexedMatrix
-++ Author: Grabmeier, Gschnitzer, Williamson
-++ Date Created: 1987
-++ Date Last Updated: July 1990
-++ Basic Operations:
-++ Related Domains: Matrix, RectangularMatrix, SquareMatrix,
-++   StorageEfficientMatrixOperations
-++ Also See:
-++ AMS Classifications:
-++ Keywords: matrix, linear algebra
-++ Examples:
-++ References:
-++ Description:
-++   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.
-IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where
-  R : Ring
-  mnRow, mnCol : Integer
-  Row ==> IndexedVector(R,mnCol)
-  Col ==> IndexedVector(R,mnRow)
-  MATLIN ==> MatrixLinearAlgebraFunctions(R,Row,Col,$)
- 
-  Exports ==> MatrixCategory(R,Row,Col)
- 
-  Implementation ==>
-    InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col) add
- 
-      swapRows!(x,i1,i2) ==
-        (i1 < minRowIndex(x)) or (i1 > maxRowIndex(x)) or _
-           (i2 < minRowIndex(x)) or (i2 > maxRowIndex(x)) =>
-             error "swapRows!: index out of range"
-        i1 = i2 => x
-        minRow := minRowIndex x
-        xx := x pretend PrimitiveArray(PrimitiveArray(R))
-        n1 := i1 - minRow; n2 := i2 - minRow
-        row1 := qelt(xx,n1)
-        qsetelt!(xx,n1,qelt(xx,n2))
-        qsetelt!(xx,n2,row1)
-        xx pretend $
- 
-      if R has commutative("*") then
- 
-        determinant x == determinant(x)$MATLIN
-        minordet    x == minordet(x)$MATLIN
- 
-      if R has EuclideanDomain then
- 
-        rowEchelon  x == rowEchelon(x)$MATLIN
- 
-      if R has IntegralDomain then
- 
-        rank        x == rank(x)$MATLIN
-        nullity     x == nullity(x)$MATLIN
-        nullSpace   x == nullSpace(x)$MATLIN
- 
-      if R has Field then
- 
-        inverse     x == inverse(x)$MATLIN
 
-@
 \section{domain MATRIX Matrix}
 <<domain MATRIX Matrix>>=
 )abbrev domain MATRIX Matrix
@@ -84,7 +17,7 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where
 ++ Date Created: 1987
 ++ Date Last Updated: July 1990
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix, RectangularMatrix, SquareMatrix
+++ Related Domains: RectangularMatrix, SquareMatrix
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, linear algebra
@@ -259,7 +192,7 @@ Matrix(R): Exports == Implementation where
 ++ Date Created: 1987
 ++ Date Last Updated: July 1990
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix, Matrix, SquareMatrix
+++ Related Domains: Matrix, SquareMatrix
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, linear algebra
@@ -346,7 +279,7 @@ RectangularMatrix(m,n,R): Exports == Implementation where
 ++ Date Created: 1987
 ++ Date Last Updated: July 1990
 ++ Basic Operations:
-++ Related Domains: IndexedMatrix, Matrix, RectangularMatrix
+++ Related Domains: Matrix, RectangularMatrix
 ++ Also See:
 ++ AMS Classifications:
 ++ Keywords: matrix, linear algebra
@@ -520,7 +453,6 @@ SquareMatrix(ndim,R): Exports == Implementation where
 <<*>>=
 <<license>>
 
-<<domain IMATRIX IndexedMatrix>>
 <<domain MATRIX Matrix>>
 <<domain RMATRIX RectangularMatrix>>
 <<domain SQMATRIX SquareMatrix>>
diff --git a/src/hyper/pages/releaseNotes.ht b/src/hyper/pages/releaseNotes.ht
index 6d8fab4c..6e485e95 100644
--- a/src/hyper/pages/releaseNotes.ht
+++ b/src/hyper/pages/releaseNotes.ht
@@ -37,6 +37,7 @@ contains additions of new features and domains including:
   Fix for an interpreter performance regression introduced in 1.4.2.
   The category AbelianMonoid has a new export: opposite?.
   The category Rng has a new export: annihilate?.
+  The domain IndexedMatrix was removed as it was unused.
 
 \endscroll
 \autobuttons
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index c98de5cc..63b0fadc 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(1963183 . 3577223100)       
+(1962192 . 3577234982)       
 (-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."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . 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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T)) 
+((-3992 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3988 . T) (-3993 . T) (-3987 . T)) 
 NIL 
 (-30) 
 ((|refine| (($ $ (|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 -3094) 
+(-32 R -3093) 
 ((|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| (QUOTE (-952 (-485))))) 
+((|HasCategory| |#1| (QUOTE (-951 (-484))))) 
 (-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 \\%")) (|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 -3996))) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
 (-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 \\%")) (|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}."))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . 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"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . 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 -3094 UP UPUP -2616) 
+(-40 -3093 UP UPUP -2615) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-3989 |has| (-348 |#2|) (-312)) (-3994 |has| (-348 |#2|) (-312)) (-3988 |has| (-348 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091)))))) (|HasCategory| (-348 |#2|) (QUOTE (-582 (-485)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485)))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091)))))) 
-(-41 R -3094) 
+((-3988 |has| (-348 |#2|) (-312)) (-3993 |has| (-348 |#2|) (-312)) (-3987 |has| (-348 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-812 (-1090)))))) (|HasCategory| (-348 |#2|) (QUOTE (-581 (-484)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-348 (-484)))))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-812 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090)))))) 
+(-41 R -3093) 
 ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-258)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) 
-((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
+((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
 (-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."))) 
-((-3996 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-758)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))))) 
+((-3995 . T) (-3996 . T)) 
+((OR (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) 
 (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
+((|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484))))) 
 (-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}."))) 
-((-3993 . T)) 
+((-3992 . 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 -3094) 
+(-54 |Base| R -3093) 
 ((|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 
@@ -158,28 +158,28 @@ 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"))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . 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}"))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-61 R L) 
 ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-312)))) 
 (-62 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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-63 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -202,11 +202,11 @@ NIL
 NIL 
 (-68) 
 ((|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."))) 
-((-3996 . T) ((-3998 "*") . T) (-3997 . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T)) 
+((-3995 . T) ((-3997 "*") . T) (-3996 . T) (-3992 . T) (-3990 . T) (-3989 . T) (-3988 . T) (-3993 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3991 . T) (-3994 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3982 . T)) 
 NIL 
 (-69 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}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-70 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}."))) 
@@ -222,24 +222,24 @@ NIL
 NIL 
 (-73 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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-74 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 (-3998 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-3997 "*")))) 
 (-75 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."))) 
 NIL 
 NIL 
 (-76 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."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
 (-77) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-797 (-328)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1090)))) (|HasCategory| (-484) (QUOTE (-454 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118))))) 
 (-78) 
 ((|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -254,11 +254,11 @@ NIL
 NIL 
 (-81) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-474)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-1015))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-473)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) 
 (-82 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}"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
 (-83 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}."))) 
@@ -280,22 +280,22 @@ 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 
-(-88 -3094 UP) 
+(-88 -3093 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 
 (-89 |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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-90 |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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-823))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-474)))) (|HasCategory| (-89 |#1|) (QUOTE (-935))) (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758)))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-582 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-813 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-473)))) (|HasCategory| (-89 |#1|) (QUOTE (-934))) (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757)))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-1066))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1090)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1090)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
 (-91 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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3997))) 
+((|HasAttribute| |#1| (QUOTE -3996))) 
 (-92 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 
@@ -306,15 +306,15 @@ NIL
 NIL 
 (-94 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"))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-95 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-96) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
 (-97 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -322,24 +322,24 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
 (-99 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-100 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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-101) 
 ((|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 
 (-102) 
 ((|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."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-758)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015))))) (|HasCategory| (-101) (QUOTE (-554 (-774)))) (|HasCategory| (-101) (QUOTE (-555 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-101) (QUOTE (-758))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015))))) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-473)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) 
 (-103) 
 ((|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 
@@ -358,13 +358,13 @@ NIL
 NIL 
 (-107) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3998 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-108 |minix| -2623 R) 
+(-108 |minix| -2622 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2623 S T$) 
+(-109 |minix| -2622 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
@@ -386,8 +386,8 @@ NIL
 NIL 
 (-114) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) 
-((-3996 . T) (-3986 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-555 (-474)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) 
+((-3995 . T) (-3985 . T) (-3996 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-473)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) 
 (-115 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 
@@ -402,7 +402,7 @@ NIL
 NIL 
 (-118) 
 ((|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."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-119 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."))) 
@@ -410,9 +410,9 @@ NIL
 NIL 
 (-120) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-121 -3094 UP UPUP) 
+(-121 -3093 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 
@@ -423,14 +423,14 @@ NIL
 (-123 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| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasAttribute| |#1| (QUOTE -3996))) 
+((|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -3995))) 
 (-124 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 
 (-125 |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."))) 
-((-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
 (-126) 
 ((|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."))) 
@@ -452,7 +452,7 @@ 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 
-(-131 R -3094) 
+(-131 R -3093) 
 ((|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 
@@ -483,10 +483,10 @@ NIL
 (-138 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 (-823))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-917))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495)))) 
 (-139 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})"))) 
-((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3994 |has| |#1| (-6 -3994)) (-1376 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-140 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."))) 
@@ -498,8 +498,8 @@ NIL
 NIL 
 (-142 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}."))) 
-((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (|HasCategory| |#1| (QUOTE (-813 (-1091))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-823))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3995)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((-3988 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3994 |has| |#1| (-6 -3994)) (-1376 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090))))) (|HasCategory| |#1| (QUOTE (-812 (-1090))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-974))) (-12 (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3994)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-143 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 
@@ -514,7 +514,7 @@ NIL
 NIL 
 (-146) 
 ((|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."))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-147) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -522,7 +522,7 @@ NIL
 NIL 
 (-148 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) 
-(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") . T) (-3988 . T) (-3993 . T) (-3987 . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-149) 
 ((|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|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -539,7 +539,7 @@ NIL
 (-152 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-859 |#2|) (|%list| (QUOTE -798) (|devaluate| |#1|)))) 
+((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
 (-153 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -576,7 +576,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 
-(-162 R -3094) 
+(-162 R -3093) 
 ((|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 
@@ -604,23 +604,23 @@ 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 
-(-169 -3094 UP UPUP R) 
+(-169 -3093 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 
-(-170 -3094 FP) 
+(-170 -3093 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 
 (-171) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-797 (-328)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1090)))) (|HasCategory| (-484) (QUOTE (-454 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118))))) 
 (-172) 
 ((|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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-173 R -3094) 
+(-173 R -3093) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -634,19 +634,19 @@ NIL
 NIL 
 (-176 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-177 |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}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-178 R -3094) 
+(-178 R -3093) 
 ((|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 
 (-179) 
 ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}."))) 
-((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-180) 
 ((|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)}.}"))) 
@@ -654,19 +654,19 @@ NIL
 NIL 
 (-181 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}"))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-182 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 
 (-183 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."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
 (-184 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-185 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -678,7 +678,7 @@ NIL
 NIL 
 (-187 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
 (-188 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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}."))) 
@@ -690,7 +690,7 @@ NIL
 NIL 
 (-190) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-191) 
 ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) 
@@ -699,28 +699,28 @@ NIL
 (-192 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 -3996))) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
 (-193 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}."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
 (-194) 
 ((|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 
-(-195 S -2623 R) 
+(-195 S -2622 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 
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-(-196 -2623 R) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3992)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) 
+(-196 -2622 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"))) 
-((-3990 |has| |#2| (-963)) (-3991 |has| |#2| (-963)) (-3993 |has| |#2| (-6 -3993)) (-3996 . T)) 
+((-3989 |has| |#2| (-962)) (-3990 |has| |#2| (-962)) (-3992 |has| |#2| (-6 -3992)) (-3995 . T)) 
 NIL 
-(-197 -2623 R) 
+(-197 -2622 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."))) 
-((-3990 |has| |#2| (-963)) (-3991 |has| |#2| (-963)) (-3993 |has| |#2| (-6 -3993)) (-3996 . T)) 
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-(-198 -2623 A B) 
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+(-198 -2622 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 
@@ -734,7 +734,7 @@ NIL
 NIL 
 (-201) 
 ((|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}."))) 
-((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-202 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."))) 
@@ -742,20 +742,20 @@ NIL
 NIL 
 (-203 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}"))) 
-((-3997 . T) (-3996 . T)) 
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 (-204 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 
 (-205 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
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 NIL 
 (-206 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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 (-207) 
 ((|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 
@@ -770,23 +770,23 @@ NIL
 NIL 
 (-210 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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(|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-312))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312)))) (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-718))) (OR (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-757)))) (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-318))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-484)))) (|HasCategory| |#4| (QUOTE (-810 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 (-211 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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(QUOTE (-1015)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-952 (-485)))) (|HasCategory| |#3| (QUOTE (-1015)))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#3| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-811 (-1091)))) (|HasCategory| |#3| (QUOTE (-963)))) (|HasAttribute| |#3| (QUOTE -3993)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-963))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (QUOTE (-813 (-1091)))) (|HasCategory| |#3| (QUOTE (-963)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-554 (-774)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) 
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+((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-318))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-810 (-1090))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1090))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE 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(|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1090)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3992)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) 
 (-212 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 (-190)))) 
 (-213 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
 (-214 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}."))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
 (-215 |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."))) 
@@ -827,15 +827,15 @@ NIL
 (-224 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| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-189)))) 
+((|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-189)))) 
 (-225 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 
 (-226 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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#3| (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#3| (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#3| (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#3| (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#3| (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| |#3| (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#3| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#3| (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-227 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.")) (|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 
@@ -848,11 +848,11 @@ 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 
-(-230 R -3094) 
+(-230 R -3093) 
 ((|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 
-(-231 R -3094) 
+(-231 R -3093) 
 ((|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 
@@ -875,10 +875,10 @@ NIL
 (-236 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 (-758))) (|HasCategory| |#2| (QUOTE (-1015)))) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) 
 (-237 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}."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
 (-238 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}."))) 
@@ -899,14 +899,14 @@ NIL
 (-242 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 -3997))) 
+((|HasAttribute| |#1| (QUOTE -3996))) 
 (-243 |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 
-(-244 S R |Mod| -2039 -3519 |exactQuo|) 
+(-244 S R |Mod| -2038 -3518 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-245 S) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
@@ -914,7 +914,7 @@ NIL
 NIL 
 (-246) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-247) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) 
@@ -926,16 +926,16 @@ NIL
 NIL 
 (-249 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."))) 
-((-3993 OR (|has| |#1| (-963)) (|has| |#1| (-411))) (-3990 |has| |#1| (-963)) (-3991 |has| |#1| (-963))) 
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+((-3992 OR (|has| |#1| (-962)) (|has| |#1| (-411))) (-3989 |has| |#1| (-962)) (-3990 |has| |#1| (-962))) 
+((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-411))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-411)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) 
 (-250 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 
 (-251 |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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
 (-252) 
 ((|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 
@@ -943,16 +943,16 @@ NIL
 (-253 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| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) 
+((|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) 
 (-254) 
 ((|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 
-(-255 -3094 S) 
+(-255 -3093 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 
-(-256 E -3094) 
+(-256 E -3093) 
 ((|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 
@@ -962,7 +962,7 @@ NIL
 NIL 
 (-258) 
 ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-259 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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}."))) 
@@ -972,7 +972,7 @@ 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 
-(-261 -3094) 
+(-261 -3093) 
 ((|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 
@@ -986,12 +986,12 @@ NIL
 NIL 
 (-264 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))}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-823))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-952 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-935))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-742))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-758))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-742))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-758)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-952 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-798 (-328)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-798 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-582 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-813 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-473)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-328)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1090)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
 (-265 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."))) 
-((-3993 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-963)) (|has| |#1| (-411)))) (|has| |#1| (-963)) (|has| |#1| (-411))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963))))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1027)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485))))) 
+((-3992 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-962)) (|has| |#1| (-411)))) (|has| |#1| (-962)) (|has| |#1| (-411))) (-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) ((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-495)) (-3987 |has| |#1| (-495))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484))))) 
 (-266 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 
@@ -1000,7 +1000,7 @@ 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 
-(-268 R -3094) 
+(-268 R -3093) 
 ((|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 
@@ -1010,8 +1010,8 @@ NIL
 NIL 
 (-270 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-484)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
 (-271 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 
@@ -1022,8 +1022,8 @@ NIL
 NIL 
 (-273 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."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| (-485) (QUOTE (-718)))) 
+((-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-717)))) 
 (-274 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1031,26 +1031,26 @@ NIL
 (-275 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-696) (QUOTE (-718)))) 
+((|HasCategory| (-695) (QUOTE (-717)))) 
 (-276 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
+((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
 (-277 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-278 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."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-279 S -3094) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-279 S -3093) 
 ((|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 (-318)))) 
-(-280 -3094) 
+(-280 -3093) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-281 E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) 
@@ -1060,7 +1060,7 @@ 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 
-(-283 -3094 UP UPUP R) 
+(-283 -3093 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 
@@ -1068,33 +1068,33 @@ 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 
-(-285 S -3094 UP UPUP R) 
+(-285 S -3093 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 
-(-286 -3094 UP UPUP R) 
+(-286 -3093 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-287 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-288 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-289 |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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) 
-(-290 S -3094 UP UPUP) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-318)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-318))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
+(-290 S -3093 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 (-318))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-291 -3094 UP UPUP) 
+(-291 -3093 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."))) 
-((-3989 |has| (-348 |#2|) (-312)) (-3994 |has| (-348 |#2|) (-312)) (-3988 |has| (-348 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 |has| (-348 |#2|) (-312)) (-3993 |has| (-348 |#2|) (-312)) (-3987 |has| (-348 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-292 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}."))) 
@@ -1102,15 +1102,15 @@ NIL
 NIL 
 (-293 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-318)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-318))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
 (-294 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-295 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-296 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}."))) 
@@ -1126,43 +1126,43 @@ NIL
 NIL 
 (-299) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-300 R UP -3094) 
+(-300 R UP -3093) 
 ((|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 
 (-301 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118)))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-318)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-318))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
 (-302 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-303 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-304 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-305 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 
-(-306 -3094 GF) 
+(-306 -3093 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 
-(-307 -3094 FP FPP) 
+(-307 -3093 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 
 (-308 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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-309 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}."))) 
@@ -1170,7 +1170,7 @@ NIL
 NIL 
 (-310 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-311 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1178,7 +1178,7 @@ NIL
 NIL 
 (-312) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-313 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."))) 
@@ -1191,10 +1191,10 @@ NIL
 (-315 S R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn'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| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-496)))) 
+((|HasCategory| |#2| (QUOTE (-495)))) 
 (-316 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) 
+((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) 
 NIL 
 (-317 S) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) 
@@ -1210,15 +1210,15 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-320 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-321 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015)))) 
+((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) 
 (-322 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-3996 . T)) 
+((-3995 . T)) 
 NIL 
 (-323 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) 
@@ -1226,7 +1226,7 @@ NIL
 NIL 
 (-324 |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) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) 
 NIL 
 (-325 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."))) 
@@ -1235,14 +1235,14 @@ NIL
 (-326 S R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-582 (-485))))) 
+((|HasCategory| |#2| (QUOTE (-581 (-484))))) 
 (-327 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
 NIL 
 (-328) 
 ((|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}."))) 
-((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3978 . T) (-3986 . T) (-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-329 |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}."))) 
@@ -1254,15 +1254,15 @@ NIL
 NIL 
 (-331 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."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-332 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}"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146)))) 
 (-333 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
 (-334 S) 
 ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1271,7 +1271,7 @@ NIL
 (-335 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-758)))) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
 (-336) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
@@ -1282,13 +1282,13 @@ NIL
 NIL 
 (-338 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-339 -3094 UP UPUP R) 
+(-339 -3093 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-340 -3094 UP) 
+(-340 -3093 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1302,28 +1302,28 @@ NIL
 NIL 
 (-343) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-344 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3979)) (|HasAttribute| |#1| (QUOTE -3987))) 
+((|HasAttribute| |#1| (QUOTE -3978)) (|HasAttribute| |#1| (QUOTE -3986))) 
 (-345) 
 ((|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\"."))) 
-((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-346 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| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-454 (-1091) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-390)))) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-454 (-1090) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-1134))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-1134)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-390)))) 
 (-347 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 
 (-348 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."))) 
-((-3983 -12 (|has| |#1| (-6 -3994)) (|has| |#1| (-390)) (|has| |#1| (-6 -3983))) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-952 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((-3982 -12 (|has| |#1| (-6 -3993)) (|has| |#1| (-390)) (|has| |#1| (-6 -3982))) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1090)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3982)) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-349 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 
@@ -1334,28 +1334,28 @@ NIL
 NIL 
 (-351 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-352 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) 
 (-353 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-354 R -3094 UP A) 
+(-354 R -3093 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-355 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 
-(-356 R -3094 UP A |ibasis|) 
+(-356 R -3093 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -952) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) 
 (-357 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1366,7 +1366,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-312)))) 
 (-359 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) 
-((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) 
+((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) 
 NIL 
 (-360 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)}."))) 
@@ -1375,10 +1375,10 @@ NIL
 (-361 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| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-555 (-474))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) 
 (-362 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}."))) 
-((-3993 OR (|has| |#1| (-963)) (|has| |#1| (-411))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) 
+((-3992 OR (|has| |#1| (-962)) (|has| |#1| (-411))) (-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) ((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-495)) (-3987 |has| |#1| (-495))) 
 NIL 
 (-363 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}."))) 
@@ -1395,36 +1395,36 @@ NIL
 (-366 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 (-758))) (|HasCategory| |#2| (QUOTE (-318)))) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-318)))) 
 (-367 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3996 . T) (-3986 . T) (-3997 . T)) 
+((-3995 . T) (-3985 . T) (-3996 . T)) 
 NIL 
 (-368 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-369 R -3094) 
+(-369 R -3093) 
 ((|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 
 (-370 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"))) 
-((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983)))) 
-(-371 R -3094) 
+((-3982 -12 (|has| |#1| (-6 -3982)) (|has| |#2| (-6 -3982))) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -3982)) (|HasAttribute| |#2| (QUOTE -3982)))) 
+(-371 R -3093) 
 ((|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 
-(-372 R -3094) 
+(-372 R -3093) 
 ((|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 
-(-373 R -3094) 
+(-373 R -3093) 
 ((|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)))) 
-(-374 R -3094) 
+(-374 R -3093) 
 ((|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 
@@ -1432,10 +1432,10 @@ 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 
-(-376 R -3094 UP) 
+(-376 R -3093 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| (QUOTE (-952 (-48))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-48))))) 
 (-377) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
@@ -1452,7 +1452,7 @@ 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 
-(-381 R UP -3094) 
+(-381 R UP -3093) 
 ((|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 
@@ -1490,16 +1490,16 @@ NIL
 NIL 
 (-390) 
 ((|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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-391 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"))) 
-((-3993 |has| (-348 (-859 |#1|)) (-496)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| (-348 (-859 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-348 (-859 |#1|)) (QUOTE (-496)))) 
+((-3992 |has| (-348 (-858 |#1|)) (-495)) (-3990 . T) (-3989 . T)) 
+((|HasCategory| (-348 (-858 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-348 (-858 |#1|)) (QUOTE (-495)))) 
 (-392 |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"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-3997 "*") |has| |#2| (-146)) (-3988 |has| |#2| (-495)) (-3993 |has| |#2| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-328)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
 (-393 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 
@@ -1526,7 +1526,7 @@ NIL
 NIL 
 (-399 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
 (-400 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1534,8 +1534,8 @@ NIL
 NIL 
 (-401 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) 
 (-402 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 
@@ -1564,7 +1564,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-409 |lv| -3094 R) 
+(-409 |lv| -3093 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1574,23 +1574,23 @@ NIL
 NIL 
 (-411) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
 (-412 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-484)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
 (-413 |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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) 
+((-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) 
 (-414 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)}"))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) 
 (-415) 
 ((|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 (-416) 
 ((|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'."))) 
@@ -1598,29 +1598,29 @@ NIL
 NIL 
 (-417 |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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
 (-418) 
 ((|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 
 (-419 |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"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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-(-420 -2623 S) 
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 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-810 (-1090))))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3992)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) 
 (-421) 
 ((|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 
 (-422 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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-423 -3094 UP UPUP R) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-423 -3093 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 
@@ -1630,12 +1630,12 @@ NIL
 NIL 
 (-425) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-797 (-328)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1090)))) (|HasCategory| (-484) (QUOTE (-454 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118))))) 
 (-426 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 -3996)) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) 
+((|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) 
 (-427 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1656,34 +1656,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-432 -3094 UP |AlExt| |AlPol|) 
+(-432 -3093 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-433) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485))))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484))))) 
 (-434 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
 (-435 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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-436 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 
-(-437 R UP -3094) 
+(-437 R UP -3093) 
 ((|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 
 (-438 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-474)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-1015))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-473)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) 
 (-439 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 
@@ -1696,17 +1696,17 @@ 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 
-(-442 -3094 |Expon| |VarSet| |DPoly|) 
+(-442 -3093 |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| (QUOTE (-555 (-1091))))) 
+((|HasCategory| |#3| (QUOTE (-554 (-1090))))) 
 (-443 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
 NIL 
 (-444 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3058 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3057 (|f| |x| |x|) |x|))) . T)) 
 NIL 
 (-445) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
@@ -1715,11 +1715,11 @@ NIL
 (-446 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 (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-447 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 (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-448 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
@@ -1727,15 +1727,15 @@ NIL
 (-449 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-450 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 (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-451 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 (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-452 A S) 
 ((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) 
 NIL 
@@ -1751,3026 +1751,3022 @@ NIL
 (-455 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-718)))) 
+((|HasCategory| |#2| (QUOTE (-717)))) 
 (-456 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}"))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
 (-457) 
 ((|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 
 (-458 |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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-318)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-318))) (|HasCategory| (-518 |#1|) (QUOTE (-118)))) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-318)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-318))) (|HasCategory| (-517 |#1|) (QUOTE (-118)))) 
 (-459 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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-460 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 -3997))) 
+((|HasAttribute| |#3| (QUOTE -3996))) 
 (-461 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 -3997))) 
-(-462 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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-463) 
+((|HasAttribute| |#7| (QUOTE -3996))) 
+(-462) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
 NIL 
-(-464) 
+(-463) 
 ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) 
 NIL 
 NIL 
-(-465 S) 
+(-464 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-466) 
+(-465) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-467 GF) 
+(-466 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) 
 NIL 
 NIL 
-(-468) 
+(-467) 
 ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-469 R) 
+(-468 R) 
 ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) 
 NIL 
 NIL 
-(-470 |Varset|) 
+(-469 |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| |#1| (QUOTE (-1015))) (|HasCategory| (-696) (QUOTE (-1015))))) 
-(-471 K -3094 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) 
+(-470 K -3093 |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 
-(-472) 
+(-471) 
 NIL 
 NIL 
 NIL 
-(-473) 
+(-472) 
 ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) 
 NIL 
 NIL 
-(-474) 
+(-473) 
 ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-475 R) 
+(-474 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-476 |Coef| UTS) 
+(-475 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-477 K -3094 |Par|) 
+(-476 K -3093 |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 
-(-478 R BP |pMod| |nextMod|) 
+(-477 R BP |pMod| |nextMod|) 
 ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) 
 NIL 
 NIL 
-(-479 OV E R P) 
+(-478 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) 
 NIL 
 NIL 
-(-480 K UP |Coef| UTS) 
+(-479 K UP |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-481 |Coef| UTS) 
+(-480 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-482 R UP) 
+(-481 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-483 S) 
+(-482 S) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-484) 
+(-483) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-485) 
+(-484) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-486) 
+(-485) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-487) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-488) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-489) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-490 |Key| |Entry| |addDom|) 
+(-489 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-491 R -3094) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+(-490 R -3093) 
 ((|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 
-(-492 R0 -3094 UP UPUP R) 
+(-491 R0 -3093 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 
-(-493) 
+(-492) 
 ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) 
 NIL 
 NIL 
-(-494 R) 
+(-493 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."))) 
-((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3770 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-495 S) 
+(-494 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
 NIL 
 NIL 
-(-496) 
+(-495) 
 ((|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."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-497 R -3094) 
+(-496 R -3093) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}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|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-498 I) 
+(-497 I) 
 ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) 
 NIL 
 NIL 
-(-499 R -3094 L) 
+(-498 R -3093 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[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|))))) #3#) |#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|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -602) (|devaluate| |#2|)))) 
-(-500) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-499) 
 ((|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 
-(-501 -3094 UP UPUP R) 
+(-500 -3093 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 
-(-502 -3094 UP) 
+(-501 -3093 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 
-(-503 R -3094 L) 
+(-502 R -3093 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[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 -602) (|devaluate| |#2|)))) 
-(-504 R -3094) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-503 R -3093) 
 ((|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| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-571))))) 
-(-505 -3094 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-570))))) 
+(-504 -3093 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 
-(-506 S) 
+(-505 S) 
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-507 -3094) 
+(-506 -3093) 
 ((|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 
-(-508 R) 
+(-507 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."))) 
-((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3770 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-509) 
+(-508) 
 ((|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 
-(-510 R -3094) 
+(-509 R -3093) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-952 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-511 -3094 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-510 -3093 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[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|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-512 R -3094) 
+(-511 R -3093) 
 ((|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 
-(-513) 
+(-512) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-514) 
+(-513) 
 ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) 
 NIL 
 NIL 
-(-515) 
+(-514) 
 ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) 
 NIL 
 NIL 
-(-516) 
+(-515) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-517 |p| |unBalanced?|) 
+(-516 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-518 |p|) 
+(-517 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) 
-(-519) 
+(-518) 
 ((|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 
-(-520 -3094) 
+(-519 -3093) 
 ((|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}."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-952 (-1091))))) 
-(-521 E -3094) 
+((-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-951 (-1090))))) 
+(-520 E -3093) 
 ((|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 
-(-522 R -3094) 
+(-521 R -3093) 
 ((|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 
-(-523) 
+(-522) 
 ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) 
 NIL 
 NIL 
-(-524 I) 
+(-523 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
 NIL 
-(-525 GF) 
+(-524 GF) 
 ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) 
 NIL 
 NIL 
-(-526 R) 
+(-525 R) 
 ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-120)))) 
-(-527) 
+(-526) 
 ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) 
 NIL 
 NIL 
-(-528 R E V P TS) 
+(-527 R E V P TS) 
 ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) 
 NIL 
 NIL 
-(-529) 
+(-528) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-530 E V R P) 
+(-529 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-531 |Coef|) 
+(-530 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) 
-(-532 |Coef|) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
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 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
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-((|HasCategory| |#1| (QUOTE (-496)))) 
-(-533) 
+(((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
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 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) 
 NIL 
 NIL 
-(-534 A B) 
+(-533 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-535 A B C) 
+(-534 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-536 R -3094 FG) 
+(-535 R -3093 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 
-(-537 S) 
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 ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) 
 NIL 
 NIL 
-(-538 R |mn|) 
+(-537 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-539 S |Index| |Entry|) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-538 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 -3997)) (|HasCategory| |#2| (QUOTE (-758))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#3| (QUOTE (-1015)))) 
-(-540 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#3| (QUOTE (-1014)))) 
+(-539 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
-(-542 R A) 
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 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-3993 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-543) 
+((-3992 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-495)))) (-3990 . T) (-3989 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-542) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
 NIL 
-(-544) 
+(-543) 
 ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-545) 
+(-544) 
 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) 
 NIL 
 NIL 
-(-546) 
+(-545) 
 ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-547) 
+(-546) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-548) 
+(-547) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-549 |Entry|) 
+(-548 |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."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-1074) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-550 S |Key| |Entry|) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3860 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-1073) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
+(-549 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 
-(-551 |Key| |Entry|) 
+(-550 |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}."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
-(-552 S) 
+(-551 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| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485)))))) 
-(-553 R S) 
+((|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484)))))) 
+(-552 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-554 S) 
+(-553 S) 
 ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-555 S) 
+(-554 S) 
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-556 -3094 UP) 
+(-555 -3093 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-557 S) 
+(-556 S) 
 ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-558) 
+(-557) 
 ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-559 S) 
+(-558 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-560 A R S) 
+(-559 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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-757)))) 
-(-561 S R) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-560 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 
-(-562 R) 
+(-561 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."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-563 R -3094) 
+(-562 R -3093) 
 ((|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 
-(-564 R UP) 
+(-563 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"))) 
-((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) 
-(-565 R E V P TS ST) 
+((-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3988 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) 
+(-564 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 
 NIL 
-(-566 OV E Z P) 
+(-565 OV E Z P) 
 ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) 
 NIL 
 NIL 
-(-567) 
+(-566) 
 ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) 
 NIL 
 NIL 
-(-568 |VarSet| R |Order|) 
+(-567 |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}}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-569 R |ls|) 
+(-568 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 
-(-570 R -3094) 
+(-569 R -3093) 
 ((|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 
-(-571) 
+(-570) 
 ((|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 
-(-572 |lv| -3094) 
+(-571 |lv| -3093) 
 ((|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 
-(-573) 
+(-572) 
 ((|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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-774)))) (|HasCategory| (-51) (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-555 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1015)))) (|HasCategory| (-1074) (QUOTE (-758))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1015))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1015)))) 
-(-574 R A) 
+((-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3860 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-554 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-1073) (QUOTE (-757))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1014)))) 
+(-573 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)."))) 
-((-3993 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-575 S R) 
+((-3992 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-495)))) (-3990 . T) (-3989 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-574 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-576 R) 
+(-575 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) 
 NIL 
-(-577 R FE) 
+(-576 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|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
 NIL 
 NIL 
-(-578 R) 
+(-577 R) 
 ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) 
 NIL 
 NIL 
-(-579 |vars|) 
+(-578 |vars|) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) 
 NIL 
 NIL 
-(-580 S R) 
+(-579 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 
-((-2562 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-581 K B) 
+((-2561 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-580 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}."))) 
-((-3991 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-579 |#2|) (QUOTE (-1015))))) 
-(-582 R) 
+((-3990 . T) (-3989 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-578 |#2|) (QUOTE (-1014))))) 
+(-581 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 
-(-583 K B) 
+(-582 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-584 S) 
+(-583 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
-(-585 S) 
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 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. 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."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-586 A B) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-585 A B) 
 ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) 
 NIL 
 NIL 
-(-587 A B) 
+(-586 A B) 
 ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
 NIL 
 NIL 
-(-588 A B C) 
+(-587 A B C) 
 ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) 
 NIL 
 NIL 
-(-589 T$) 
+(-588 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-591 S) 
+(-590 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-592 R) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-591 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-593 S E |un|) 
+(-592 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) 
 NIL 
 NIL 
-(-594 A S) 
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 ((|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 -3997))) 
-(-595 S) 
+((|HasAttribute| |#1| (QUOTE -3996))) 
+(-594 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 
-(-596 M R S) 
+(-595 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}."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-716)))) 
-(-597 R -3094 L) 
+((-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-715)))) 
+(-596 R -3093 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 
-(-598 A -2494) 
+(-597 A -2493) 
 ((|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}}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-599 A) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-598 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}}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-600 A M) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-599 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-601 S A) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-600 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-312)))) 
-(-602 A) 
+(-601 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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-603 -3094 UP) 
+(-602 -3093 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)))) 
-(-604 A L) 
+(-603 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-605 S) 
+(-604 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-606) 
+(-605) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-607 R) 
+(-606 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-608 |VarSet| R) 
+(-607 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-609 A S) 
+(-608 A S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
 NIL 
 NIL 
-(-610 S) 
+(-609 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}."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-611 -3094 |Row| |Col| M) 
+(-610 -3093 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-612 -3094) 
+(-611 -3093) 
 ((|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|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-613 R E OV P) 
+(-612 R E OV P) 
 ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) 
 NIL 
 NIL 
-(-614 |n| R) 
+(-613 |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."))) 
-((-3993 . T) (-3996 . T) (-3990 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1091))))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-615) 
+((-3992 . T) (-3995 . T) (-3989 . T) (-3990 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1090))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-614) 
 ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) 
 NIL 
 NIL 
-(-616 |VarSet|) 
+(-615 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-617 A S) 
+(-616 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-618 S) 
+(-617 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-619) 
+(-618) 
 ((|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 
 NIL 
-(-620 |VarSet|) 
+(-619 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
 NIL 
-(-621 A) 
+(-620 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) 
 NIL 
 NIL 
-(-622 A C) 
+(-621 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) 
 NIL 
 NIL 
-(-623 A B C) 
+(-622 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) 
 NIL 
 NIL 
-(-624) 
+(-623) 
 ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-625 A) 
+(-624 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) 
 NIL 
 NIL 
-(-626 A C) 
+(-625 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) 
 NIL 
 NIL 
-(-627 A B C) 
+(-626 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) 
 NIL 
 NIL 
-(-628 S R |Row| |Col|) 
+(-627 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 (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496)))) 
-(-629 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3997 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495)))) 
+(-628 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"))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
-(-630 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-631 R |Row| |Col| M) 
+(-630 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that m*n = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-632 R) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-631 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."))) 
-((-3996 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-633 R) 
+((-3995 . T) (-3996 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-632 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 
 NIL 
-(-634 T$) 
+(-633 T$) 
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `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 
-(-635 R Q) 
+(-634 R Q) 
 ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) 
 NIL 
 NIL 
-(-636 S) 
+(-635 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}."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
-(-637 U) 
+(-636 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}."))) 
 NIL 
 NIL 
-(-638) 
+(-637) 
 ((|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|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-639 OV E -3094 PG) 
+(-638 OV E -3093 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 
-(-640 R) 
+(-639 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
 NIL 
 NIL 
-(-641 S D1 D2 I) 
+(-640 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
 NIL 
 NIL 
-(-642 S) 
+(-641 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
-(-643 S) 
+(-642 S) 
 ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) 
 NIL 
 NIL 
-(-644 S T$) 
+(-643 S T$) 
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) 
 NIL 
 NIL 
-(-645 S -2671 I) 
+(-644 S -2670 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 
-(-646 E OV R P) 
+(-645 E OV R P) 
 ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) 
 NIL 
 NIL 
-(-647 R) 
+(-646 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)}.}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-648 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-647 R1 UP1 UPUP1 R2 UP2 UPUP2) 
 ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-649) 
+(-648) 
 ((|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 
-(-650 R |Mod| -2039 -3519 |exactQuo|) 
+(-649 R |Mod| -2038 -3518 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-651 R P) 
+(-650 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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-(-652 IS E |ff|) 
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+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| (-995) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-995) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-995) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-651 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-653 R M) 
+(-652 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-654 R |Mod| -2039 -3519 |exactQuo|) 
+(-653 R |Mod| -2038 -3518 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-655 S R) 
+(-654 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-656 R) 
+(-655 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-657 -3094) 
+(-656 -3093) 
 ((|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]]}."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-658 S) 
+(-657 S) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-659) 
+(-658) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-660 S) 
+(-659 S) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-661) 
+(-660) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-662 S R UP) 
+(-661 S R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-318)))) 
-(-663 R UP) 
+(-662 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."))) 
-((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 |has| |#1| (-312)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-664 S) 
+(-663 S) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-665) 
+(-664) 
 ((|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| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-666 T$) 
+(-665 T$) 
 ((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}."))) 
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-667 T$) 
+(-666 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}."))) 
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-668 -3094 UP) 
+(-667 -3093 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 
-(-669 |VarSet| E1 E2 R S PR PS) 
+(-668 |VarSet| E1 E2 R S PR PS) 
 ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-670 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-671 E OV R PPR) 
+(-670 E OV R PPR) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-672 |vl| R) 
+(-671 |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."))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-673 E OV R PRF) 
+(((-3997 "*") |has| |#2| (-146)) (-3988 |has| |#2| (-495)) (-3993 |has| |#2| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-328)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-672 E OV R PRF) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-674 E OV R P) 
+(-673 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) 
 NIL 
 NIL 
-(-675 R S M) 
+(-674 R S M) 
 ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) 
 NIL 
 NIL 
-(-676 R M) 
+(-675 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}."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-758)))) 
-(-677 S) 
+((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757)))) 
+(-676 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}."))) 
-((-3996 . T) (-3986 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-678 S) 
+((-3995 . T) (-3985 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-677 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-3986 . T) (-3997 . T)) 
+((-3985 . T) (-3996 . T)) 
 NIL 
-(-679) 
+(-678) 
 ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) 
 NIL 
 NIL 
-(-680 S) 
+(-679 S) 
 ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) 
 NIL 
 NIL 
-(-681 |Coef| |Var|) 
+(-680 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-682 OV E R P) 
+(-681 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) 
 NIL 
 NIL 
-(-683 E OV R P) 
+(-682 E OV R P) 
 ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-684 S R) 
+(-683 S 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}."))) 
 NIL 
 NIL 
-(-685 R) 
+(-684 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-686 S) 
+(-685 S) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-687) 
+(-686) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-688 S) 
+(-687 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-689) 
+(-688) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-690 |Par|) 
+(-689 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-691 -3094) 
+(-690 -3093) 
 ((|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 
-(-692 P -3094) 
+(-691 P -3093) 
 ((|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 
-(-693 T$) 
+(-692 T$) 
 NIL 
 NIL 
 NIL 
-(-694 UP -3094) 
+(-693 UP -3093) 
 ((|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 
-(-695 R) 
+(-694 R) 
 ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-696) 
+(-695) 
 ((|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."))) 
-(((-3998 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-697 R -3094) 
+(-696 R -3093) 
 ((|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 
-(-698) 
+(-697) 
 ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) 
 NIL 
 NIL 
-(-699 S) 
+(-698 S) 
 ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) 
 NIL 
 NIL 
-(-700 R |PolR| E |PolE|) 
+(-699 R |PolR| E |PolE|) 
 ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) 
 NIL 
 NIL 
-(-701 R E V P TS) 
+(-700 R E V P TS) 
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of 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 
-(-702 -3094 |ExtF| |SUEx| |ExtP| |n|) 
+(-701 -3093 |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 
-(-703 BP E OV R P) 
+(-702 BP E OV R P) 
 ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) 
 NIL 
 NIL 
-(-704 |Par|) 
+(-703 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) 
 NIL 
 NIL 
-(-705 R |VarSet|) 
+(-704 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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-(-706 R) 
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+(-705 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)}"))) 
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-(-707 R S) 
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+(-706 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-708 R) 
+(-707 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485)))))) 
-(-709 R E V P) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484)))))) 
+(-708 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.}"))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-710 S) 
+(-709 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 (-496))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-711) 
+((-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-710) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
 NIL 
-(-712) 
+(-711) 
 ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) 
 NIL 
 NIL 
-(-713) 
+(-712) 
 ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) 
 NIL 
 NIL 
-(-714 |Curve|) 
+(-713 |Curve|) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-715 S) 
+(-714 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|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-716) 
+(-715) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\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 
-(-717 S) 
+(-716 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 
-(-718) 
+(-717) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-719) 
+(-718) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-720) 
+(-719) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-721 S R) 
+(-720 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-318)))) 
-(-722 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-318)))) 
+(-721 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-723) 
+(-722) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-724 R) 
+(-723 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-348 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) 
-(-725 OR R OS S) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-348 (-484)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) 
+(-724 OR 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 
-(-726 R -3094 L) 
+(-725 R -3093 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 
-(-727 R -3094) 
+(-726 R -3093) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-728 R -3094) 
+(-727 R -3093) 
 ((|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 
-(-729 -3094 UP UPUP R) 
+(-728 -3093 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
 NIL 
 NIL 
-(-730 -3094 UP L LQ) 
+(-729 -3093 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."))) 
 NIL 
 NIL 
-(-731 -3094 UP L LQ) 
+(-730 -3093 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 
 NIL 
-(-732 -3094 UP) 
+(-731 -3093 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-733 -3094 L UP A LO) 
+(-732 -3093 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
 NIL 
 NIL 
-(-734 -3094 UP) 
+(-733 -3093 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)))) 
-(-735 -3094 LO) 
+(-734 -3093 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 
-(-736 -3094 LODO) 
+(-735 -3093 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 
-(-737 -2623 S |f|) 
+(-736 -2622 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}."))) 
-((-3990 |has| |#2| (-963)) (-3991 |has| |#2| (-963)) (-3993 |has| |#2| (-6 -3993)) (-3996 . T)) 
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(-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3992)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) 
+(-737 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| (-740 (-1091)) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| (-740 (-1091)) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-740 (-1091)) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-740 (-1091)) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-740 (-1091)) (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-739 |Kernels| R |var|) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| (-739 (-1090)) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-739 (-1090)) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-739 (-1090)) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-739 (-1090)) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-739 (-1090)) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-738 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-3998 "*") |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 . T) (-3991 . T) (-3990 . T)) 
+(((-3997 "*") |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 |has| |#2| (-312)) (-3987 |has| |#2| (-312)) (-3992 . T) (-3990 . T) (-3989 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-740 S) 
+(-739 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 
-(-741 S) 
+(-740 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| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-758)))) 
-(-742) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-741) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-743 P R) 
+(-742 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) 
-(-744 S) 
+(-743 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-3996 . T) (-3986 . T) (-3997 . T)) 
+((-3995 . T) (-3985 . T) (-3996 . T)) 
 NIL 
-(-745 R) 
+(-744 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."))) 
-((-3993 |has| |#1| (-757))) 
-((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-746 R S) 
+((-3992 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-745 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 
-(-747 R) 
+(-746 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-748 A S) 
+(-747 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 
-(-749 S) 
+(-748 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-750) 
+(-749) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-751) 
+(-750) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 
-(-752 R) 
+(-751 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3993 |has| |#1| (-757))) 
-((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-753 R S) 
+((-3992 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-752 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-754) 
+(-753) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-755 -2623 S) 
+(-754 -2622 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-756) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-757) 
+(-756) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-758) 
+(-757) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-759 T$ |f|) 
+(-758 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| (QUOTE (-554 (-774))))) 
-(-760 S) 
+((|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-759 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-761) 
+(-760) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-762 S R) 
+(-761 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-763 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-762 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-764 R C) 
+(-763 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 (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-765 R |sigma| -3246) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-764 R |sigma| -3245) 
 ((|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."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-766 |x| R |sigma| -3246) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-765 |x| R |sigma| -3245) 
 ((|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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-767 R) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-766 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| (QUOTE (-38 (-348 (-485)))))) 
-(-768) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484)))))) 
+(-767) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-769) 
+(-768) 
 ((|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 
-(-770) 
+(-769) 
 ((|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 
-(-771 S) 
+(-770 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 
-(-772) 
+(-771) 
 ((|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 
-(-773) 
+(-772) 
 ((|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 
-(-774) 
+(-773) 
 ((|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 
-(-775 |VariableList|) 
+(-774 |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 
-(-776) 
+(-775) 
 ((|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 
-(-777 R |vl| |wl| |wtlevel|) 
+(-776 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)"))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-778 R PS UP) 
+(-777 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 
-(-779 R |x| |pt|) 
+(-778 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 
-(-780 |p|) 
+(-779 |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)."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-781 |p|) 
+(-780 |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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-782 |p|) 
+(-781 |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)."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-780 |#1|) (QUOTE (-823))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-1091)))) (|HasCategory| (-780 |#1|) (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-120))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-474)))) (|HasCategory| (-780 |#1|) (QUOTE (-935))) (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758)))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-1067))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-328)))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-780 |#1|) (QUOTE (-582 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-189))) (|HasCategory| (-780 |#1|) (QUOTE (-813 (-1091)))) (|HasCategory| (-780 |#1|) (QUOTE (-190))) (|HasCategory| (-780 |#1|) (QUOTE (-811 (-1091)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -780) (|devaluate| |#1|)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (QUOTE (-258))) (|HasCategory| (-780 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (|HasCategory| (-780 |#1|) (QUOTE (-118))))) 
-(-783 |p| PADIC) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1090)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-473)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-1066))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-328)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1090)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1090)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -454) (QUOTE (-1090)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-258))) (|HasCategory| (-779 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))))) 
+(-782 |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)}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-952 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758)))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-784 S T$) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-797 (-328)))) (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-483))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-783 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 (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774)))))) 
-(-785) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) 
+(-784) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|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 
-(-786) 
+(-785) 
 ((|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 
-(-787) 
+(-786) 
 ((|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 
-(-788 CF1 CF2) 
+(-787 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-789 |ComponentFunction|) 
+(-788 |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 
-(-790 CF1 CF2) 
+(-789 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-791 |ComponentFunction|) 
+(-790 |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 
-(-792) 
+(-791) 
 ((|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 
-(-793 CF1 CF2) 
+(-792 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-794 |ComponentFunction|) 
+(-793 |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 
-(-795) 
+(-794) 
 ((|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 
-(-796 R) 
+(-795 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 
-(-797 R S L) 
+(-796 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 
-(-798 S) 
+(-797 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 
-(-799 |Base| |Subject| |Pat|) 
+(-798 |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 (-2562 (|HasCategory| |#2| (QUOTE (-952 (-1091))))) (-2562 (|HasCategory| |#2| (QUOTE (-963))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (-2562 (|HasCategory| |#2| (QUOTE (-952 (-1091)))))) (|HasCategory| |#2| (QUOTE (-952 (-1091))))) 
-(-800 R S) 
+((-12 (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1090))))) (-2561 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1090)))))) (|HasCategory| |#2| (QUOTE (-951 (-1090))))) 
+(-799 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 
-(-801 R A B) 
+(-800 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 
-(-802 R) 
+(-801 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 
-(-803 R -2671) 
+(-802 R -2670) 
 ((|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 
-(-804 R S) 
+(-803 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 
-(-805 |VarSet|) 
+(-804 |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 
-(-806 UP R) 
+(-805 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-807 A T$ S) 
+(-806 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 
-(-808 T$ S) 
+(-807 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 
-(-809 UP -3094) 
+(-808 UP -3093) 
 ((|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 
-(-810 R S) 
+(-809 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-811 S) 
+(-810 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-812 A S) 
+(-811 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 
-(-813 S) 
+(-812 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 
-(-814 S) 
+(-813 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 (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-815 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-814 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3993 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-758)))) 
-(-816 |n| R) 
+((-3992 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-757)))) 
+(-815 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 
-(-817 S) 
+(-816 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."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-818 S) 
+(-817 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 
-(-819 |p|) 
+(-818 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) 
-(-820 R E |VarSet| S) 
+(-819 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 
-(-821 R S) 
+(-820 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 
-(-822 S) 
+(-821 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 (-118)))) 
-(-823) 
+(-822) 
 ((|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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-824 R0 -3094 UP UPUP R) 
+(-823 R0 -3093 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 
-(-825 UP UPUP R) 
+(-824 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 
-(-826 UP UPUP) 
+(-825 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 
-(-827 R) 
+(-826 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-828 R) 
+(-827 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 
-(-829 E OV R P) 
+(-828 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 
-(-830) 
+(-829) 
 ((|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 
-(-831 -3094) 
+(-830 -3093) 
 ((|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 
-(-832) 
+(-831) 
 ((|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}."))) 
-(((-3998 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-833 R) 
+(-832 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 
-(-834) 
+(-833) 
 ((|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)}"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-835 |xx| -3094) 
+(-834 |xx| -3093) 
 ((|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 
-(-836 -3094 P) 
+(-835 -3093 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-837 R |Var| |Expon| GR) 
+(-836 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 
-(-838) 
+(-837) 
 ((|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 
-(-839 S) 
+(-838 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 
-(-840) 
+(-839) 
 ((|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 
-(-841) 
+(-840) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-842) 
+(-841) 
 ((|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 
-(-843 R -3094) 
+(-842 R -3093) 
 ((|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 
-(-844 S A B) 
+(-843 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 
-(-845 S R -3094) 
+(-844 S R -3093) 
 ((|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 
-(-846 I) 
+(-845 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 
-(-847 S E) 
+(-846 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 
-(-848 S R L) 
+(-847 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 
-(-849 S E V R P) 
+(-848 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 -798) (|devaluate| |#1|)))) 
-(-850 -2671) 
+((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+(-849 -2670) 
 ((|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 
-(-851 R -3094 -2671) 
+(-850 R -3093 -2670) 
 ((|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 
-(-852 S R Q) 
+(-851 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 
-(-853 S) 
+(-852 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 
-(-854 S R P) 
+(-853 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 
-(-855) 
+(-854) 
 ((|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 
-(-856 R) 
+(-855 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-857 |lv| R) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-856 |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 
-(-858 |TheField| |ThePols|) 
+(-857 |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 (-757)))) 
-(-859 R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-858 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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| (-1091) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| (-1091) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-1091) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-1091) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-1091) (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-860 R S) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| (-1090) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-1090) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-1090) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1090) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-1090) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-859 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 
-(-861 |x| R) 
+(-860 |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 
-(-862 S R E |VarSet|) 
+(-861 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 (-823))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-798 (-328)))) (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| |#4| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| |#4| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#4| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-555 (-474))))) 
-(-863 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-328)))) (|HasCategory| |#2| (QUOTE (-797 (-328)))) (|HasCategory| |#4| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) 
+(-862 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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-864 E V R P -3094) 
+(-863 E V R P -3093) 
 ((|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 
-(-865 E |Vars| R P S) 
+(-864 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 
-(-866 E V R P -3094) 
+(-865 E V R P -3093) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-390)))) 
-(-867) 
+(-866) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-868) 
+(-867) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-869 R E) 
+(-868 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-870 R L) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3993))) 
+(-869 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 
-(-871 S) 
+(-870 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"))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-872 A B) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-871 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 
-(-873) 
+(-872) 
 ((|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 
-(-874 -3094) 
+(-873 -3093) 
 ((|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 
-(-875 I) 
+(-874 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 
-(-876) 
+(-875) 
 ((|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 
-(-877 A B) 
+(-876 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"))) 
-((-3993 -12 (|has| |#2| (-411)) (|has| |#1| (-411)))) 
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-(-878) 
+((-3992 -12 (|has| |#2| (-411)) (|has| |#1| (-411)))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) 
+(-877) 
 ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-879 T$) 
+(-878 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-880 T$) 
+(-879 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-881 S T$) 
+(-880 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-882) 
+(-881) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-883 S) 
+(-882 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
-(-884 R |polR|) 
+(-883 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 (-390)))) 
-(-885) 
+(-884) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-886) 
+(-885) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-887 S |Coef| |Expon| |Var|) 
+(-886 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 
-(-888 |Coef| |Expon| |Var|) 
+(-887 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-889) 
+(-888) 
 ((|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 
-(-890 S R E |VarSet| P) 
+(-889 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 (-496)))) 
-(-891 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-495)))) 
+(-890 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."))) 
-((-3996 . T)) 
+((-3995 . T)) 
 NIL 
-(-892 R E V P) 
+(-891 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 (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-390)))) 
-(-893 K) 
+(-892 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 
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-(-894 |VarSet| E RC P) 
+(-893 |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."))) 
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-(-895 R) 
+(-894 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}."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-896 R1 R2) 
+(-895 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
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-(-897 R) 
+(-896 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
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-(-898 K) 
+(-897 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 
-(-899 R E OV PPR) 
+(-898 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 
-(-900 K R UP -3094) 
+(-899 K R UP -3093) 
 ((|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)}."))) 
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-(-901 R |Var| |Expon| |Dpoly|) 
+(-900 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|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258))))) 
-(-902 |vl| |nv|) 
+(-901 |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 
-(-903 R E V P TS) 
+(-902 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 
-(-904) 
+(-903) 
 ((|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 
-(-905 A S) 
+(-904 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 (-823))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-952 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) 
-(-906 S) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-951 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1066)))) 
+(-905 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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-907 A B R S) 
+(-906 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 
-(-908 |n| K) 
+(-907 |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 
-(-909) 
+(-908) 
 ((|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 
-(-910 S) 
+(-909 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."))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
-(-911 R) 
+(-910 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.}"))) 
-((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-912 S R) 
+((-3988 |has| |#1| (-246)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-911 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 (-484))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-246)))) 
-(-913 R) 
+((|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-246)))) 
+(-912 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 |has| |#1| (-246)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-914 QR R QS S) 
+(-913 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-915 S) 
+(-914 S) 
 ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-916 S) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-915 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-917) 
+(-916) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-918 -3094 UP UPUP |radicnd| |n|) 
+(-917 -3093 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
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-((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091)))))) (|HasCategory| (-348 |#2|) (QUOTE (-582 (-485)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485)))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091)))))) 
-(-919 |bb|) 
+((-3988 |has| (-348 |#2|) (-312)) (-3993 |has| (-348 |#2|) (-312)) (-3987 |has| (-348 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-812 (-1090)))))) (|HasCategory| (-348 |#2|) (QUOTE (-581 (-484)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-348 (-484)))))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-348 |#2|) (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-812 (-1090))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1090)))))) 
+(-918 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118))))) 
-(-920) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-797 (-328)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1090)))) (|HasCategory| (-484) (QUOTE (-454 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118))))) 
+(-919) 
 ((|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 
-(-921) 
+(-920) 
 ((|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 
-(-922 RP) 
+(-921 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 
-(-923 S) 
+(-922 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 
-(-924 A S) 
+(-923 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 -3997)) (|HasCategory| |#2| (QUOTE (-1015)))) 
-(-925 S) 
+((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-1014)))) 
+(-924 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 
-(-926 S) 
+(-925 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 
-(-927) 
+(-926) 
 ((|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}}"))) 
-((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
+((-3988 . T) (-3993 . T) (-3987 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3992 . T)) 
 NIL 
-(-928 R -3094) 
+(-927 R -3093) 
 ((|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 
-(-929 R -3094) 
+(-928 R -3093) 
 ((|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 
-(-930 -3094 UP) 
+(-929 -3093 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 
-(-931 -3094 UP) 
+(-930 -3093 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 
-(-932 S) 
+(-931 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 
-(-933 F1 UP UPUP R F2) 
+(-932 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 
-(-934) 
+(-933) 
 ((|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 
-(-935) 
+(-934) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-936 |Pol|) 
+(-935 |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 
-(-937 |Pol|) 
+(-936 |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 
-(-938) 
+(-937) 
 ((|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 
-(-939 |TheField|) 
+(-938 |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"))) 
-((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-485))))) 
-(-940 -3094 L) 
+((-3988 . T) (-3993 . T) (-3987 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3992 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-348 (-484)) (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-348 (-484)) (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-348 (-484)) (QUOTE (-951 (-484))))) 
+(-939 -3093 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 
-(-941 S) 
+(-940 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(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) 
 NIL 
 NIL 
-(-942 R E V P) 
+(-941 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."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-943) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-942) 
 ((|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 
-(-944 R) 
+(-943 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 (-3998 "*")))) 
-(-945 R) 
+((|HasAttribute| |#1| (QUOTE (-3997 "*")))) 
+(-944 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 (-312))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) 
-(-946 S) 
+(-945 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-947 S) 
+(-946 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-948 S) 
+(-947 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 
-(-949 -3094 |Expon| |VarSet| |FPol| |LFPol|) 
+(-948 -3093 |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"))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-950) 
+(-949) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-951 A S) 
+(-950 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 
-(-952 S) 
+(-951 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 
-(-953 Q R) 
+(-952 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-954 R) 
+(-953 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 
-(-955) 
+(-954) 
 ((|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 
-(-956 UP) 
+(-955 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 
-(-957 R) 
+(-956 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 
-(-958 T$) 
+(-957 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| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-959 T$) 
+(-958 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 
-(-960 R |ls|) 
+(-959 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}."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (|HasCategory| (-705 |#1| (-775 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -705) (|devaluate| |#1|) (|%list| (QUOTE -775) (|devaluate| |#2|)))))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-555 (-474)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-775 |#2|) (QUOTE (-318))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-72)))) 
-(-961) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-473)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-774 |#2|) (QUOTE (-318))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) 
+(-960) 
 ((|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 
-(-962 S) 
+(-961 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 
-(-963) 
+(-962) 
 ((|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."))) 
-((-3993 . T)) 
+((-3992 . T)) 
 NIL 
-(-964 |xx| -3094) 
+(-963 |xx| -3093) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-965 S) 
+(-964 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 
-(-966 S |m| |n| R |Row| |Col|) 
+(-965 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 (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146)))) 
-(-967 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146)))) 
+(-966 |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"))) 
-((-3996 . T) (-3991 . T) (-3990 . T)) 
+((-3995 . T) (-3990 . T) (-3989 . T)) 
 NIL 
-(-968 |m| |n| R) 
+(-967 |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}."))) 
-((-3996 . T) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-554 (-774))))) 
-(-969 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3995 . T) (-3990 . T) (-3989 . T)) 
+((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) 
+(-968 |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 
-(-970 R) 
+(-969 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 
-(-971 S) 
+(-970 S) 
 ((|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")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-972) 
+(-971) 
 ((|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")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-973 S T$) 
+(-972 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 (-1015)))) 
-(-974 S) 
+((|HasCategory| |#1| (QUOTE (-1014)))) 
+(-973 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.")) (|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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-975) 
+(-974) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-976 |TheField| |ThePolDom|) 
+(-975 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-977) 
+(-976) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-978 S R E V) 
+(-977 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-906 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#4| (QUOTE (-555 (-1091))))) 
-(-979 R E V) 
+((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-905 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-1090))))) 
+(-978 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-980) 
+(-979) 
 ((|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 
-(-981 S |TheField| |ThePols|) 
+(-980 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 
-(-982 |TheField| |ThePols|) 
+(-981 |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 
-(-983 R E V P TS) 
+(-982 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 
-(-984 S R E V P) 
+(-983 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 
-(-985 R E V P) 
+(-984 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}."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-986 R E V P TS) 
+(-985 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 
-(-987) 
+(-986) 
 ((|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 
-(-988) 
+(-987) 
 ((|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 
-(-989 |Base| R -3094) 
+(-988 |Base| R -3093) 
 ((|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 
-(-990 |f|) 
+(-989 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-991 |Base| R -3094) 
+(-990 |Base| R -3093) 
 ((|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 
-(-992 R |ls|) 
+(-991 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 
-(-993 R UP M) 
+(-992 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."))) 
-((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))))) 
-(-994 UP SAE UPA) 
+((-3988 |has| |#1| (-312)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))))) 
+(-993 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 
-(-995 UP SAE UPA) 
+(-994 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 
-(-996) 
+(-995) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-997) 
+(-996) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-998 S) 
+(-997 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 
-(-999) 
+(-998) 
 ((|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 
-(-1000 R) 
+(-999 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 
-(-1001 R) 
+(-1000 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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| (-1002 (-1091)) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| (-1002 (-1091)) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-1002 (-1091)) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-1002 (-1091)) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-1002 (-1091)) (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1002 S) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| (-1001 (-1090)) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-1001 (-1090)) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-1001 (-1090)) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1001 (-1090)) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-1001 (-1090)) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1090)))) (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1001 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 
-(-1003 S) 
+(-1002 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015)))) 
-(-1004 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
+(-1003 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 (-757)))) 
-(-1005) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1004) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1006 S) 
+(-1005 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1003 |#1|) (QUOTE (-1015)))) 
-(-1007 R S) 
+((|HasCategory| (-1002 |#1|) (QUOTE (-1014)))) 
+(-1006 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1008 S) 
+(-1007 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1009 S L) 
+(-1008 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 
-(-1010) 
+(-1009) 
 ((|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 
-(-1011 S) 
+(-1010 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)}}"))) 
-((-3996 . T) (-3986 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-1012 A S) 
+((-3995 . T) (-3985 . T) (-3996 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-1011 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1013 S) 
+(-1012 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-3986 . T)) 
+((-3985 . T)) 
 NIL 
-(-1014 S) 
+(-1013 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 
-(-1015) 
+(-1014) 
 ((|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 
-(-1016 |m| |n|) 
+(-1015 |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| $ #1="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| $ #1#) $ (|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 
-(-1017) 
+(-1016) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1018 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1017 |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 
-(-1019 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1018 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1020 R E V P TS) 
+(-1019 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 
-(-1021 R E V P TS) 
+(-1020 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 
-(-1022 R E V P) 
+(-1021 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.}"))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-1023) 
+(-1022) 
 ((|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 
-(-1024 T$) 
+(-1023 T$) 
 ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) 
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1025 T$) 
+(-1024 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) 
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+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1026 S) 
+(-1025 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1027) 
+(-1026) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1028 |dimtot| |dim1| S) 
+(-1027 |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}."))) 
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-(-1029 R |x|) 
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(-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1090))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-951 (-348 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-348 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(|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3992)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1090)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) 
+(-1028 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 (-390)))) 
-(-1030) 
+(-1029) 
 ((|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 
-(-1031) 
+(-1030) 
 ((|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 
-(-1032 R -3094) 
+(-1031 R -3093) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1033 R) 
+(-1032 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1034) 
+(-1033) 
 ((|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 
-(-1035) 
+(-1034) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|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."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1036 S) 
+(-1035 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-3996 . T) (-3997 . T)) 
+((-3995 . T) (-3996 . T)) 
 NIL 
-(-1037 S |ndim| R |Row| |Col|) 
+(-1036 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
-(-1038 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3997 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
+(-1037 |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."))) 
-((-3996 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3995 . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1039 R |Row| |Col| M) 
+(-1038 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 
-(-1040 R |VarSet|) 
+(-1039 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#2| (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1041 |Coef| |Var| SMP) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-328)))) (|HasCategory| |#2| (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-328))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1040 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1042 R E V P) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-1041 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}"))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-1043 UP -3094) 
+(-1042 UP -3093) 
 ((|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 
-(-1044 R) 
+(-1043 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 
-(-1045 R) 
+(-1044 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 
-(-1046 R) 
+(-1045 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 
-(-1047 S A) 
+(-1046 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 (-758)))) 
-(-1048 R) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1047 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 
-(-1049 R) 
+(-1048 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 
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-(-1050) 
+(-1049) 
 ((|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 
-(-1051) 
+(-1050) 
 ((|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 
-(-1052) 
+(-1051) 
 ((|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 
-(-1053) 
+(-1052) 
 ((|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 
-(-1054) 
+(-1053) 
 ((|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 
-(-1055 V C) 
+(-1054 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 
-(-1056 V C) 
+(-1055 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1015)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1015))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1015)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-554 (-774)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72)))) 
-(-1057 |ndim| R) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-1054 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72)))) 
+(-1056 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
-((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3996 . T) (-3990 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1091))))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-1058 S) 
+((-3992 . T) (-3984 |has| |#2| (-6 (-3997 "*"))) (-3995 . T) (-3989 . T) (-3990 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1090))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-1057 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1059) 
+(-1058) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-1060 R E V P TS) 
+(-1059 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 
-(-1061 R E V P) 
+(-1060 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."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1062) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-1061) 
 ((|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 
-(-1063 S) 
+(-1062 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}."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1064 A S) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1063 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}.")) (|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.")) (|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 
-(-1065 S) 
+(-1064 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}.")) (|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.")) (|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 
-(-1066 |Key| |Ent| |dent|) 
+(-1065 |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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) 
-(-1067) 
+((-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) 
+(-1066) 
 ((|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 non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|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 
-(-1068) 
+(-1067) 
 ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1069 |Coef|) 
+(-1068 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1070 S) 
+(-1069 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1071 S) 
+((-3996 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1070 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 
-(-1072 A B) 
+(-1071 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 
-(-1073 A B C) 
+(-1072 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 
-(-1074) 
+(-1073) 
 ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|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"))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-758)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-555 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-117) (QUOTE (-758))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) 
-(-1075 |Entry|) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-473)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) 
+(-1074 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015))) (|HasCategory| (-1074) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-1076 A) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3860 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| (-1073) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
+(-1075 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 (-312))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485)))))) 
-(-1077 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484)))))) 
+(-1076 |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 
-(-1078 |Coef|) 
+(-1077 |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 
-(-1079 R UP) 
+(-1078 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 (-258)))) 
-(-1080 |n| R) 
+(-1079 |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 
-(-1081 S1 S2) 
+(-1080 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 
-(-1082) 
+(-1081) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1083 |Coef| |var| |cen|) 
+(-1082 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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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-(-1084 R -3094) 
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(-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-554 (-473))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-741)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-757))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| 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(-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-797 (-328))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-757)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1083 R -3093) 
 ((|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 
-(-1085 R) 
+(-1084 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 
-(-1086 R) 
+(-1085 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1087 R S) 
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+(-1086 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 
-(-1088 E OV R P) 
+(-1087 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 
-(-1089 |Coef| |var| |cen|) 
+(-1088 |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."))) 
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-(-1090 |Coef| |var| |cen|) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-484)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1089 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1091) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1090) 
 ((|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 
-(-1092 R) 
+(-1091 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 
-(-1093 R) 
+(-1092 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-886) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-1094) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3993))) 
+(-1093) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1095) 
+(-1094) 
 ((|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 
-(-1096) 
+(-1095) 
 ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1097 N) 
+(-1096 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1098 N) 
+(-1097 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 
-(-1099) 
+(-1098) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1100 R) 
+(-1099 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 
-(-1101) 
+(-1100) 
 ((|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 
-(-1102 S) 
+(-1101 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 
-(-1103 |Key| |Entry|) 
+(-1102 |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}"))) 
-((-3996 . T) (-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-1104 S) 
+((-3995 . T) (-3996 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+(-1103 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 
-(-1105 S) 
+(-1104 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 
-(-1106 R) 
+(-1105 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 
-(-1107 S |Key| |Entry|) 
+(-1106 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 
-(-1108 |Key| |Entry|) 
+(-1107 |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})}."))) 
-((-3997 . T)) 
+((-3996 . T)) 
 NIL 
-(-1109 |Key| |Entry|) 
+(-1108 |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 
-(-1110) 
+(-1109) 
 ((|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 
-(-1111 S) 
+(-1110 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 
-(-1112) 
+(-1111) 
 ((|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 
-(-1113 R) 
+(-1112 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 
-(-1114) 
+(-1113) 
 ((|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 
-(-1115 S) 
+(-1114 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1116) 
+(-1115) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1117 S) 
+(-1116 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1118 S) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1117 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1119) 
+(-1118) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1120 R -3094) 
+(-1119 R -3093) 
 ((|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 
-(-1121 R |Row| |Col| M) 
+(-1120 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 
-(-1122 R -3094) 
+(-1121 R -3093) 
 ((|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 -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -798) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -798) (|devaluate| |#1|))))) 
-(-1123 |Coef|) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) 
+(-1122 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1124 S R E V P) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-1123 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 (-318)))) 
-(-1125 R E V P) 
+(-1124 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-1126 |Curve|) 
+(-1125 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 
-(-1127) 
+(-1126) 
 ((|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 
-(-1128 S) 
+(-1127 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 (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774))))) 
-(-1129 -3094) 
+((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-1128 -3093) 
 ((|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 
-(-1130) 
+(-1129) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1131) 
+(-1130) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1132 S) 
+(-1131 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 (-758)))) 
-(-1133) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1132) 
 ((|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 
-(-1134 S) 
+(-1133 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 
-(-1135) 
+(-1134) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1136) 
+(-1135) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1137) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1138) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1139) 
+(-1138) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1140 |Coef| |var| |cen|) 
+(-1139 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3998 "*") OR (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-742))) (|has| |#1| (-146)) (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-823)))) (-3989 OR (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-742))) (|has| |#1| (-496)) (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-823)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasCategory| (-485) (QUOTE (-1027))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-952 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-555 (-474))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-935)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-758))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-952 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-1067)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -260) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-798 (-328))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-758)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1141 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
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(QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-757)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1140 |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 
-(-1142 |Coef|) 
+(-1141 |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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1143 S |Coef| UTS) 
+(-1142 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 (-312)))) 
-(-1144 |Coef| UTS) 
+(-1143 |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)}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1145 |Coef| UTS) 
+(-1144 |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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(|HasCategory| |#2| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118)))))) 
-(-1146 ZP) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118))))) (OR (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-120))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (|HasCategory| (-484) (QUOTE (-1026))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-741)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1090)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-797 (-328))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-822))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-118))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-812 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118)))))) 
+(-1145 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1147 S) 
+(-1146 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015)))) 
-(-1148 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
+(-1147 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757)))) 
-(-1149 |x| R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1148 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3992 |has| |#2| (-312)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-996) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-996) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-996) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1150 |x| R |y| S) 
+(((-3997 "*") |has| |#2| (-146)) (-3988 |has| |#2| (-495)) (-3991 |has| |#2| (-312)) (-3993 |has| |#2| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-328)))) (|HasCategory| (-995) (QUOTE (-797 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-995) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-328))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-995) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-348 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-812 (-1090)))) (|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-1149 |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 
-(-1151 R Q UP) 
+(-1150 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 
-(-1152 R UP) 
+(-1151 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 
-(-1153 R UP) 
+(-1152 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 
-(-1154 R U) 
+(-1153 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 
-(-1155 S R) 
+(-1154 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| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067)))) 
-(-1156 R) 
+((|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1066)))) 
+(-1155 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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3991 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-1157 R PR S PS) 
+(-1156 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 
-(-1158 S |Coef| |Expon|) 
+(-1157 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| (QUOTE (-811 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) 
-(-1159 |Coef| |Expon|) 
+((|HasCategory| |#2| (QUOTE (-810 (-1090)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#2|) (QUOTE (-1090)))))) 
+(-1158 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1160 RC P) 
+(-1159 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1161 |Coef| |var| |cen|) 
+(-1160 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1162 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
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+(-1161 |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 
-(-1163 |Coef|) 
+(-1162 |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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1164 S |Coef| ULS) 
+(-1163 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 
-(-1165 |Coef| ULS) 
+(-1164 |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)}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1166 |Coef| ULS) 
+(-1165 |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)}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485)))))) 
-(-1167 R FE |var| |cen|) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-484)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-484)))))) 
+(-1166 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))}."))) 
-(((-3998 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-348 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) 
-(-1168 A S) 
+(((-3997 "*") |has| (-1160 |#2| |#3| |#4|) (-146)) (-3988 |has| (-1160 |#2| |#3| |#4|) (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-951 (-348 (-484)))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-951 (-348 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-951 (-484)))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-495)))) 
+(-1167 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3997))) 
-(-1169 S) 
+((|HasAttribute| |#1| (QUOTE -3996))) 
+(-1168 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1170 |Coef| |var| |cen|) 
+(-1169 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1171 |Coef1| |Coef2| UTS1 UTS2) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1170 |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 
-(-1172 S |Coef|) 
+(-1171 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| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-873))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-1173 |Coef|) 
+((|HasCategory| |#2| (QUOTE (-29 (-484)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasSignature| |#2| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-484))))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-1172 |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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1174 |Coef| UTS) 
+(-1173 |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 
-(-1175 -3094 UP L UTS) 
+(-1174 -3093 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 (-496)))) 
-(-1176) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-1175) 
 ((|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 
-(-1177 |sym|) 
+(-1176 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1178 S R) 
+(-1177 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 (-917))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1179 R) 
+((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1178 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-3997 . T) (-3996 . T)) 
+((-3996 . T) (-3995 . T)) 
 NIL 
-(-1180 R) 
+(-1179 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-3997 . T) (-3996 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-1181 A B) 
+((-3996 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-1180 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 
-(-1182) 
+(-1181) 
 ((|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 
-(-1183) 
+(-1182) 
 ((|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 
-(-1184) 
+(-1183) 
 ((|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 
-(-1185) 
+(-1184) 
 ((|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 
-(-1186) 
+(-1185) 
 ((|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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1187 A S) 
+(-1186 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1188 S) 
+(-1187 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3990 . T) (-3989 . T)) 
 NIL 
-(-1189 R) 
+(-1188 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 
-(-1190 K R UP -3094) 
+(-1189 K R UP -3093) 
 ((|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 
-(-1191) 
+(-1190) 
 ((|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 
-(-1192) 
+(-1191) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1193 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1192 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)"))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1194 R E V P) 
+(-1193 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}."))) 
-((-3997 . T) (-3996 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1195 R) 
+((-3996 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-1194 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)"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1196 |vl| R) 
+(-1195 |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."))) 
-((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1197 R |VarSet| XPOLY) 
+((-3992 . T) (-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3988))) 
+(-1196 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 
-(-1198 S -3094) 
+(-1197 S -3093) 
 ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1199 -3094) 
+(-1198 -3093) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
-(-1200 |vl| R) 
+(-1199 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-1201 |VarSet| R) 
+(-1200 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-656 (-348 (-485))))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1202 R) 
+((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-348 (-484))))) (|HasAttribute| |#2| (QUOTE -3988))) 
+(-1201 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."))) 
-((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989))) 
-(-1203 |vl| R) 
+((-3988 |has| |#1| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3988))) 
+(-1202 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) 
 NIL 
-(-1204 R E) 
+(-1203 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989))) 
-(-1205 |VarSet| R) 
+((-3992 . T) (-3993 |has| |#1| (-6 -3993)) (-3988 |has| |#1| (-6 -3988)) (-3990 . T) (-3989 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3988))) 
+(-1204 |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."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1206) 
+((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3988))) 
+(-1205) 
 ((|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 
-(-1207 A) 
+(-1206 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 
-(-1208 R |ls| |ls2|) 
+(-1207 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 
-(-1209 R) 
+(-1208 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 
-(-1210 |p|) 
+(-1209 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4788,4 +4784,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1963163 1963168 1963173 1963178) (-2 NIL 1963143 1963148 1963153 1963158) (-1 NIL 1963123 1963128 1963133 1963138) (0 NIL 1963103 1963108 1963113 1963118) (-1210 "ZMOD.spad" 1962912 1962925 1963041 1963098) (-1209 "ZLINDEP.spad" 1962010 1962021 1962902 1962907) (-1208 "ZDSOLVE.spad" 1951971 1951993 1962000 1962005) (-1207 "YSTREAM.spad" 1951466 1951477 1951961 1951966) (-1206 "YDIAGRAM.spad" 1951100 1951109 1951456 1951461) (-1205 "XRPOLY.spad" 1950320 1950340 1950956 1951025) (-1204 "XPR.spad" 1948115 1948128 1950038 1950137) (-1203 "XPOLYC.spad" 1947434 1947450 1948041 1948110) (-1202 "XPOLY.spad" 1946989 1947000 1947290 1947359) (-1201 "XPBWPOLY.spad" 1945460 1945480 1946795 1946864) (-1200 "XFALG.spad" 1942508 1942524 1945386 1945455) (-1199 "XF.spad" 1940971 1940986 1942410 1942503) (-1198 "XF.spad" 1939414 1939431 1940855 1940860) (-1197 "XEXPPKG.spad" 1938673 1938699 1939404 1939409) (-1196 "XDPOLY.spad" 1938287 1938303 1938529 1938598) (-1195 "XALG.spad" 1937955 1937966 1938243 1938282) (-1194 "WUTSET.spad" 1933958 1933975 1937589 1937616) (-1193 "WP.spad" 1933165 1933209 1933816 1933883) (-1192 "WHILEAST.spad" 1932963 1932972 1933155 1933160) (-1191 "WHEREAST.spad" 1932634 1932643 1932953 1932958) (-1190 "WFFINTBS.spad" 1930297 1930319 1932624 1932629) (-1189 "WEIER.spad" 1928519 1928530 1930287 1930292) (-1188 "VSPACE.spad" 1928192 1928203 1928487 1928514) (-1187 "VSPACE.spad" 1927885 1927898 1928182 1928187) (-1186 "VOID.spad" 1927562 1927571 1927875 1927880) (-1185 "VIEWDEF.spad" 1922763 1922772 1927552 1927557) (-1184 "VIEW3D.spad" 1906724 1906733 1922753 1922758) (-1183 "VIEW2D.spad" 1894623 1894632 1906714 1906719) (-1182 "VIEW.spad" 1892343 1892352 1894613 1894618) (-1181 "VECTOR2.spad" 1890982 1890995 1892333 1892338) (-1180 "VECTOR.spad" 1889701 1889712 1889952 1889979) (-1179 "VECTCAT.spad" 1887613 1887624 1889669 1889696) (-1178 "VECTCAT.spad" 1885334 1885347 1887392 1887397) (-1177 "VARIABLE.spad" 1885114 1885129 1885324 1885329) (-1176 "UTYPE.spad" 1884758 1884767 1885104 1885109) (-1175 "UTSODETL.spad" 1884053 1884077 1884714 1884719) (-1174 "UTSODE.spad" 1882269 1882289 1884043 1884048) (-1173 "UTSCAT.spad" 1879748 1879764 1882167 1882264) (-1172 "UTSCAT.spad" 1876895 1876913 1879316 1879321) (-1171 "UTS2.spad" 1876490 1876525 1876885 1876890) (-1170 "UTS.spad" 1871502 1871530 1875022 1875119) (-1169 "URAGG.spad" 1866223 1866234 1871492 1871497) (-1168 "URAGG.spad" 1860908 1860921 1866179 1866184) (-1167 "UPXSSING.spad" 1858676 1858702 1860112 1860245) (-1166 "UPXSCONS.spad" 1856494 1856514 1856867 1857016) (-1165 "UPXSCCA.spad" 1855065 1855085 1856340 1856489) (-1164 "UPXSCCA.spad" 1853778 1853800 1855055 1855060) (-1163 "UPXSCAT.spad" 1852367 1852383 1853624 1853773) (-1162 "UPXS2.spad" 1851910 1851963 1852357 1852362) (-1161 "UPXS.spad" 1849265 1849293 1850101 1850250) (-1160 "UPSQFREE.spad" 1847680 1847694 1849255 1849260) (-1159 "UPSCAT.spad" 1845475 1845499 1847578 1847675) (-1158 "UPSCAT.spad" 1842971 1842997 1845076 1845081) (-1157 "UPOLYC2.spad" 1842442 1842461 1842961 1842966) (-1156 "UPOLYC.spad" 1837522 1837533 1842284 1842437) (-1155 "UPOLYC.spad" 1832520 1832533 1837284 1837289) (-1154 "UPMP.spad" 1831452 1831465 1832510 1832515) (-1153 "UPDIVP.spad" 1831017 1831031 1831442 1831447) (-1152 "UPDECOMP.spad" 1829278 1829292 1831007 1831012) (-1151 "UPCDEN.spad" 1828495 1828511 1829268 1829273) (-1150 "UP2.spad" 1827859 1827880 1828485 1828490) (-1149 "UP.spad" 1825329 1825344 1825716 1825869) (-1148 "UNISEG2.spad" 1824826 1824839 1825285 1825290) (-1147 "UNISEG.spad" 1824179 1824190 1824745 1824750) (-1146 "UNIFACT.spad" 1823282 1823294 1824169 1824174) (-1145 "ULSCONS.spad" 1817325 1817345 1817695 1817844) (-1144 "ULSCCAT.spad" 1815062 1815082 1817171 1817320) (-1143 "ULSCCAT.spad" 1812907 1812929 1815018 1815023) (-1142 "ULSCAT.spad" 1811147 1811163 1812753 1812902) (-1141 "ULS2.spad" 1810661 1810714 1811137 1811142) (-1140 "ULS.spad" 1802927 1802955 1803872 1804295) (-1139 "UINT8.spad" 1802804 1802813 1802917 1802922) (-1138 "UINT64.spad" 1802680 1802689 1802794 1802799) (-1137 "UINT32.spad" 1802556 1802565 1802670 1802675) (-1136 "UINT16.spad" 1802432 1802441 1802546 1802551) (-1135 "UFD.spad" 1801497 1801506 1802358 1802427) (-1134 "UFD.spad" 1800624 1800635 1801487 1801492) (-1133 "UDVO.spad" 1799505 1799514 1800614 1800619) (-1132 "UDPO.spad" 1797086 1797097 1799461 1799466) (-1131 "TYPEAST.spad" 1797005 1797014 1797076 1797081) (-1130 "TYPE.spad" 1796937 1796946 1796995 1797000) (-1129 "TWOFACT.spad" 1795589 1795604 1796927 1796932) (-1128 "TUPLE.spad" 1795096 1795107 1795501 1795506) (-1127 "TUBETOOL.spad" 1791963 1791972 1795086 1795091) (-1126 "TUBE.spad" 1790610 1790627 1791953 1791958) (-1125 "TSETCAT.spad" 1778681 1778698 1790578 1790605) (-1124 "TSETCAT.spad" 1766738 1766757 1778637 1778642) (-1123 "TS.spad" 1765366 1765382 1766332 1766429) (-1122 "TRMANIP.spad" 1759730 1759747 1765054 1765059) (-1121 "TRIMAT.spad" 1758693 1758718 1759720 1759725) (-1120 "TRIGMNIP.spad" 1757220 1757237 1758683 1758688) (-1119 "TRIGCAT.spad" 1756732 1756741 1757210 1757215) (-1118 "TRIGCAT.spad" 1756242 1756253 1756722 1756727) (-1117 "TREE.spad" 1754882 1754893 1755914 1755941) (-1116 "TRANFUN.spad" 1754721 1754730 1754872 1754877) (-1115 "TRANFUN.spad" 1754558 1754569 1754711 1754716) (-1114 "TOPSP.spad" 1754232 1754241 1754548 1754553) (-1113 "TOOLSIGN.spad" 1753895 1753906 1754222 1754227) (-1112 "TEXTFILE.spad" 1752456 1752465 1753885 1753890) (-1111 "TEX1.spad" 1752012 1752023 1752446 1752451) (-1110 "TEX.spad" 1749206 1749215 1752002 1752007) (-1109 "TBCMPPK.spad" 1747307 1747330 1749196 1749201) (-1108 "TBAGG.spad" 1746365 1746388 1747287 1747302) (-1107 "TBAGG.spad" 1745431 1745456 1746355 1746360) (-1106 "TANEXP.spad" 1744839 1744850 1745421 1745426) (-1105 "TALGOP.spad" 1744563 1744574 1744829 1744834) (-1104 "TABLEAU.spad" 1744044 1744055 1744553 1744558) (-1103 "TABLE.spad" 1742319 1742342 1742589 1742616) (-1102 "TABLBUMP.spad" 1739098 1739109 1742309 1742314) (-1101 "SYSTEM.spad" 1738326 1738335 1739088 1739093) (-1100 "SYSSOLP.spad" 1735809 1735820 1738316 1738321) (-1099 "SYSPTR.spad" 1735708 1735717 1735799 1735804) (-1098 "SYSNNI.spad" 1734931 1734942 1735698 1735703) (-1097 "SYSINT.spad" 1734335 1734346 1734921 1734926) (-1096 "SYNTAX.spad" 1730669 1730678 1734325 1734330) (-1095 "SYMTAB.spad" 1728737 1728746 1730659 1730664) (-1094 "SYMS.spad" 1724766 1724775 1728727 1728732) (-1093 "SYMPOLY.spad" 1723899 1723910 1723981 1724108) (-1092 "SYMFUNC.spad" 1723400 1723411 1723889 1723894) (-1091 "SYMBOL.spad" 1720895 1720904 1723390 1723395) (-1090 "SUTS.spad" 1718008 1718036 1719427 1719524) (-1089 "SUPXS.spad" 1715350 1715378 1716199 1716348) (-1088 "SUPFRACF.spad" 1714455 1714473 1715340 1715345) (-1087 "SUP2.spad" 1713847 1713860 1714445 1714450) (-1086 "SUP.spad" 1710931 1710942 1711704 1711857) (-1085 "SUMRF.spad" 1709905 1709916 1710921 1710926) (-1084 "SUMFS.spad" 1709534 1709551 1709895 1709900) (-1083 "SULS.spad" 1701787 1701815 1702745 1703168) (-1082 "syntax.spad" 1701556 1701565 1701777 1701782) (-1081 "SUCH.spad" 1701246 1701261 1701546 1701551) (-1080 "SUBSPACE.spad" 1693377 1693392 1701236 1701241) (-1079 "SUBRESP.spad" 1692547 1692561 1693333 1693338) (-1078 "STTFNC.spad" 1689015 1689031 1692537 1692542) (-1077 "STTF.spad" 1685114 1685130 1689005 1689010) (-1076 "STTAYLOR.spad" 1677791 1677802 1685021 1685026) (-1075 "STRTBL.spad" 1676178 1676195 1676327 1676354) (-1074 "STRING.spad" 1675046 1675055 1675431 1675458) (-1073 "STREAM3.spad" 1674619 1674634 1675036 1675041) (-1072 "STREAM2.spad" 1673747 1673760 1674609 1674614) (-1071 "STREAM1.spad" 1673453 1673464 1673737 1673742) (-1070 "STREAM.spad" 1670449 1670460 1673056 1673071) (-1069 "STINPROD.spad" 1669385 1669401 1670439 1670444) (-1068 "STEPAST.spad" 1668619 1668628 1669375 1669380) (-1067 "STEP.spad" 1667936 1667945 1668609 1668614) (-1066 "STBL.spad" 1666326 1666354 1666493 1666508) (-1065 "STAGG.spad" 1665025 1665036 1666316 1666321) (-1064 "STAGG.spad" 1663722 1663735 1665015 1665020) (-1063 "STACK.spad" 1663144 1663155 1663394 1663421) (-1062 "SRING.spad" 1662904 1662913 1663134 1663139) (-1061 "SREGSET.spad" 1660636 1660653 1662538 1662565) (-1060 "SRDCMPK.spad" 1659213 1659233 1660626 1660631) (-1059 "SRAGG.spad" 1654396 1654405 1659181 1659208) (-1058 "SRAGG.spad" 1649599 1649610 1654386 1654391) (-1057 "SQMATRIX.spad" 1647276 1647294 1648192 1648279) (-1056 "SPLTREE.spad" 1642018 1642031 1646814 1646841) (-1055 "SPLNODE.spad" 1638638 1638651 1642008 1642013) (-1054 "SPFCAT.spad" 1637447 1637456 1638628 1638633) (-1053 "SPECOUT.spad" 1635999 1636008 1637437 1637442) (-1052 "SPADXPT.spad" 1628090 1628099 1635989 1635994) (-1051 "spad-parser.spad" 1627555 1627564 1628080 1628085) (-1050 "SPADAST.spad" 1627256 1627265 1627545 1627550) (-1049 "SPACEC.spad" 1611471 1611482 1627246 1627251) (-1048 "SPACE3.spad" 1611247 1611258 1611461 1611466) (-1047 "SORTPAK.spad" 1610796 1610809 1611203 1611208) (-1046 "SOLVETRA.spad" 1608559 1608570 1610786 1610791) (-1045 "SOLVESER.spad" 1607015 1607026 1608549 1608554) (-1044 "SOLVERAD.spad" 1603041 1603052 1607005 1607010) (-1043 "SOLVEFOR.spad" 1601503 1601521 1603031 1603036) (-1042 "SNTSCAT.spad" 1601103 1601120 1601471 1601498) (-1041 "SMTS.spad" 1599420 1599446 1600697 1600794) (-1040 "SMP.spad" 1597228 1597248 1597618 1597745) (-1039 "SMITH.spad" 1596073 1596098 1597218 1597223) (-1038 "SMATCAT.spad" 1594191 1594221 1596017 1596068) (-1037 "SMATCAT.spad" 1592241 1592273 1594069 1594074) (-1036 "SKAGG.spad" 1591210 1591221 1592209 1592236) (-1035 "SINT.spad" 1590509 1590518 1591076 1591205) (-1034 "SIMPAN.spad" 1590237 1590246 1590499 1590504) (-1033 "SIGNRF.spad" 1589362 1589373 1590227 1590232) (-1032 "SIGNEF.spad" 1588648 1588665 1589352 1589357) (-1031 "syntax.spad" 1588065 1588074 1588638 1588643) (-1030 "SIG.spad" 1587427 1587436 1588055 1588060) (-1029 "SHP.spad" 1585371 1585386 1587383 1587388) (-1028 "SHDP.spad" 1574864 1574891 1575381 1575478) (-1027 "SGROUP.spad" 1574472 1574481 1574854 1574859) (-1026 "SGROUP.spad" 1574078 1574089 1574462 1574467) (-1025 "catdef.spad" 1573788 1573800 1573899 1574073) (-1024 "catdef.spad" 1573344 1573356 1573609 1573783) (-1023 "SGCF.spad" 1566483 1566492 1573334 1573339) (-1022 "SFRTCAT.spad" 1565429 1565446 1566451 1566478) (-1021 "SFRGCD.spad" 1564492 1564512 1565419 1565424) (-1020 "SFQCMPK.spad" 1559305 1559325 1564482 1564487) (-1019 "SEXOF.spad" 1559148 1559188 1559295 1559300) (-1018 "SEXCAT.spad" 1556976 1557016 1559138 1559143) (-1017 "SEX.spad" 1556868 1556877 1556966 1556971) (-1016 "SETMN.spad" 1555328 1555345 1556858 1556863) (-1015 "SETCAT.spad" 1554813 1554822 1555318 1555323) (-1014 "SETCAT.spad" 1554296 1554307 1554803 1554808) (-1013 "SETAGG.spad" 1550845 1550856 1554276 1554291) (-1012 "SETAGG.spad" 1547402 1547415 1550835 1550840) (-1011 "SET.spad" 1545711 1545722 1546808 1546847) (-1010 "syntax.spad" 1545414 1545423 1545701 1545706) (-1009 "SEGXCAT.spad" 1544570 1544583 1545404 1545409) (-1008 "SEGCAT.spad" 1543495 1543506 1544560 1544565) (-1007 "SEGBIND2.spad" 1543193 1543206 1543485 1543490) (-1006 "SEGBIND.spad" 1542951 1542962 1543140 1543145) (-1005 "SEGAST.spad" 1542681 1542690 1542941 1542946) (-1004 "SEG2.spad" 1542116 1542129 1542637 1542642) (-1003 "SEG.spad" 1541929 1541940 1542035 1542040) (-1002 "SDVAR.spad" 1541205 1541216 1541919 1541924) (-1001 "SDPOL.spad" 1538897 1538908 1539188 1539315) (-1000 "SCPKG.spad" 1536986 1536997 1538887 1538892) (-999 "SCOPE.spad" 1536164 1536172 1536976 1536981) (-998 "SCACHE.spad" 1534861 1534871 1536154 1536159) (-997 "SASTCAT.spad" 1534771 1534779 1534851 1534856) (-996 "SAOS.spad" 1534644 1534652 1534761 1534766) (-995 "SAERFFC.spad" 1534358 1534377 1534634 1534639) (-994 "SAEFACT.spad" 1534060 1534079 1534348 1534353) (-993 "SAE.spad" 1531711 1531726 1532321 1532456) (-992 "RURPK.spad" 1529371 1529386 1531701 1531706) (-991 "RULESET.spad" 1528825 1528848 1529361 1529366) (-990 "RULECOLD.spad" 1528678 1528690 1528815 1528820) (-989 "RULE.spad" 1526927 1526950 1528668 1528673) (-988 "RTVALUE.spad" 1526663 1526671 1526917 1526922) (-987 "syntax.spad" 1526381 1526389 1526653 1526658) (-986 "RSETGCD.spad" 1522824 1522843 1526371 1526376) (-985 "RSETCAT.spad" 1512793 1512809 1522792 1522819) (-984 "RSETCAT.spad" 1502782 1502800 1512783 1512788) (-983 "RSDCMPK.spad" 1501283 1501302 1502772 1502777) (-982 "RRCC.spad" 1499668 1499697 1501273 1501278) (-981 "RRCC.spad" 1498051 1498082 1499658 1499663) (-980 "RPTAST.spad" 1497754 1497762 1498041 1498046) (-979 "RPOLCAT.spad" 1477259 1477273 1497622 1497749) (-978 "RPOLCAT.spad" 1456557 1456573 1476922 1476927) (-977 "ROMAN.spad" 1455886 1455894 1456423 1456552) (-976 "ROIRC.spad" 1454967 1454998 1455876 1455881) (-975 "RNS.spad" 1453944 1453952 1454869 1454962) (-974 "RNS.spad" 1453007 1453017 1453934 1453939) (-973 "RNGBIND.spad" 1452168 1452181 1452962 1452967) (-972 "RNG.spad" 1451777 1451785 1452158 1452163) (-971 "RNG.spad" 1451384 1451394 1451767 1451772) (-970 "RMODULE.spad" 1451166 1451176 1451374 1451379) (-969 "RMCAT2.spad" 1450587 1450643 1451156 1451161) (-968 "RMATRIX.spad" 1449397 1449415 1449739 1449778) (-967 "RMATCAT.spad" 1444977 1445007 1449353 1449392) (-966 "RMATCAT.spad" 1440447 1440479 1444825 1444830) (-965 "RLINSET.spad" 1440152 1440162 1440437 1440442) (-964 "RINTERP.spad" 1440041 1440060 1440142 1440147) (-963 "RING.spad" 1439512 1439520 1440021 1440036) (-962 "RING.spad" 1438991 1439001 1439502 1439507) (-961 "RIDIST.spad" 1438384 1438392 1438981 1438986) (-960 "RGCHAIN.spad" 1436939 1436954 1437832 1437859) (-959 "RGBCSPC.spad" 1436729 1436740 1436929 1436934) (-958 "RGBCMDL.spad" 1436292 1436303 1436719 1436724) (-957 "RFFACTOR.spad" 1435755 1435765 1436282 1436287) (-956 "RFFACT.spad" 1435491 1435502 1435745 1435750) (-955 "RFDIST.spad" 1434488 1434496 1435481 1435486) (-954 "RF.spad" 1432163 1432173 1434478 1434483) (-953 "RETSOL.spad" 1431583 1431595 1432153 1432158) (-952 "RETRACT.spad" 1431012 1431022 1431573 1431578) (-951 "RETRACT.spad" 1430439 1430451 1431002 1431007) (-950 "RETAST.spad" 1430252 1430260 1430429 1430434) (-949 "RESRING.spad" 1429600 1429646 1430190 1430247) (-948 "RESLATC.spad" 1428925 1428935 1429590 1429595) (-947 "REPSQ.spad" 1428657 1428667 1428915 1428920) (-946 "REPDB.spad" 1428365 1428375 1428647 1428652) (-945 "REP2.spad" 1418080 1418090 1428207 1428212) (-944 "REP1.spad" 1412301 1412311 1418030 1418035) (-943 "REP.spad" 1409856 1409864 1412291 1412296) (-942 "REGSET.spad" 1407682 1407698 1409490 1409517) (-941 "REF.spad" 1407201 1407211 1407672 1407677) (-940 "REDORDER.spad" 1406408 1406424 1407191 1407196) (-939 "RECLOS.spad" 1405305 1405324 1406008 1406101) (-938 "REALSOLV.spad" 1404446 1404454 1405295 1405300) (-937 "REAL0Q.spad" 1401745 1401759 1404436 1404441) (-936 "REAL0.spad" 1398590 1398604 1401735 1401740) (-935 "REAL.spad" 1398463 1398471 1398580 1398585) (-934 "RDUCEAST.spad" 1398185 1398193 1398453 1398458) (-933 "RDIV.spad" 1397841 1397865 1398175 1398180) (-932 "RDIST.spad" 1397409 1397419 1397831 1397836) (-931 "RDETRS.spad" 1396274 1396291 1397399 1397404) (-930 "RDETR.spad" 1394414 1394431 1396264 1396269) (-929 "RDEEFS.spad" 1393514 1393530 1394404 1394409) (-928 "RDEEF.spad" 1392525 1392541 1393504 1393509) (-927 "RCFIELD.spad" 1389744 1389752 1392427 1392520) (-926 "RCFIELD.spad" 1387049 1387059 1389734 1389739) (-925 "RCAGG.spad" 1384986 1384996 1387039 1387044) (-924 "RCAGG.spad" 1382850 1382862 1384905 1384910) (-923 "RATRET.spad" 1382211 1382221 1382840 1382845) (-922 "RATFACT.spad" 1381904 1381915 1382201 1382206) (-921 "RANDSRC.spad" 1381224 1381232 1381894 1381899) (-920 "RADUTIL.spad" 1380981 1380989 1381214 1381219) (-919 "RADIX.spad" 1378026 1378039 1379571 1379664) (-918 "RADFF.spad" 1375943 1375979 1376061 1376217) (-917 "RADCAT.spad" 1375539 1375547 1375933 1375938) (-916 "RADCAT.spad" 1375133 1375143 1375529 1375534) (-915 "QUEUE.spad" 1374547 1374557 1374805 1374832) (-914 "QUATCT2.spad" 1374168 1374186 1374537 1374542) (-913 "QUATCAT.spad" 1372339 1372349 1374098 1374163) (-912 "QUATCAT.spad" 1370275 1370287 1372036 1372041) (-911 "QUAT.spad" 1368882 1368892 1369224 1369289) (-910 "QUAGG.spad" 1367716 1367726 1368850 1368877) (-909 "QQUTAST.spad" 1367485 1367493 1367706 1367711) (-908 "QFORM.spad" 1367104 1367118 1367475 1367480) (-907 "QFCAT2.spad" 1366797 1366813 1367094 1367099) (-906 "QFCAT.spad" 1365500 1365510 1366699 1366792) (-905 "QFCAT.spad" 1363836 1363848 1365037 1365042) (-904 "QEQUAT.spad" 1363395 1363403 1363826 1363831) (-903 "QCMPACK.spad" 1358310 1358329 1363385 1363390) (-902 "QALGSET2.spad" 1356306 1356324 1358300 1358305) (-901 "QALGSET.spad" 1352411 1352443 1356220 1356225) (-900 "PWFFINTB.spad" 1349827 1349848 1352401 1352406) (-899 "PUSHVAR.spad" 1349166 1349185 1349817 1349822) (-898 "PTRANFN.spad" 1345302 1345312 1349156 1349161) (-897 "PTPACK.spad" 1342390 1342400 1345292 1345297) (-896 "PTFUNC2.spad" 1342213 1342227 1342380 1342385) (-895 "PTCAT.spad" 1341468 1341478 1342181 1342208) (-894 "PSQFR.spad" 1340783 1340807 1341458 1341463) (-893 "PSEUDLIN.spad" 1339669 1339679 1340773 1340778) (-892 "PSETPK.spad" 1326374 1326390 1339547 1339552) (-891 "PSETCAT.spad" 1320774 1320797 1326354 1326369) (-890 "PSETCAT.spad" 1315148 1315173 1320730 1320735) (-889 "PSCURVE.spad" 1314147 1314155 1315138 1315143) (-888 "PSCAT.spad" 1312930 1312959 1314045 1314142) (-887 "PSCAT.spad" 1311803 1311834 1312920 1312925) (-886 "PRTITION.spad" 1310501 1310509 1311793 1311798) (-885 "PRTDAST.spad" 1310220 1310228 1310491 1310496) (-884 "PRS.spad" 1299838 1299855 1310176 1310181) (-883 "PRQAGG.spad" 1299273 1299283 1299806 1299833) (-882 "PROPLOG.spad" 1298877 1298885 1299263 1299268) (-881 "PROPFUN2.spad" 1298500 1298513 1298867 1298872) (-880 "PROPFUN1.spad" 1297906 1297917 1298490 1298495) (-879 "PROPFRML.spad" 1296474 1296485 1297896 1297901) (-878 "PROPERTY.spad" 1295970 1295978 1296464 1296469) (-877 "PRODUCT.spad" 1293667 1293679 1293951 1294006) (-876 "PRINT.spad" 1293419 1293427 1293657 1293662) (-875 "PRIMES.spad" 1291680 1291690 1293409 1293414) (-874 "PRIMELT.spad" 1289801 1289815 1291670 1291675) (-873 "PRIMCAT.spad" 1289444 1289452 1289791 1289796) (-872 "PRIMARR2.spad" 1288211 1288223 1289434 1289439) (-871 "PRIMARR.spad" 1287266 1287276 1287436 1287463) (-870 "PREASSOC.spad" 1286648 1286660 1287256 1287261) (-869 "PR.spad" 1285166 1285178 1285865 1285992) (-868 "PPCURVE.spad" 1284303 1284311 1285156 1285161) (-867 "PORTNUM.spad" 1284094 1284102 1284293 1284298) (-866 "POLYROOT.spad" 1282943 1282965 1284050 1284055) (-865 "POLYLIFT.spad" 1282208 1282231 1282933 1282938) (-864 "POLYCATQ.spad" 1280334 1280356 1282198 1282203) (-863 "POLYCAT.spad" 1273836 1273857 1280202 1280329) (-862 "POLYCAT.spad" 1266858 1266881 1273226 1273231) (-861 "POLY2UP.spad" 1266310 1266324 1266848 1266853) (-860 "POLY2.spad" 1265907 1265919 1266300 1266305) (-859 "POLY.spad" 1263575 1263585 1264090 1264217) (-858 "POLUTIL.spad" 1262540 1262569 1263531 1263536) (-857 "POLTOPOL.spad" 1261288 1261303 1262530 1262535) (-856 "POINT.spad" 1260171 1260181 1260258 1260285) (-855 "PNTHEORY.spad" 1256873 1256881 1260161 1260166) (-854 "PMTOOLS.spad" 1255648 1255662 1256863 1256868) (-853 "PMSYM.spad" 1255197 1255207 1255638 1255643) (-852 "PMQFCAT.spad" 1254788 1254802 1255187 1255192) (-851 "PMPREDFS.spad" 1254250 1254272 1254778 1254783) (-850 "PMPRED.spad" 1253737 1253751 1254240 1254245) (-849 "PMPLCAT.spad" 1252814 1252832 1253666 1253671) (-848 "PMLSAGG.spad" 1252399 1252413 1252804 1252809) (-847 "PMKERNEL.spad" 1251978 1251990 1252389 1252394) (-846 "PMINS.spad" 1251558 1251568 1251968 1251973) (-845 "PMFS.spad" 1251135 1251153 1251548 1251553) (-844 "PMDOWN.spad" 1250425 1250439 1251125 1251130) (-843 "PMASSFS.spad" 1249400 1249416 1250415 1250420) (-842 "PMASS.spad" 1248418 1248426 1249390 1249395) (-841 "PLOTTOOL.spad" 1248198 1248206 1248408 1248413) (-840 "PLOT3D.spad" 1244662 1244670 1248188 1248193) (-839 "PLOT1.spad" 1243835 1243845 1244652 1244657) (-838 "PLOT.spad" 1238758 1238766 1243825 1243830) (-837 "PLEQN.spad" 1226160 1226187 1238748 1238753) (-836 "PINTERPA.spad" 1225944 1225960 1226150 1226155) (-835 "PINTERP.spad" 1225566 1225585 1225934 1225939) (-834 "PID.spad" 1224540 1224548 1225492 1225561) (-833 "PICOERCE.spad" 1224197 1224207 1224530 1224535) (-832 "PI.spad" 1223814 1223822 1224171 1224192) (-831 "PGROEB.spad" 1222423 1222437 1223804 1223809) (-830 "PGE.spad" 1214096 1214104 1222413 1222418) (-829 "PGCD.spad" 1213050 1213067 1214086 1214091) (-828 "PFRPAC.spad" 1212199 1212209 1213040 1213045) (-827 "PFR.spad" 1208902 1208912 1212101 1212194) (-826 "PFOTOOLS.spad" 1208160 1208176 1208892 1208897) (-825 "PFOQ.spad" 1207530 1207548 1208150 1208155) (-824 "PFO.spad" 1206949 1206976 1207520 1207525) (-823 "PFECAT.spad" 1204659 1204667 1206875 1206944) (-822 "PFECAT.spad" 1202397 1202407 1204615 1204620) (-821 "PFBRU.spad" 1200285 1200297 1202387 1202392) (-820 "PFBR.spad" 1197845 1197868 1200275 1200280) (-819 "PF.spad" 1197419 1197431 1197650 1197743) (-818 "PERMGRP.spad" 1192189 1192199 1197409 1197414) (-817 "PERMCAT.spad" 1190850 1190860 1192169 1192184) (-816 "PERMAN.spad" 1189406 1189420 1190840 1190845) (-815 "PERM.spad" 1185216 1185226 1189239 1189254) (-814 "PENDTREE.spad" 1184630 1184640 1184910 1184915) (-813 "PDSPC.spad" 1183443 1183453 1184620 1184625) (-812 "PDSPC.spad" 1182254 1182266 1183433 1183438) (-811 "PDRING.spad" 1182096 1182106 1182234 1182249) (-810 "PDMOD.spad" 1181912 1181924 1182064 1182091) (-809 "PDECOMP.spad" 1181382 1181399 1181902 1181907) (-808 "PDDOM.spad" 1180820 1180833 1181372 1181377) (-807 "PDDOM.spad" 1180256 1180271 1180810 1180815) (-806 "PCOMP.spad" 1180109 1180122 1180246 1180251) (-805 "PBWLB.spad" 1178707 1178724 1180099 1180104) (-804 "PATTERN2.spad" 1178445 1178457 1178697 1178702) (-803 "PATTERN1.spad" 1176789 1176805 1178435 1178440) (-802 "PATTERN.spad" 1171364 1171374 1176779 1176784) (-801 "PATRES2.spad" 1171036 1171050 1171354 1171359) (-800 "PATRES.spad" 1168619 1168631 1171026 1171031) (-799 "PATMATCH.spad" 1166860 1166891 1168371 1168376) (-798 "PATMAB.spad" 1166289 1166299 1166850 1166855) (-797 "PATLRES.spad" 1165375 1165389 1166279 1166284) (-796 "PATAB.spad" 1165139 1165149 1165365 1165370) (-795 "PARTPERM.spad" 1163195 1163203 1165129 1165134) (-794 "PARSURF.spad" 1162629 1162657 1163185 1163190) (-793 "PARSU2.spad" 1162426 1162442 1162619 1162624) (-792 "script-parser.spad" 1161946 1161954 1162416 1162421) (-791 "PARSCURV.spad" 1161380 1161408 1161936 1161941) (-790 "PARSC2.spad" 1161171 1161187 1161370 1161375) (-789 "PARPCURV.spad" 1160633 1160661 1161161 1161166) (-788 "PARPC2.spad" 1160424 1160440 1160623 1160628) (-787 "PARAMAST.spad" 1159552 1159560 1160414 1160419) (-786 "PAN2EXPR.spad" 1158964 1158972 1159542 1159547) (-785 "PALETTE.spad" 1158078 1158086 1158954 1158959) (-784 "PAIR.spad" 1157152 1157165 1157721 1157726) (-783 "PADICRC.spad" 1154557 1154575 1155720 1155813) (-782 "PADICRAT.spad" 1152617 1152629 1152830 1152923) (-781 "PADICCT.spad" 1151166 1151178 1152543 1152612) (-780 "PADIC.spad" 1150869 1150881 1151092 1151161) (-779 "PADEPAC.spad" 1149558 1149577 1150859 1150864) (-778 "PADE.spad" 1148310 1148326 1149548 1149553) (-777 "OWP.spad" 1147558 1147588 1148168 1148235) (-776 "OVERSET.spad" 1147131 1147139 1147548 1147553) (-775 "OVAR.spad" 1146912 1146935 1147121 1147126) (-774 "OUTFORM.spad" 1136320 1136328 1146902 1146907) (-773 "OUTBFILE.spad" 1135754 1135762 1136310 1136315) (-772 "OUTBCON.spad" 1134824 1134832 1135744 1135749) (-771 "OUTBCON.spad" 1133892 1133902 1134814 1134819) (-770 "OUT.spad" 1133010 1133018 1133882 1133887) (-769 "OSI.spad" 1132485 1132493 1133000 1133005) (-768 "OSGROUP.spad" 1132403 1132411 1132475 1132480) (-767 "ORTHPOL.spad" 1130914 1130924 1132346 1132351) (-766 "OREUP.spad" 1130408 1130436 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(-629 "MATCAT.spad" 929452 929474 937858 937885) (-628 "MATCAT.spad" 920886 920910 929294 929299) (-627 "MAPPKG3.spad" 919801 919815 920876 920881) (-626 "MAPPKG2.spad" 919139 919151 919791 919796) (-625 "MAPPKG1.spad" 917967 917977 919129 919134) (-624 "MAPPAST.spad" 917306 917314 917957 917962) (-623 "MAPHACK3.spad" 917118 917132 917296 917301) (-622 "MAPHACK2.spad" 916887 916899 917108 917113) (-621 "MAPHACK1.spad" 916531 916541 916877 916882) (-620 "MAGMA.spad" 914337 914354 916521 916526) (-619 "MACROAST.spad" 913932 913940 914327 914332) (-618 "LZSTAGG.spad" 911186 911196 913922 913927) (-617 "LZSTAGG.spad" 908438 908450 911176 911181) (-616 "LWORD.spad" 905183 905200 908428 908433) (-615 "LSTAST.spad" 904967 904975 905173 905178) (-614 "LSQM.spad" 903245 903259 903639 903690) (-613 "LSPP.spad" 902780 902797 903235 903240) (-612 "LSMP1.spad" 900623 900637 902770 902775) (-611 "LSMP.spad" 899480 899508 900613 900618) (-610 "LSAGG.spad" 899149 899159 899448 899475) (-609 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(-405 "GRDEF.spad" 647015 647023 648626 648631) (-404 "GRAY.spad" 645486 645494 647005 647010) (-403 "GRALG.spad" 644581 644593 645476 645481) (-402 "GRALG.spad" 643674 643688 644571 644576) (-401 "GPOLSET.spad" 643132 643155 643344 643371) (-400 "GOSPER.spad" 642409 642427 643122 643127) (-399 "GMODPOL.spad" 641557 641584 642377 642404) (-398 "GHENSEL.spad" 640640 640654 641547 641552) (-397 "GENUPS.spad" 636933 636946 640630 640635) (-396 "GENUFACT.spad" 636510 636520 636923 636928) (-395 "GENPGCD.spad" 636112 636129 636500 636505) (-394 "GENMFACT.spad" 635564 635583 636102 636107) (-393 "GENEEZ.spad" 633523 633536 635554 635559) (-392 "GDMP.spad" 630912 630929 631686 631813) (-391 "GCNAALG.spad" 624835 624862 630706 630773) (-390 "GCDDOM.spad" 624027 624035 624761 624830) (-389 "GCDDOM.spad" 623281 623291 624017 624022) (-388 "GBINTERN.spad" 619301 619339 623271 623276) (-387 "GBF.spad" 615084 615122 619291 619296) (-386 "GBEUCLID.spad" 612966 613004 615074 615079) (-385 "GB.spad" 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581364 581369) (-364 "FS2EXPXP.spad" 575030 575053 575879 575884) (-363 "FS2.spad" 574685 574701 575020 575025) (-362 "FS.spad" 568957 568967 574464 574680) (-361 "FS.spad" 563031 563043 568540 568545) (-360 "FRUTIL.spad" 561985 561995 563021 563026) (-359 "FRNAALG.spad" 557262 557272 561927 561980) (-358 "FRNAALG.spad" 552551 552563 557218 557223) (-357 "FRNAAF2.spad" 551999 552017 552541 552546) (-356 "FRMOD.spad" 551407 551437 551928 551933) (-355 "FRIDEAL2.spad" 551011 551043 551397 551402) (-354 "FRIDEAL.spad" 550236 550257 550991 551006) (-353 "FRETRCT.spad" 549755 549765 550226 550231) (-352 "FRETRCT.spad" 549181 549193 549654 549659) (-351 "FRAMALG.spad" 547561 547574 549137 549176) (-350 "FRAMALG.spad" 545973 545988 547551 547556) (-349 "FRAC2.spad" 545578 545590 545963 545968) (-348 "FRAC.spad" 543565 543575 543952 544125) (-347 "FR2.spad" 542901 542913 543555 543560) (-346 "FR.spad" 536689 536699 541962 542031) (-345 "FPS.spad" 533528 533536 536579 536684) (-344 "FPS.spad" 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(-323 "FLAGG2.spad" 505672 505688 506945 506950) (-322 "FLAGG.spad" 502738 502748 505652 505667) (-321 "FLAGG.spad" 499705 499717 502621 502626) (-320 "FINRALG.spad" 497790 497803 499661 499700) (-319 "FINRALG.spad" 495801 495816 497674 497679) (-318 "FINITE.spad" 494953 494961 495791 495796) (-317 "FINITE.spad" 494103 494113 494943 494948) (-316 "FINAALG.spad" 483288 483298 494045 494098) (-315 "FINAALG.spad" 472485 472497 483244 483249) (-314 "FILECAT.spad" 471019 471036 472475 472480) (-313 "FILE.spad" 470602 470612 471009 471014) (-312 "FIELD.spad" 470008 470016 470504 470597) (-311 "FIELD.spad" 469500 469510 469998 470003) (-310 "FGROUP.spad" 468163 468173 469480 469495) (-309 "FGLMICPK.spad" 466958 466973 468153 468158) (-308 "FFX.spad" 466344 466359 466677 466770) (-307 "FFSLPE.spad" 465855 465876 466334 466339) (-306 "FFPOLY2.spad" 464915 464932 465845 465850) (-305 "FFPOLY.spad" 456257 456268 464905 464910) (-304 "FFP.spad" 455665 455685 455976 456069) (-303 "FFNBX.spad" 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"EXIT.spad" 370024 370032 370343 370348) (-261 "EVALCYC.spad" 369484 369498 370014 370019) (-260 "EVALAB.spad" 369064 369074 369474 369479) (-259 "EVALAB.spad" 368642 368654 369054 369059) (-258 "EUCDOM.spad" 366232 366240 368568 368637) (-257 "EUCDOM.spad" 363884 363894 366222 366227) (-256 "ES2.spad" 363397 363413 363874 363879) (-255 "ES1.spad" 362967 362983 363387 363392) (-254 "ES.spad" 355838 355846 362957 362962) (-253 "ES.spad" 348630 348640 355751 355756) (-252 "ERROR.spad" 345957 345965 348620 348625) (-251 "EQTBL.spad" 344293 344315 344502 344529) (-250 "EQ2.spad" 344011 344023 344283 344288) (-249 "EQ.spad" 338917 338927 341712 341818) (-248 "EP.spad" 335243 335253 338907 338912) (-247 "ENV.spad" 333921 333929 335233 335238) (-246 "ENTIRER.spad" 333589 333597 333865 333916) (-245 "ENTIRER.spad" 333301 333311 333579 333584) (-244 "EMR.spad" 332589 332630 333227 333296) (-243 "ELTAGG.spad" 330843 330862 332579 332584) (-242 "ELTAGG.spad" 329061 329082 330799 330804) (-241 "ELTAB.spad" 328536 328549 329051 329056) (-240 "ELFUTS.spad" 327971 327990 328526 328531) (-239 "ELEMFUN.spad" 327660 327668 327961 327966) (-238 "ELEMFUN.spad" 327347 327357 327650 327655) (-237 "ELAGG.spad" 325318 325328 327327 327342) (-236 "ELAGG.spad" 323226 323238 325237 325242) (-235 "ELABOR.spad" 322572 322580 323216 323221) (-234 "ELABEXPR.spad" 321504 321512 322562 322567) (-233 "EFUPXS.spad" 318280 318310 321460 321465) (-232 "EFULS.spad" 315116 315139 318236 318241) (-231 "EFSTRUC.spad" 313131 313147 315106 315111) (-230 "EF.spad" 307907 307923 313121 313126) (-229 "EAB.spad" 306207 306215 307897 307902) (-228 "DVARCAT.spad" 303213 303223 306197 306202) (-227 "DVARCAT.spad" 300217 300229 303203 303208) (-226 "DSMP.spad" 297950 297964 298255 298382) (-225 "DSEXT.spad" 297252 297262 297940 297945) (-224 "DSEXT.spad" 296474 296486 297164 297169) (-223 "DROPT1.spad" 296139 296149 296464 296469) (-222 "DROPT0.spad" 291004 291012 296129 296134) (-221 "DROPT.spad" 284963 284971 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"CTORCAT.spad" 170602 170610 171351 171356) (-159 "CTORCAT.spad" 169841 169851 170592 170597) (-158 "CTORCALL.spad" 169430 169440 169831 169836) (-157 "CTOR.spad" 169121 169129 169420 169425) (-156 "CSTTOOLS.spad" 168366 168379 169111 169116) (-155 "CRFP.spad" 162138 162151 168356 168361) (-154 "CRCEAST.spad" 161858 161866 162128 162133) (-153 "CRAPACK.spad" 160925 160935 161848 161853) (-152 "CPMATCH.spad" 160426 160441 160847 160852) (-151 "CPIMA.spad" 160131 160150 160416 160421) (-150 "COORDSYS.spad" 155140 155150 160121 160126) (-149 "CONTOUR.spad" 154567 154575 155130 155135) (-148 "CONTFRAC.spad" 150317 150327 154469 154562) (-147 "CONDUIT.spad" 150075 150083 150307 150312) (-146 "COMRING.spad" 149749 149757 150013 150070) (-145 "COMPPROP.spad" 149267 149275 149739 149744) (-144 "COMPLPAT.spad" 149034 149049 149257 149262) (-143 "COMPLEX2.spad" 148749 148761 149024 149029) (-142 "COMPLEX.spad" 144455 144465 144699 144957) (-141 "COMPILER.spad" 144004 144012 144445 144450) (-140 "COMPFACT.spad" 143606 143620 143994 143999) (-139 "COMPCAT.spad" 141681 141691 143343 143601) (-138 "COMPCAT.spad" 139497 139509 141161 141166) (-137 "COMMUPC.spad" 139245 139263 139487 139492) (-136 "COMMONOP.spad" 138778 138786 139235 139240) (-135 "COMMAAST.spad" 138541 138549 138768 138773) (-134 "COMM.spad" 138352 138360 138531 138536) (-133 "COMBOPC.spad" 137275 137283 138342 138347) (-132 "COMBINAT.spad" 136042 136052 137265 137270) (-131 "COMBF.spad" 133464 133480 136032 136037) (-130 "COLOR.spad" 132301 132309 133454 133459) (-129 "COLONAST.spad" 131967 131975 132291 132296) (-128 "CMPLXRT.spad" 131678 131695 131957 131962) (-127 "CLLCTAST.spad" 131340 131348 131668 131673) (-126 "CLIP.spad" 127448 127456 131330 131335) (-125 "CLIF.spad" 126103 126119 127404 127443) (-124 "CLAGG.spad" 122640 122650 126093 126098) (-123 "CLAGG.spad" 119061 119073 122516 122521) (-122 "CINTSLPE.spad" 118416 118429 119051 119056) (-121 "CHVAR.spad" 116554 116576 118406 118411) (-120 "CHARZ.spad" 116469 116477 116534 116549) (-119 "CHARPOL.spad" 115995 116005 116459 116464) (-118 "CHARNZ.spad" 115757 115765 115975 115990) (-117 "CHAR.spad" 113125 113133 115747 115752) (-116 "CFCAT.spad" 112453 112461 113115 113120) (-115 "CDEN.spad" 111673 111687 112443 112448) (-114 "CCLASS.spad" 109853 109861 111115 111154) (-113 "CATEGORY.spad" 108927 108935 109843 109848) (-112 "CATCTOR.spad" 108818 108826 108917 108922) (-111 "CATAST.spad" 108444 108452 108808 108813) (-110 "CASEAST.spad" 108158 108166 108434 108439) (-109 "CARTEN2.spad" 107548 107575 108148 108153) (-108 "CARTEN.spad" 103300 103324 107538 107543) (-107 "CARD.spad" 100595 100603 103274 103295) (-106 "CAPSLAST.spad" 100377 100385 100585 100590) (-105 "CACHSET.spad" 100001 100009 100367 100372) (-104 "CABMON.spad" 99556 99564 99991 99996) (-103 "BYTEORD.spad" 99231 99239 99546 99551) (-102 "BYTEBUF.spad" 97198 97206 98484 98511) (-101 "BYTE.spad" 96673 96681 97188 97193) (-100 "BTREE.spad" 95811 95821 96345 96372) (-99 "BTOURN.spad" 94882 94891 95483 95510) (-98 "BTCAT.spad" 94275 94284 94850 94877) (-97 "BTCAT.spad" 93688 93699 94265 94270) (-96 "BTAGG.spad" 93155 93162 93656 93683) (-95 "BTAGG.spad" 92642 92651 93145 93150) (-94 "BSTREE.spad" 91449 91458 92314 92341) (-93 "BRILL.spad" 89655 89665 91439 91444) (-92 "BRAGG.spad" 88612 88621 89645 89650) (-91 "BRAGG.spad" 87533 87544 88568 88573) (-90 "BPADICRT.spad" 85593 85604 85839 85932) (-89 "BPADIC.spad" 85266 85277 85519 85588) (-88 "BOUNDZRO.spad" 84923 84939 85256 85261) (-87 "BOP1.spad" 82382 82391 84913 84918) (-86 "BOP.spad" 77525 77532 82372 82377) (-85 "BOOLEAN.spad" 77074 77081 77515 77520) (-84 "BOOLE.spad" 76725 76732 77064 77069) (-83 "BOOLE.spad" 76374 76383 76715 76720) (-82 "BMODULE.spad" 76087 76098 76342 76369) (-81 "BITS.spad" 75519 75526 75733 75760) (-80 "catdef.spad" 75402 75412 75509 75514) (-79 "catdef.spad" 75153 75163 75392 75397) (-78 "BINDING.spad" 74575 74582 75143 75148) (-77 "BINARY.spad" 72810 72817 73165 73258) (-76 "BGAGG.spad" 72016 72025 72790 72805) (-75 "BGAGG.spad" 71230 71241 72006 72011) (-74 "BEZOUT.spad" 70371 70397 71180 71185) (-73 "BBTREE.spad" 67314 67323 70043 70070) (-72 "BASTYPE.spad" 66814 66821 67304 67309) (-71 "BASTYPE.spad" 66312 66321 66804 66809) (-70 "BALFACT.spad" 65772 65784 66302 66307) (-69 "AUTOMOR.spad" 65223 65232 65752 65767) (-68 "ATTREG.spad" 61946 61953 64975 65218) (-67 "ATTRAST.spad" 61663 61670 61936 61941) (-66 "ATRIG.spad" 61133 61140 61653 61658) (-65 "ATRIG.spad" 60601 60610 61123 61128) (-64 "ASTCAT.spad" 60505 60512 60591 60596) (-63 "ASTCAT.spad" 60407 60416 60495 60500) (-62 "ASTACK.spad" 59811 59820 60079 60106) (-61 "ASSOCEQ.spad" 58645 58656 59767 59772) (-60 "ARRAY2.spad" 58078 58087 58317 58344) (-59 "ARRAY12.spad" 56791 56802 58068 58073) (-58 "ARRAY1.spad" 55670 55679 56016 56043) (-57 "ARR2CAT.spad" 51452 51473 55638 55665) (-56 "ARR2CAT.spad" 47254 47277 51442 51447) (-55 "ARITY.spad" 46626 46633 47244 47249) (-54 "APPRULE.spad" 45910 45932 46616 46621) (-53 "APPLYORE.spad" 45529 45542 45900 45905) (-52 "ANY1.spad" 44600 44609 45519 45524) (-51 "ANY.spad" 43451 43458 44590 44595) (-50 "ANTISYM.spad" 41896 41912 43431 43446) (-49 "ANON.spad" 41605 41612 41886 41891) (-48 "AN.spad" 40073 40080 41436 41529) (-47 "AMR.spad" 38258 38269 39971 40068) (-46 "AMR.spad" 36306 36319 38021 38026) (-45 "ALIST.spad" 33544 33565 33894 33921) (-44 "ALGSC.spad" 32679 32705 33416 33469) (-43 "ALGPKG.spad" 28462 28473 32635 32640) (-42 "ALGMFACT.spad" 27655 27669 28452 28457) (-41 "ALGMANIP.spad" 25156 25171 27499 27504) (-40 "ALGFF.spad" 22974 23001 23191 23347) (-39 "ALGFACT.spad" 22093 22103 22964 22969) (-38 "ALGEBRA.spad" 21926 21935 22049 22088) (-37 "ALGEBRA.spad" 21791 21802 21916 21921) (-36 "ALAGG.spad" 21303 21324 21759 21786) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-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 1962172 1962177 1962182 1962187) (-2 NIL 1962152 1962157 1962162 1962167) (-1 NIL 1962132 1962137 1962142 1962147) (0 NIL 1962112 1962117 1962122 1962127) (-1209 "ZMOD.spad" 1961921 1961934 1962050 1962107) (-1208 "ZLINDEP.spad" 1961019 1961030 1961911 1961916) (-1207 "ZDSOLVE.spad" 1950980 1951002 1961009 1961014) (-1206 "YSTREAM.spad" 1950475 1950486 1950970 1950975) (-1205 "YDIAGRAM.spad" 1950109 1950118 1950465 1950470) (-1204 "XRPOLY.spad" 1949329 1949349 1949965 1950034) (-1203 "XPR.spad" 1947124 1947137 1949047 1949146) (-1202 "XPOLYC.spad" 1946443 1946459 1947050 1947119) (-1201 "XPOLY.spad" 1945998 1946009 1946299 1946368) (-1200 "XPBWPOLY.spad" 1944469 1944489 1945804 1945873) (-1199 "XFALG.spad" 1941517 1941533 1944395 1944464) (-1198 "XF.spad" 1939980 1939995 1941419 1941512) (-1197 "XF.spad" 1938423 1938440 1939864 1939869) (-1196 "XEXPPKG.spad" 1937682 1937708 1938413 1938418) (-1195 "XDPOLY.spad" 1937296 1937312 1937538 1937607) (-1194 "XALG.spad" 1936964 1936975 1937252 1937291) (-1193 "WUTSET.spad" 1932967 1932984 1936598 1936625) (-1192 "WP.spad" 1932174 1932218 1932825 1932892) (-1191 "WHILEAST.spad" 1931972 1931981 1932164 1932169) (-1190 "WHEREAST.spad" 1931643 1931652 1931962 1931967) (-1189 "WFFINTBS.spad" 1929306 1929328 1931633 1931638) (-1188 "WEIER.spad" 1927528 1927539 1929296 1929301) (-1187 "VSPACE.spad" 1927201 1927212 1927496 1927523) (-1186 "VSPACE.spad" 1926894 1926907 1927191 1927196) (-1185 "VOID.spad" 1926571 1926580 1926884 1926889) (-1184 "VIEWDEF.spad" 1921772 1921781 1926561 1926566) (-1183 "VIEW3D.spad" 1905733 1905742 1921762 1921767) (-1182 "VIEW2D.spad" 1893632 1893641 1905723 1905728) (-1181 "VIEW.spad" 1891352 1891361 1893622 1893627) (-1180 "VECTOR2.spad" 1889991 1890004 1891342 1891347) (-1179 "VECTOR.spad" 1888710 1888721 1888961 1888988) (-1178 "VECTCAT.spad" 1886622 1886633 1888678 1888705) (-1177 "VECTCAT.spad" 1884343 1884356 1886401 1886406) (-1176 "VARIABLE.spad" 1884123 1884138 1884333 1884338) (-1175 "UTYPE.spad" 1883767 1883776 1884113 1884118) (-1174 "UTSODETL.spad" 1883062 1883086 1883723 1883728) (-1173 "UTSODE.spad" 1881278 1881298 1883052 1883057) (-1172 "UTSCAT.spad" 1878757 1878773 1881176 1881273) (-1171 "UTSCAT.spad" 1875904 1875922 1878325 1878330) (-1170 "UTS2.spad" 1875499 1875534 1875894 1875899) (-1169 "UTS.spad" 1870511 1870539 1874031 1874128) (-1168 "URAGG.spad" 1865232 1865243 1870501 1870506) (-1167 "URAGG.spad" 1859917 1859930 1865188 1865193) (-1166 "UPXSSING.spad" 1857685 1857711 1859121 1859254) (-1165 "UPXSCONS.spad" 1855503 1855523 1855876 1856025) (-1164 "UPXSCCA.spad" 1854074 1854094 1855349 1855498) (-1163 "UPXSCCA.spad" 1852787 1852809 1854064 1854069) (-1162 "UPXSCAT.spad" 1851376 1851392 1852633 1852782) (-1161 "UPXS2.spad" 1850919 1850972 1851366 1851371) (-1160 "UPXS.spad" 1848274 1848302 1849110 1849259) (-1159 "UPSQFREE.spad" 1846689 1846703 1848264 1848269) (-1158 "UPSCAT.spad" 1844484 1844508 1846587 1846684) (-1157 "UPSCAT.spad" 1841980 1842006 1844085 1844090) (-1156 "UPOLYC2.spad" 1841451 1841470 1841970 1841975) (-1155 "UPOLYC.spad" 1836531 1836542 1841293 1841446) (-1154 "UPOLYC.spad" 1831529 1831542 1836293 1836298) (-1153 "UPMP.spad" 1830461 1830474 1831519 1831524) (-1152 "UPDIVP.spad" 1830026 1830040 1830451 1830456) (-1151 "UPDECOMP.spad" 1828287 1828301 1830016 1830021) (-1150 "UPCDEN.spad" 1827504 1827520 1828277 1828282) (-1149 "UP2.spad" 1826868 1826889 1827494 1827499) (-1148 "UP.spad" 1824338 1824353 1824725 1824878) (-1147 "UNISEG2.spad" 1823835 1823848 1824294 1824299) (-1146 "UNISEG.spad" 1823188 1823199 1823754 1823759) (-1145 "UNIFACT.spad" 1822291 1822303 1823178 1823183) (-1144 "ULSCONS.spad" 1816334 1816354 1816704 1816853) (-1143 "ULSCCAT.spad" 1814071 1814091 1816180 1816329) (-1142 "ULSCCAT.spad" 1811916 1811938 1814027 1814032) (-1141 "ULSCAT.spad" 1810156 1810172 1811762 1811911) (-1140 "ULS2.spad" 1809670 1809723 1810146 1810151) (-1139 "ULS.spad" 1801936 1801964 1802881 1803304) (-1138 "UINT8.spad" 1801813 1801822 1801926 1801931) (-1137 "UINT64.spad" 1801689 1801698 1801803 1801808) (-1136 "UINT32.spad" 1801565 1801574 1801679 1801684) (-1135 "UINT16.spad" 1801441 1801450 1801555 1801560) (-1134 "UFD.spad" 1800506 1800515 1801367 1801436) (-1133 "UFD.spad" 1799633 1799644 1800496 1800501) (-1132 "UDVO.spad" 1798514 1798523 1799623 1799628) (-1131 "UDPO.spad" 1796095 1796106 1798470 1798475) (-1130 "TYPEAST.spad" 1796014 1796023 1796085 1796090) (-1129 "TYPE.spad" 1795946 1795955 1796004 1796009) (-1128 "TWOFACT.spad" 1794598 1794613 1795936 1795941) (-1127 "TUPLE.spad" 1794105 1794116 1794510 1794515) (-1126 "TUBETOOL.spad" 1790972 1790981 1794095 1794100) (-1125 "TUBE.spad" 1789619 1789636 1790962 1790967) (-1124 "TSETCAT.spad" 1777690 1777707 1789587 1789614) (-1123 "TSETCAT.spad" 1765747 1765766 1777646 1777651) (-1122 "TS.spad" 1764375 1764391 1765341 1765438) (-1121 "TRMANIP.spad" 1758739 1758756 1764063 1764068) (-1120 "TRIMAT.spad" 1757702 1757727 1758729 1758734) (-1119 "TRIGMNIP.spad" 1756229 1756246 1757692 1757697) (-1118 "TRIGCAT.spad" 1755741 1755750 1756219 1756224) (-1117 "TRIGCAT.spad" 1755251 1755262 1755731 1755736) (-1116 "TREE.spad" 1753891 1753902 1754923 1754950) (-1115 "TRANFUN.spad" 1753730 1753739 1753881 1753886) (-1114 "TRANFUN.spad" 1753567 1753578 1753720 1753725) (-1113 "TOPSP.spad" 1753241 1753250 1753557 1753562) (-1112 "TOOLSIGN.spad" 1752904 1752915 1753231 1753236) (-1111 "TEXTFILE.spad" 1751465 1751474 1752894 1752899) (-1110 "TEX1.spad" 1751021 1751032 1751455 1751460) (-1109 "TEX.spad" 1748215 1748224 1751011 1751016) (-1108 "TBCMPPK.spad" 1746316 1746339 1748205 1748210) (-1107 "TBAGG.spad" 1745374 1745397 1746296 1746311) (-1106 "TBAGG.spad" 1744440 1744465 1745364 1745369) (-1105 "TANEXP.spad" 1743848 1743859 1744430 1744435) (-1104 "TALGOP.spad" 1743572 1743583 1743838 1743843) (-1103 "TABLEAU.spad" 1743053 1743064 1743562 1743567) (-1102 "TABLE.spad" 1741328 1741351 1741598 1741625) (-1101 "TABLBUMP.spad" 1738107 1738118 1741318 1741323) (-1100 "SYSTEM.spad" 1737335 1737344 1738097 1738102) (-1099 "SYSSOLP.spad" 1734818 1734829 1737325 1737330) (-1098 "SYSPTR.spad" 1734717 1734726 1734808 1734813) (-1097 "SYSNNI.spad" 1733940 1733951 1734707 1734712) (-1096 "SYSINT.spad" 1733344 1733355 1733930 1733935) (-1095 "SYNTAX.spad" 1729678 1729687 1733334 1733339) (-1094 "SYMTAB.spad" 1727746 1727755 1729668 1729673) (-1093 "SYMS.spad" 1723775 1723784 1727736 1727741) (-1092 "SYMPOLY.spad" 1722908 1722919 1722990 1723117) (-1091 "SYMFUNC.spad" 1722409 1722420 1722898 1722903) (-1090 "SYMBOL.spad" 1719904 1719913 1722399 1722404) (-1089 "SUTS.spad" 1717017 1717045 1718436 1718533) (-1088 "SUPXS.spad" 1714359 1714387 1715208 1715357) (-1087 "SUPFRACF.spad" 1713464 1713482 1714349 1714354) (-1086 "SUP2.spad" 1712856 1712869 1713454 1713459) (-1085 "SUP.spad" 1709940 1709951 1710713 1710866) (-1084 "SUMRF.spad" 1708914 1708925 1709930 1709935) (-1083 "SUMFS.spad" 1708543 1708560 1708904 1708909) (-1082 "SULS.spad" 1700796 1700824 1701754 1702177) (-1081 "syntax.spad" 1700565 1700574 1700786 1700791) (-1080 "SUCH.spad" 1700255 1700270 1700555 1700560) (-1079 "SUBSPACE.spad" 1692386 1692401 1700245 1700250) (-1078 "SUBRESP.spad" 1691556 1691570 1692342 1692347) (-1077 "STTFNC.spad" 1688024 1688040 1691546 1691551) (-1076 "STTF.spad" 1684123 1684139 1688014 1688019) (-1075 "STTAYLOR.spad" 1676800 1676811 1684030 1684035) (-1074 "STRTBL.spad" 1675187 1675204 1675336 1675363) (-1073 "STRING.spad" 1674055 1674064 1674440 1674467) (-1072 "STREAM3.spad" 1673628 1673643 1674045 1674050) (-1071 "STREAM2.spad" 1672756 1672769 1673618 1673623) (-1070 "STREAM1.spad" 1672462 1672473 1672746 1672751) (-1069 "STREAM.spad" 1669458 1669469 1672065 1672080) (-1068 "STINPROD.spad" 1668394 1668410 1669448 1669453) (-1067 "STEPAST.spad" 1667628 1667637 1668384 1668389) (-1066 "STEP.spad" 1666945 1666954 1667618 1667623) (-1065 "STBL.spad" 1665335 1665363 1665502 1665517) (-1064 "STAGG.spad" 1664034 1664045 1665325 1665330) (-1063 "STAGG.spad" 1662731 1662744 1664024 1664029) (-1062 "STACK.spad" 1662153 1662164 1662403 1662430) (-1061 "SRING.spad" 1661913 1661922 1662143 1662148) (-1060 "SREGSET.spad" 1659645 1659662 1661547 1661574) (-1059 "SRDCMPK.spad" 1658222 1658242 1659635 1659640) (-1058 "SRAGG.spad" 1653405 1653414 1658190 1658217) (-1057 "SRAGG.spad" 1648608 1648619 1653395 1653400) (-1056 "SQMATRIX.spad" 1646285 1646303 1647201 1647288) (-1055 "SPLTREE.spad" 1641027 1641040 1645823 1645850) (-1054 "SPLNODE.spad" 1637647 1637660 1641017 1641022) (-1053 "SPFCAT.spad" 1636456 1636465 1637637 1637642) (-1052 "SPECOUT.spad" 1635008 1635017 1636446 1636451) (-1051 "SPADXPT.spad" 1627099 1627108 1634998 1635003) (-1050 "spad-parser.spad" 1626564 1626573 1627089 1627094) (-1049 "SPADAST.spad" 1626265 1626274 1626554 1626559) (-1048 "SPACEC.spad" 1610480 1610491 1626255 1626260) (-1047 "SPACE3.spad" 1610256 1610267 1610470 1610475) (-1046 "SORTPAK.spad" 1609805 1609818 1610212 1610217) (-1045 "SOLVETRA.spad" 1607568 1607579 1609795 1609800) (-1044 "SOLVESER.spad" 1606024 1606035 1607558 1607563) (-1043 "SOLVERAD.spad" 1602050 1602061 1606014 1606019) (-1042 "SOLVEFOR.spad" 1600512 1600530 1602040 1602045) (-1041 "SNTSCAT.spad" 1600112 1600129 1600480 1600507) (-1040 "SMTS.spad" 1598429 1598455 1599706 1599803) (-1039 "SMP.spad" 1596237 1596257 1596627 1596754) (-1038 "SMITH.spad" 1595082 1595107 1596227 1596232) (-1037 "SMATCAT.spad" 1593200 1593230 1595026 1595077) (-1036 "SMATCAT.spad" 1591250 1591282 1593078 1593083) (-1035 "SKAGG.spad" 1590219 1590230 1591218 1591245) (-1034 "SINT.spad" 1589518 1589527 1590085 1590214) (-1033 "SIMPAN.spad" 1589246 1589255 1589508 1589513) (-1032 "SIGNRF.spad" 1588371 1588382 1589236 1589241) (-1031 "SIGNEF.spad" 1587657 1587674 1588361 1588366) (-1030 "syntax.spad" 1587074 1587083 1587647 1587652) (-1029 "SIG.spad" 1586436 1586445 1587064 1587069) (-1028 "SHP.spad" 1584380 1584395 1586392 1586397) (-1027 "SHDP.spad" 1573873 1573900 1574390 1574487) (-1026 "SGROUP.spad" 1573481 1573490 1573863 1573868) (-1025 "SGROUP.spad" 1573087 1573098 1573471 1573476) (-1024 "catdef.spad" 1572797 1572809 1572908 1573082) (-1023 "catdef.spad" 1572353 1572365 1572618 1572792) (-1022 "SGCF.spad" 1565492 1565501 1572343 1572348) (-1021 "SFRTCAT.spad" 1564438 1564455 1565460 1565487) (-1020 "SFRGCD.spad" 1563501 1563521 1564428 1564433) (-1019 "SFQCMPK.spad" 1558314 1558334 1563491 1563496) (-1018 "SEXOF.spad" 1558157 1558197 1558304 1558309) (-1017 "SEXCAT.spad" 1555985 1556025 1558147 1558152) (-1016 "SEX.spad" 1555877 1555886 1555975 1555980) (-1015 "SETMN.spad" 1554337 1554354 1555867 1555872) (-1014 "SETCAT.spad" 1553822 1553831 1554327 1554332) (-1013 "SETCAT.spad" 1553305 1553316 1553812 1553817) (-1012 "SETAGG.spad" 1549854 1549865 1553285 1553300) (-1011 "SETAGG.spad" 1546411 1546424 1549844 1549849) (-1010 "SET.spad" 1544720 1544731 1545817 1545856) (-1009 "syntax.spad" 1544423 1544432 1544710 1544715) (-1008 "SEGXCAT.spad" 1543579 1543592 1544413 1544418) (-1007 "SEGCAT.spad" 1542504 1542515 1543569 1543574) (-1006 "SEGBIND2.spad" 1542202 1542215 1542494 1542499) (-1005 "SEGBIND.spad" 1541960 1541971 1542149 1542154) (-1004 "SEGAST.spad" 1541690 1541699 1541950 1541955) (-1003 "SEG2.spad" 1541125 1541138 1541646 1541651) (-1002 "SEG.spad" 1540938 1540949 1541044 1541049) (-1001 "SDVAR.spad" 1540214 1540225 1540928 1540933) (-1000 "SDPOL.spad" 1537906 1537917 1538197 1538324) (-999 "SCPKG.spad" 1535996 1536006 1537896 1537901) (-998 "SCOPE.spad" 1535174 1535182 1535986 1535991) (-997 "SCACHE.spad" 1533871 1533881 1535164 1535169) (-996 "SASTCAT.spad" 1533781 1533789 1533861 1533866) (-995 "SAOS.spad" 1533654 1533662 1533771 1533776) (-994 "SAERFFC.spad" 1533368 1533387 1533644 1533649) (-993 "SAEFACT.spad" 1533070 1533089 1533358 1533363) (-992 "SAE.spad" 1530721 1530736 1531331 1531466) (-991 "RURPK.spad" 1528381 1528396 1530711 1530716) (-990 "RULESET.spad" 1527835 1527858 1528371 1528376) (-989 "RULECOLD.spad" 1527688 1527700 1527825 1527830) (-988 "RULE.spad" 1525937 1525960 1527678 1527683) (-987 "RTVALUE.spad" 1525673 1525681 1525927 1525932) (-986 "syntax.spad" 1525391 1525399 1525663 1525668) (-985 "RSETGCD.spad" 1521834 1521853 1525381 1525386) (-984 "RSETCAT.spad" 1511803 1511819 1521802 1521829) (-983 "RSETCAT.spad" 1501792 1501810 1511793 1511798) (-982 "RSDCMPK.spad" 1500293 1500312 1501782 1501787) (-981 "RRCC.spad" 1498678 1498707 1500283 1500288) (-980 "RRCC.spad" 1497061 1497092 1498668 1498673) (-979 "RPTAST.spad" 1496764 1496772 1497051 1497056) (-978 "RPOLCAT.spad" 1476269 1476283 1496632 1496759) (-977 "RPOLCAT.spad" 1455567 1455583 1475932 1475937) (-976 "ROMAN.spad" 1454896 1454904 1455433 1455562) (-975 "ROIRC.spad" 1453977 1454008 1454886 1454891) (-974 "RNS.spad" 1452954 1452962 1453879 1453972) (-973 "RNS.spad" 1452017 1452027 1452944 1452949) (-972 "RNGBIND.spad" 1451178 1451191 1451972 1451977) (-971 "RNG.spad" 1450787 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1430593 1430605 1431163 1431168) (-951 "RETRACT.spad" 1430022 1430032 1430583 1430588) (-950 "RETRACT.spad" 1429449 1429461 1430012 1430017) (-949 "RETAST.spad" 1429262 1429270 1429439 1429444) (-948 "RESRING.spad" 1428610 1428656 1429200 1429257) (-947 "RESLATC.spad" 1427935 1427945 1428600 1428605) (-946 "REPSQ.spad" 1427667 1427677 1427925 1427930) (-945 "REPDB.spad" 1427375 1427385 1427657 1427662) (-944 "REP2.spad" 1417090 1417100 1427217 1427222) (-943 "REP1.spad" 1411311 1411321 1417040 1417045) (-942 "REP.spad" 1408866 1408874 1411301 1411306) (-941 "REGSET.spad" 1406692 1406708 1408500 1408527) (-940 "REF.spad" 1406211 1406221 1406682 1406687) (-939 "REDORDER.spad" 1405418 1405434 1406201 1406206) (-938 "RECLOS.spad" 1404315 1404334 1405018 1405111) (-937 "REALSOLV.spad" 1403456 1403464 1404305 1404310) (-936 "REAL0Q.spad" 1400755 1400769 1403446 1403451) (-935 "REAL0.spad" 1397600 1397614 1400745 1400750) (-934 "REAL.spad" 1397473 1397481 1397590 1397595) (-933 "RDUCEAST.spad" 1397195 1397203 1397463 1397468) (-932 "RDIV.spad" 1396851 1396875 1397185 1397190) (-931 "RDIST.spad" 1396419 1396429 1396841 1396846) (-930 "RDETRS.spad" 1395284 1395301 1396409 1396414) (-929 "RDETR.spad" 1393424 1393441 1395274 1395279) (-928 "RDEEFS.spad" 1392524 1392540 1393414 1393419) (-927 "RDEEF.spad" 1391535 1391551 1392514 1392519) (-926 "RCFIELD.spad" 1388754 1388762 1391437 1391530) (-925 "RCFIELD.spad" 1386059 1386069 1388744 1388749) (-924 "RCAGG.spad" 1383996 1384006 1386049 1386054) (-923 "RCAGG.spad" 1381860 1381872 1383915 1383920) (-922 "RATRET.spad" 1381221 1381231 1381850 1381855) (-921 "RATFACT.spad" 1380914 1380925 1381211 1381216) (-920 "RANDSRC.spad" 1380234 1380242 1380904 1380909) (-919 "RADUTIL.spad" 1379991 1379999 1380224 1380229) (-918 "RADIX.spad" 1377036 1377049 1378581 1378674) (-917 "RADFF.spad" 1374953 1374989 1375071 1375227) (-916 "RADCAT.spad" 1374549 1374557 1374943 1374948) (-915 "RADCAT.spad" 1374143 1374153 1374539 1374544) (-914 "QUEUE.spad" 1373557 1373567 1373815 1373842) (-913 "QUATCT2.spad" 1373178 1373196 1373547 1373552) (-912 "QUATCAT.spad" 1371349 1371359 1373108 1373173) (-911 "QUATCAT.spad" 1369285 1369297 1371046 1371051) (-910 "QUAT.spad" 1367892 1367902 1368234 1368299) (-909 "QUAGG.spad" 1366726 1366736 1367860 1367887) (-908 "QQUTAST.spad" 1366495 1366503 1366716 1366721) (-907 "QFORM.spad" 1366114 1366128 1366485 1366490) (-906 "QFCAT2.spad" 1365807 1365823 1366104 1366109) (-905 "QFCAT.spad" 1364510 1364520 1365709 1365802) (-904 "QFCAT.spad" 1362846 1362858 1364047 1364052) (-903 "QEQUAT.spad" 1362405 1362413 1362836 1362841) (-902 "QCMPACK.spad" 1357320 1357339 1362395 1362400) (-901 "QALGSET2.spad" 1355316 1355334 1357310 1357315) (-900 "QALGSET.spad" 1351421 1351453 1355230 1355235) (-899 "PWFFINTB.spad" 1348837 1348858 1351411 1351416) (-898 "PUSHVAR.spad" 1348176 1348195 1348827 1348832) (-897 "PTRANFN.spad" 1344312 1344322 1348166 1348171) (-896 "PTPACK.spad" 1341400 1341410 1344302 1344307) (-895 "PTFUNC2.spad" 1341223 1341237 1341390 1341395) (-894 "PTCAT.spad" 1340478 1340488 1341191 1341218) (-893 "PSQFR.spad" 1339793 1339817 1340468 1340473) (-892 "PSEUDLIN.spad" 1338679 1338689 1339783 1339788) (-891 "PSETPK.spad" 1325384 1325400 1338557 1338562) (-890 "PSETCAT.spad" 1319784 1319807 1325364 1325379) (-889 "PSETCAT.spad" 1314158 1314183 1319740 1319745) (-888 "PSCURVE.spad" 1313157 1313165 1314148 1314153) (-887 "PSCAT.spad" 1311940 1311969 1313055 1313152) (-886 "PSCAT.spad" 1310813 1310844 1311930 1311935) (-885 "PRTITION.spad" 1309511 1309519 1310803 1310808) (-884 "PRTDAST.spad" 1309230 1309238 1309501 1309506) (-883 "PRS.spad" 1298848 1298865 1309186 1309191) (-882 "PRQAGG.spad" 1298283 1298293 1298816 1298843) (-881 "PROPLOG.spad" 1297887 1297895 1298273 1298278) (-880 "PROPFUN2.spad" 1297510 1297523 1297877 1297882) (-879 "PROPFUN1.spad" 1296916 1296927 1297500 1297505) (-878 "PROPFRML.spad" 1295484 1295495 1296906 1296911) (-877 "PROPERTY.spad" 1294980 1294988 1295474 1295479) (-876 "PRODUCT.spad" 1292677 1292689 1292961 1293016) (-875 "PRINT.spad" 1292429 1292437 1292667 1292672) (-874 "PRIMES.spad" 1290690 1290700 1292419 1292424) (-873 "PRIMELT.spad" 1288811 1288825 1290680 1290685) (-872 "PRIMCAT.spad" 1288454 1288462 1288801 1288806) (-871 "PRIMARR2.spad" 1287221 1287233 1288444 1288449) (-870 "PRIMARR.spad" 1286276 1286286 1286446 1286473) (-869 "PREASSOC.spad" 1285658 1285670 1286266 1286271) (-868 "PR.spad" 1284176 1284188 1284875 1285002) (-867 "PPCURVE.spad" 1283313 1283321 1284166 1284171) (-866 "PORTNUM.spad" 1283104 1283112 1283303 1283308) (-865 "POLYROOT.spad" 1281953 1281975 1283060 1283065) (-864 "POLYLIFT.spad" 1281218 1281241 1281943 1281948) (-863 "POLYCATQ.spad" 1279344 1279366 1281208 1281213) (-862 "POLYCAT.spad" 1272846 1272867 1279212 1279339) (-861 "POLYCAT.spad" 1265868 1265891 1272236 1272241) (-860 "POLY2UP.spad" 1265320 1265334 1265858 1265863) (-859 "POLY2.spad" 1264917 1264929 1265310 1265315) (-858 "POLY.spad" 1262585 1262595 1263100 1263227) (-857 "POLUTIL.spad" 1261550 1261579 1262541 1262546) (-856 "POLTOPOL.spad" 1260298 1260313 1261540 1261545) (-855 "POINT.spad" 1259181 1259191 1259268 1259295) (-854 "PNTHEORY.spad" 1255883 1255891 1259171 1259176) (-853 "PMTOOLS.spad" 1254658 1254672 1255873 1255878) (-852 "PMSYM.spad" 1254207 1254217 1254648 1254653) (-851 "PMQFCAT.spad" 1253798 1253812 1254197 1254202) (-850 "PMPREDFS.spad" 1253260 1253282 1253788 1253793) (-849 "PMPRED.spad" 1252747 1252761 1253250 1253255) (-848 "PMPLCAT.spad" 1251824 1251842 1252676 1252681) (-847 "PMLSAGG.spad" 1251409 1251423 1251814 1251819) (-846 "PMKERNEL.spad" 1250988 1251000 1251399 1251404) (-845 "PMINS.spad" 1250568 1250578 1250978 1250983) (-844 "PMFS.spad" 1250145 1250163 1250558 1250563) (-843 "PMDOWN.spad" 1249435 1249449 1250135 1250140) (-842 "PMASSFS.spad" 1248410 1248426 1249425 1249430) (-841 "PMASS.spad" 1247428 1247436 1248400 1248405) (-840 "PLOTTOOL.spad" 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1201417 1203625 1203630) (-820 "PFBRU.spad" 1199295 1199307 1201397 1201402) (-819 "PFBR.spad" 1196855 1196878 1199285 1199290) (-818 "PF.spad" 1196429 1196441 1196660 1196753) (-817 "PERMGRP.spad" 1191199 1191209 1196419 1196424) (-816 "PERMCAT.spad" 1189860 1189870 1191179 1191194) (-815 "PERMAN.spad" 1188416 1188430 1189850 1189855) (-814 "PERM.spad" 1184226 1184236 1188249 1188264) (-813 "PENDTREE.spad" 1183640 1183650 1183920 1183925) (-812 "PDSPC.spad" 1182453 1182463 1183630 1183635) (-811 "PDSPC.spad" 1181264 1181276 1182443 1182448) (-810 "PDRING.spad" 1181106 1181116 1181244 1181259) (-809 "PDMOD.spad" 1180922 1180934 1181074 1181101) (-808 "PDECOMP.spad" 1180392 1180409 1180912 1180917) (-807 "PDDOM.spad" 1179830 1179843 1180382 1180387) (-806 "PDDOM.spad" 1179266 1179281 1179820 1179825) (-805 "PCOMP.spad" 1179119 1179132 1179256 1179261) (-804 "PBWLB.spad" 1177717 1177734 1179109 1179114) (-803 "PATTERN2.spad" 1177455 1177467 1177707 1177712) (-802 "PATTERN1.spad" 1175799 1175815 1177445 1177450) (-801 "PATTERN.spad" 1170374 1170384 1175789 1175794) (-800 "PATRES2.spad" 1170046 1170060 1170364 1170369) (-799 "PATRES.spad" 1167629 1167641 1170036 1170041) (-798 "PATMATCH.spad" 1165870 1165901 1167381 1167386) (-797 "PATMAB.spad" 1165299 1165309 1165860 1165865) (-796 "PATLRES.spad" 1164385 1164399 1165289 1165294) (-795 "PATAB.spad" 1164149 1164159 1164375 1164380) (-794 "PARTPERM.spad" 1162205 1162213 1164139 1164144) (-793 "PARSURF.spad" 1161639 1161667 1162195 1162200) (-792 "PARSU2.spad" 1161436 1161452 1161629 1161634) (-791 "script-parser.spad" 1160956 1160964 1161426 1161431) (-790 "PARSCURV.spad" 1160390 1160418 1160946 1160951) (-789 "PARSC2.spad" 1160181 1160197 1160380 1160385) (-788 "PARPCURV.spad" 1159643 1159671 1160171 1160176) (-787 "PARPC2.spad" 1159434 1159450 1159633 1159638) (-786 "PARAMAST.spad" 1158562 1158570 1159424 1159429) (-785 "PAN2EXPR.spad" 1157974 1157982 1158552 1158557) (-784 "PALETTE.spad" 1157088 1157096 1157964 1157969) (-783 "PAIR.spad" 1156162 1156175 1156731 1156736) (-782 "PADICRC.spad" 1153567 1153585 1154730 1154823) (-781 "PADICRAT.spad" 1151627 1151639 1151840 1151933) (-780 "PADICCT.spad" 1150176 1150188 1151553 1151622) (-779 "PADIC.spad" 1149879 1149891 1150102 1150171) (-778 "PADEPAC.spad" 1148568 1148587 1149869 1149874) (-777 "PADE.spad" 1147320 1147336 1148558 1148563) (-776 "OWP.spad" 1146568 1146598 1147178 1147245) (-775 "OVERSET.spad" 1146141 1146149 1146558 1146563) (-774 "OVAR.spad" 1145922 1145945 1146131 1146136) (-773 "OUTFORM.spad" 1135330 1135338 1145912 1145917) (-772 "OUTBFILE.spad" 1134764 1134772 1135320 1135325) (-771 "OUTBCON.spad" 1133834 1133842 1134754 1134759) (-770 "OUTBCON.spad" 1132902 1132912 1133824 1133829) (-769 "OUT.spad" 1132020 1132028 1132892 1132897) (-768 "OSI.spad" 1131495 1131503 1132010 1132015) (-767 "OSGROUP.spad" 1131413 1131421 1131485 1131490) (-766 "ORTHPOL.spad" 1129924 1129934 1131356 1131361) (-765 "OREUP.spad" 1129418 1129446 1129645 1129684) (-764 "ORESUP.spad" 1128760 1128784 1129139 1129178) (-763 "OREPCTO.spad" 1126649 1126661 1128680 1128685) (-762 "OREPCAT.spad" 1120836 1120846 1126605 1126644) (-761 "OREPCAT.spad" 1114913 1114925 1120684 1120689) (-760 "ORDTYPE.spad" 1114150 1114158 1114903 1114908) (-759 "ORDTYPE.spad" 1113385 1113395 1114140 1114145) (-758 "ORDSTRCT.spad" 1113171 1113186 1113334 1113339) (-757 "ORDSET.spad" 1112871 1112879 1113161 1113166) (-756 "ORDRING.spad" 1112688 1112696 1112851 1112866) (-755 "ORDMON.spad" 1112543 1112551 1112678 1112683) (-754 "ORDFUNS.spad" 1111675 1111691 1112533 1112538) (-753 "ORDFIN.spad" 1111495 1111503 1111665 1111670) (-752 "ORDCOMP2.spad" 1110788 1110800 1111485 1111490) (-751 "ORDCOMP.spad" 1109314 1109324 1110396 1110425) (-750 "OPSIG.spad" 1108976 1108984 1109304 1109309) (-749 "OPQUERY.spad" 1108557 1108565 1108966 1108971) (-748 "OPERCAT.spad" 1108023 1108033 1108547 1108552) (-747 "OPERCAT.spad" 1107487 1107499 1108013 1108018) (-746 "OP.spad" 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"ODEINT.spad" 1071492 1071508 1072047 1072052) (-726 "ODEEF.spad" 1066987 1067003 1071482 1071487) (-725 "ODECONST.spad" 1066532 1066550 1066977 1066982) (-724 "OCTCT2.spad" 1066173 1066191 1066522 1066527) (-723 "OCT.spad" 1064488 1064498 1065202 1065241) (-722 "OCAMON.spad" 1064336 1064344 1064478 1064483) (-721 "OC.spad" 1062132 1062142 1064292 1064331) (-720 "OC.spad" 1059667 1059679 1061829 1061834) (-719 "OASGP.spad" 1059482 1059490 1059657 1059662) (-718 "OAMONS.spad" 1059004 1059012 1059472 1059477) (-717 "OAMON.spad" 1058762 1058770 1058994 1058999) (-716 "OAMON.spad" 1058518 1058528 1058752 1058757) (-715 "OAGROUP.spad" 1058056 1058064 1058508 1058513) (-714 "OAGROUP.spad" 1057592 1057602 1058046 1058051) (-713 "NUMTUBE.spad" 1057183 1057199 1057582 1057587) (-712 "NUMQUAD.spad" 1045159 1045167 1057173 1057178) (-711 "NUMODE.spad" 1036511 1036519 1045149 1045154) (-710 "NUMFMT.spad" 1035351 1035359 1036501 1036506) (-709 "NUMERIC.spad" 1027466 1027476 1035157 1035162) (-708 "NTSCAT.spad" 1025974 1025990 1027434 1027461) (-707 "NTPOLFN.spad" 1025551 1025561 1025917 1025922) (-706 "NSUP2.spad" 1024943 1024955 1025541 1025546) (-705 "NSUP.spad" 1018380 1018390 1022800 1022953) (-704 "NSMP.spad" 1015292 1015311 1015584 1015711) (-703 "NREP.spad" 1013694 1013708 1015282 1015287) (-702 "NPCOEF.spad" 1012940 1012960 1013684 1013689) (-701 "NORMRETR.spad" 1012538 1012577 1012930 1012935) (-700 "NORMPK.spad" 1010480 1010499 1012528 1012533) (-699 "NORMMA.spad" 1010168 1010194 1010470 1010475) (-698 "NONE1.spad" 1009844 1009854 1010158 1010163) (-697 "NONE.spad" 1009585 1009593 1009834 1009839) (-696 "NODE1.spad" 1009072 1009088 1009575 1009580) (-695 "NNI.spad" 1007967 1007975 1009046 1009067) (-694 "NLINSOL.spad" 1006593 1006603 1007957 1007962) (-693 "NFINTBAS.spad" 1004153 1004170 1006583 1006588) (-692 "NETCLT.spad" 1004127 1004138 1004143 1004148) (-691 "NCODIV.spad" 1002351 1002367 1004117 1004122) (-690 "NCNTFRAC.spad" 1001993 1002007 1002341 1002346) (-689 "NCEP.spad" 1000159 1000173 1001983 1001988) (-688 "NASRING.spad" 999763 999771 1000149 1000154) (-687 "NASRING.spad" 999365 999375 999753 999758) (-686 "NARNG.spad" 998765 998773 999355 999360) (-685 "NARNG.spad" 998163 998173 998755 998760) (-684 "NAALG.spad" 997728 997738 998131 998158) (-683 "NAALG.spad" 997313 997325 997718 997723) (-682 "MULTSQFR.spad" 994271 994288 997303 997308) (-681 "MULTFACT.spad" 993654 993671 994261 994266) (-680 "MTSCAT.spad" 991748 991769 993552 993649) (-679 "MTHING.spad" 991407 991417 991738 991743) (-678 "MSYSCMD.spad" 990841 990849 991397 991402) (-677 "MSETAGG.spad" 990686 990696 990809 990836) (-676 "MSET.spad" 988632 988642 990380 990419) (-675 "MRING.spad" 985609 985621 988340 988407) (-674 "MRF2.spad" 985171 985185 985599 985604) (-673 "MRATFAC.spad" 984717 984734 985161 985166) (-672 "MPRFF.spad" 982757 982776 984707 984712) (-671 "MPOLY.spad" 980561 980576 980920 981047) (-670 "MPCPF.spad" 979825 979844 980551 980556) (-669 "MPC3.spad" 979642 979682 979815 979820) (-668 "MPC2.spad" 979296 979329 979632 979637) (-667 "MONOTOOL.spad" 977647 977664 979286 979291) (-666 "catdef.spad" 977080 977091 977301 977642) (-665 "catdef.spad" 976478 976489 976734 977075) (-664 "MONOID.spad" 975799 975807 976468 976473) (-663 "MONOID.spad" 975118 975128 975789 975794) (-662 "MONOGEN.spad" 973866 973879 974978 975113) (-661 "MONOGEN.spad" 972636 972651 973750 973755) (-660 "MONADWU.spad" 970716 970724 972626 972631) (-659 "MONADWU.spad" 968794 968804 970706 970711) (-658 "MONAD.spad" 967954 967962 968784 968789) (-657 "MONAD.spad" 967112 967122 967944 967949) (-656 "MOEBIUS.spad" 965848 965862 967092 967107) (-655 "MODULE.spad" 965718 965728 965816 965843) (-654 "MODULE.spad" 965608 965620 965708 965713) (-653 "MODRING.spad" 964943 964982 965588 965603) (-652 "MODOP.spad" 963600 963612 964765 964832) (-651 "MODMONOM.spad" 963331 963349 963590 963595) (-650 "MODMON.spad" 960401 960413 961116 961269) (-649 "MODFIELD.spad" 959763 959802 960303 960396) (-648 "MMLFORM.spad" 958623 958631 959753 959758) (-647 "MMAP.spad" 958365 958399 958613 958618) (-646 "MLO.spad" 956824 956834 958321 958360) (-645 "MLIFT.spad" 955436 955453 956814 956819) (-644 "MKUCFUNC.spad" 954971 954989 955426 955431) (-643 "MKRECORD.spad" 954559 954572 954961 954966) (-642 "MKFUNC.spad" 953966 953976 954549 954554) (-641 "MKFLCFN.spad" 952934 952944 953956 953961) (-640 "MKBCFUNC.spad" 952429 952447 952924 952929) (-639 "MHROWRED.spad" 950940 950950 952419 952424) (-638 "MFINFACT.spad" 950340 950362 950930 950935) (-637 "MESH.spad" 948135 948143 950330 950335) (-636 "MDDFACT.spad" 946354 946364 948125 948130) (-635 "MDAGG.spad" 945645 945655 946334 946349) (-634 "MCDEN.spad" 944855 944867 945635 945640) (-633 "MAYBE.spad" 944155 944166 944845 944850) (-632 "MATSTOR.spad" 941471 941481 944145 944150) (-631 "MATRIX.spad" 940250 940260 940734 940761) (-630 "MATLIN.spad" 937618 937642 940134 940139) (-629 "MATCAT2.spad" 936900 936948 937608 937613) (-628 "MATCAT.spad" 928462 928484 936868 936895) (-627 "MATCAT.spad" 919896 919920 928304 928309) (-626 "MAPPKG3.spad" 918811 918825 919886 919891) (-625 "MAPPKG2.spad" 918149 918161 918801 918806) (-624 "MAPPKG1.spad" 916977 916987 918139 918144) (-623 "MAPPAST.spad" 916316 916324 916967 916972) (-622 "MAPHACK3.spad" 916128 916142 916306 916311) (-621 "MAPHACK2.spad" 915897 915909 916118 916123) (-620 "MAPHACK1.spad" 915541 915551 915887 915892) (-619 "MAGMA.spad" 913347 913364 915531 915536) (-618 "MACROAST.spad" 912942 912950 913337 913342) (-617 "LZSTAGG.spad" 910196 910206 912932 912937) (-616 "LZSTAGG.spad" 907448 907460 910186 910191) (-615 "LWORD.spad" 904193 904210 907438 907443) (-614 "LSTAST.spad" 903977 903985 904183 904188) (-613 "LSQM.spad" 902255 902269 902649 902700) (-612 "LSPP.spad" 901790 901807 902245 902250) (-611 "LSMP1.spad" 899633 899647 901780 901785) (-610 "LSMP.spad" 898490 898518 899623 899628) (-609 "LSAGG.spad" 898159 898169 898458 898485) (-608 "LSAGG.spad" 897848 897860 898149 898154) (-607 "LPOLY.spad" 896810 896829 897704 897773) (-606 "LPEFRAC.spad" 896081 896091 896800 896805) (-605 "LOGIC.spad" 895683 895691 896071 896076) (-604 "LOGIC.spad" 895283 895293 895673 895678) (-603 "LODOOPS.spad" 894213 894225 895273 895278) (-602 "LODOF.spad" 893259 893276 894170 894175) (-601 "LODOCAT.spad" 891925 891935 893215 893254) (-600 "LODOCAT.spad" 890589 890601 891881 891886) (-599 "LODO2.spad" 889903 889915 890310 890349) (-598 "LODO1.spad" 889344 889354 889624 889663) (-597 "LODO.spad" 888769 888785 889065 889104) (-596 "LODEEF.spad" 887571 887589 888759 888764) (-595 "LO.spad" 886972 886986 887505 887532) (-594 "LNAGG.spad" 883159 883169 886962 886967) (-593 "LNAGG.spad" 879310 879322 883115 883120) (-592 "LMOPS.spad" 876078 876095 879300 879305) (-591 "LMODULE.spad" 875862 875872 876068 876073) (-590 "LMDICT.spad" 875243 875253 875491 875518) (-589 "LLINSET.spad" 874950 874960 875233 875238) (-588 "LITERAL.spad" 874856 874867 874940 874945) (-587 "LIST3.spad" 874167 874181 874846 874851) (-586 "LIST2MAP.spad" 871094 871106 874157 874162) (-585 "LIST2.spad" 869796 869808 871084 871089) (-584 "LIST.spad" 867678 867688 869021 869048) (-583 "LINSET.spad" 867457 867467 867668 867673) (-582 "LINFORM.spad" 866920 866932 867425 867452) (-581 "LINEXP.spad" 865663 865673 866910 866915) (-580 "LINELT.spad" 865034 865046 865546 865573) (-579 "LINDEP.spad" 863883 863895 864946 864951) (-578 "LINBASIS.spad" 863519 863534 863873 863878) (-577 "LIMITRF.spad" 861466 861476 863509 863514) (-576 "LIMITPS.spad" 860376 860389 861456 861461) (-575 "LIECAT.spad" 859860 859870 860302 860371) (-574 "LIECAT.spad" 859372 859384 859816 859821) (-573 "LIE.spad" 857376 857388 858650 858792) (-572 "LIB.spad" 855547 855555 855993 856008) (-571 "LGROBP.spad" 852900 852919 855537 855542) (-570 "LFCAT.spad" 851959 851967 852890 852895) (-569 "LF.spad" 850914 850930 851949 851954) (-568 "LEXTRIPK.spad" 846537 846552 850904 850909) (-567 "LEXP.spad" 844556 844583 846517 846532) (-566 "LETAST.spad" 844255 844263 844546 844551) (-565 "LEADCDET.spad" 842661 842678 844245 844250) (-564 "LAZM3PK.spad" 841405 841427 842651 842656) (-563 "LAUPOL.spad" 840072 840085 840972 841041) (-562 "LAPLACE.spad" 839655 839671 840062 840067) (-561 "LALG.spad" 839431 839441 839635 839650) (-560 "LALG.spad" 839215 839227 839421 839426) (-559 "LA.spad" 838655 838669 839137 839176) (-558 "KVTFROM.spad" 838398 838408 838645 838650) (-557 "KTVLOGIC.spad" 837942 837950 838388 838393) (-556 "KRCFROM.spad" 837688 837698 837932 837937) (-555 "KOVACIC.spad" 836419 836436 837678 837683) (-554 "KONVERT.spad" 836141 836151 836409 836414) (-553 "KOERCE.spad" 835878 835888 836131 836136) (-552 "KERNEL2.spad" 835581 835593 835868 835873) (-551 "KERNEL.spad" 834301 834311 835430 835435) (-550 "KDAGG.spad" 833410 833432 834281 834296) (-549 "KDAGG.spad" 832527 832551 833400 833405) (-548 "KAFILE.spad" 831417 831433 831652 831679) (-547 "JVMOP.spad" 831330 831338 831407 831412) (-546 "JVMMDACC.spad" 830384 830392 831320 831325) (-545 "JVMFDACC.spad" 829700 829708 830374 830379) (-544 "JVMCSTTG.spad" 828429 828437 829690 829695) (-543 "JVMCFACC.spad" 827875 827883 828419 828424) (-542 "JVMBCODE.spad" 827786 827794 827865 827870) (-541 "JORDAN.spad" 825603 825615 827064 827206) (-540 "JOINAST.spad" 825305 825313 825593 825598) (-539 "IXAGG.spad" 823438 823462 825295 825300) (-538 "IXAGG.spad" 821426 821452 823285 823290) (-537 "IVECTOR.spad" 820241 820256 820396 820423) (-536 "ITUPLE.spad" 819417 819427 820231 820236) (-535 "ITRIGMNP.spad" 818264 818283 819407 819412) (-534 "ITFUN3.spad" 817770 817784 818254 818259) (-533 "ITFUN2.spad" 817514 817526 817760 817765) (-532 "ITFORM.spad" 816869 816877 817504 817509) (-531 "ITAYLOR.spad" 814863 814878 816733 816830) (-530 "ISUPS.spad" 807312 807327 813849 813946) (-529 "ISUMP.spad" 806813 806829 807302 807307) (-528 "ISAST.spad" 806532 806540 806803 806808) (-527 "IRURPK.spad" 805249 805268 806522 806527) (-526 "IRSN.spad" 803253 803261 805239 805244) (-525 "IRRF2F.spad" 801746 801756 803209 803214) (-524 "IRREDFFX.spad" 801347 801358 801736 801741) (-523 "IROOT.spad" 799686 799696 801337 801342) (-522 "IRFORM.spad" 799010 799018 799676 799681) (-521 "IR2F.spad" 798224 798240 799000 799005) (-520 "IR2.spad" 797252 797268 798214 798219) (-519 "IR.spad" 795088 795102 797134 797161) (-518 "IPRNTPK.spad" 794848 794856 795078 795083) (-517 "IPF.spad" 794413 794425 794653 794746) (-516 "IPADIC.spad" 794182 794208 794339 794408) (-515 "IP4ADDR.spad" 793739 793747 794172 794177) (-514 "IOMODE.spad" 793261 793269 793729 793734) (-513 "IOBFILE.spad" 792646 792654 793251 793256) (-512 "IOBCON.spad" 792511 792519 792636 792641) (-511 "INVLAPLA.spad" 792160 792176 792501 792506) (-510 "INTTR.spad" 785554 785571 792150 792155) (-509 "INTTOOLS.spad" 783362 783378 785181 785186) (-508 "INTSLPE.spad" 782690 782698 783352 783357) (-507 "INTRVL.spad" 782256 782266 782604 782685) (-506 "INTRF.spad" 780688 780702 782246 782251) (-505 "INTRET.spad" 780120 780130 780678 780683) (-504 "INTRAT.spad" 778855 778872 780110 780115) (-503 "INTPM.spad" 777318 777334 778576 778581) (-502 "INTPAF.spad" 775194 775212 777247 777252) (-501 "INTHERTR.spad" 774468 774485 775184 775189) (-500 "INTHERAL.spad" 774138 774162 774458 774463) (-499 "INTHEORY.spad" 770577 770585 774128 774133) (-498 "INTG0.spad" 764341 764359 770506 770511) (-497 "INTFACT.spad" 763408 763418 764331 764336) (-496 "INTEF.spad" 761819 761835 763398 763403) (-495 "INTDOM.spad" 760442 760450 761745 761814) (-494 "INTDOM.spad" 759127 759137 760432 760437) (-493 "INTCAT.spad" 757394 757404 759041 759122) (-492 "INTBIT.spad" 756901 756909 757384 757389) (-491 "INTALG.spad" 756089 756116 756891 756896) (-490 "INTAF.spad" 755589 755605 756079 756084) (-489 "INTABL.spad" 753971 754002 754134 754161) (-488 "INT8.spad" 753851 753859 753961 753966) (-487 "INT64.spad" 753730 753738 753841 753846) (-486 "INT32.spad" 753609 753617 753720 753725) (-485 "INT16.spad" 753488 753496 753599 753604) (-484 "INT.spad" 753014 753022 753354 753483) (-483 "INS.spad" 750517 750525 752916 753009) (-482 "INS.spad" 748106 748116 750507 750512) (-481 "INPSIGN.spad" 747576 747589 748096 748101) (-480 "INPRODPF.spad" 746672 746691 747566 747571) (-479 "INPRODFF.spad" 745760 745784 746662 746667) (-478 "INNMFACT.spad" 744735 744752 745750 745755) (-477 "INMODGCD.spad" 744239 744269 744725 744730) (-476 "INFSP.spad" 742536 742558 744229 744234) (-475 "INFPROD0.spad" 741616 741635 742526 742531) (-474 "INFORM1.spad" 741241 741251 741606 741611) (-473 "INFORM.spad" 738452 738460 741231 741236) (-472 "INFINITY.spad" 738004 738012 738442 738447) (-471 "INETCLTS.spad" 737981 737989 737994 737999) (-470 "INEP.spad" 736527 736549 737971 737976) (-469 "INDE.spad" 736176 736193 736437 736442) (-468 "INCRMAPS.spad" 735613 735623 736166 736171) (-467 "INBFILE.spad" 734709 734717 735603 735608) (-466 "INBFF.spad" 730559 730570 734699 734704) (-465 "INBCON.spad" 728825 728833 730549 730554) (-464 "INBCON.spad" 727089 727099 728815 728820) (-463 "INAST.spad" 726750 726758 727079 727084) (-462 "IMPTAST.spad" 726458 726466 726740 726745) (-461 "IMATQF.spad" 725552 725596 726414 726419) (-460 "IMATLIN.spad" 724173 724197 725508 725513) (-459 "IIARRAY2.spad" 723642 723680 723845 723872) (-458 "IFF.spad" 723055 723071 723326 723419) (-457 "IFAST.spad" 722669 722677 723045 723050) (-456 "IFARRAY.spad" 720196 720211 721894 721921) (-455 "IFAMON.spad" 720058 720075 720152 720157) (-454 "IEVALAB.spad" 719471 719483 720048 720053) (-453 "IEVALAB.spad" 718882 718896 719461 719466) (-452 "indexedp.spad" 718438 718450 718872 718877) (-451 "IDPOAMS.spad" 718116 718128 718350 718355) (-450 "IDPOAM.spad" 717758 717770 718028 718033) (-449 "IDPO.spad" 717172 717184 717670 717675) (-448 "IDPC.spad" 715887 715899 717162 717167) (-447 "IDPAM.spad" 715554 715566 715799 715804) (-446 "IDPAG.spad" 715223 715235 715466 715471) (-445 "IDENT.spad" 714875 714883 715213 715218) (-444 "catdef.spad" 714646 714657 714758 714870) (-443 "IDECOMP.spad" 711885 711903 714636 714641) (-442 "IDEAL.spad" 706847 706886 711833 711838) (-441 "ICDEN.spad" 706060 706076 706837 706842) (-440 "ICARD.spad" 705453 705461 706050 706055) (-439 "IBPTOOLS.spad" 704060 704077 705443 705448) (-438 "IBITS.spad" 703573 703586 703706 703733) (-437 "IBATOOL.spad" 700558 700577 703563 703568) (-436 "IBACHIN.spad" 699065 699080 700548 700553) (-435 "IARRAY2.spad" 698126 698152 698737 698764) (-434 "IARRAY1.spad" 697205 697220 697351 697378) (-433 "IAN.spad" 695587 695595 697036 697129) (-432 "IALGFACT.spad" 695198 695231 695577 695582) (-431 "HYPCAT.spad" 694622 694630 695188 695193) (-430 "HYPCAT.spad" 694044 694054 694612 694617) (-429 "HOSTNAME.spad" 693860 693868 694034 694039) (-428 "HOMOTOP.spad" 693603 693613 693850 693855) (-427 "HOAGG.spad" 690885 690895 693593 693598) (-426 "HOAGG.spad" 687917 687929 690627 690632) (-425 "HEXADEC.spad" 686142 686150 686507 686600) (-424 "HEUGCD.spad" 685233 685244 686132 686137) (-423 "HELLFDIV.spad" 684839 684863 685223 685228) (-422 "HEAP.spad" 684296 684306 684511 684538) (-421 "HEADAST.spad" 683837 683845 684286 684291) (-420 "HDP.spad" 673470 673486 673847 673944) (-419 "HDMP.spad" 671017 671032 671633 671760) (-418 "HB.spad" 669292 669300 671007 671012) (-417 "HASHTBL.spad" 667626 667657 667837 667864) (-416 "HASAST.spad" 667342 667350 667616 667621) (-415 "HACKPI.spad" 666833 666841 667244 667337) (-414 "GTSET.spad" 665760 665776 666467 666494) (-413 "GSTBL.spad" 664143 664178 664317 664332) (-412 "GSERIES.spad" 661515 661542 662334 662483) (-411 "GROUP.spad" 660788 660796 661495 661510) (-410 "GROUP.spad" 660069 660079 660778 660783) (-409 "GROEBSOL.spad" 658563 658584 660059 660064) (-408 "GRMOD.spad" 657144 657156 658553 658558) (-407 "GRMOD.spad" 655723 655737 657134 657139) (-406 "GRIMAGE.spad" 648636 648644 655713 655718) (-405 "GRDEF.spad" 647015 647023 648626 648631) (-404 "GRAY.spad" 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"DRAWHACK.spad" 282444 282454 283126 283131) (-218 "DRAWCX.spad" 279922 279930 282434 282439) (-217 "DRAWCURV.spad" 279469 279484 279912 279917) (-216 "DRAWCFUN.spad" 269001 269009 279459 279464) (-215 "DRAW.spad" 261877 261890 268991 268996) (-214 "DQAGG.spad" 260055 260065 261845 261872) (-213 "DPOLCAT.spad" 255412 255428 259923 260050) (-212 "DPOLCAT.spad" 250855 250873 255368 255373) (-211 "DPMO.spad" 243558 243574 243696 243902) (-210 "DPMM.spad" 236274 236292 236399 236605) (-209 "DOMTMPLT.spad" 236045 236053 236264 236269) (-208 "DOMCTOR.spad" 235800 235808 236035 236040) (-207 "DOMAIN.spad" 234911 234919 235790 235795) (-206 "DMP.spad" 232504 232519 233074 233201) (-205 "DMEXT.spad" 232371 232381 232472 232499) (-204 "DLP.spad" 231731 231741 232361 232366) (-203 "DLIST.spad" 230352 230362 230956 230983) (-202 "DLAGG.spad" 228769 228779 230342 230347) (-201 "DIVRING.spad" 228311 228319 228713 228764) (-200 "DIVRING.spad" 227897 227907 228301 228306) (-199 "DISPLAY.spad" 226087 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(-118 "CHARNZ.spad" 115757 115765 115975 115990) (-117 "CHAR.spad" 113125 113133 115747 115752) (-116 "CFCAT.spad" 112453 112461 113115 113120) (-115 "CDEN.spad" 111673 111687 112443 112448) (-114 "CCLASS.spad" 109853 109861 111115 111154) (-113 "CATEGORY.spad" 108927 108935 109843 109848) (-112 "CATCTOR.spad" 108818 108826 108917 108922) (-111 "CATAST.spad" 108444 108452 108808 108813) (-110 "CASEAST.spad" 108158 108166 108434 108439) (-109 "CARTEN2.spad" 107548 107575 108148 108153) (-108 "CARTEN.spad" 103300 103324 107538 107543) (-107 "CARD.spad" 100595 100603 103274 103295) (-106 "CAPSLAST.spad" 100377 100385 100585 100590) (-105 "CACHSET.spad" 100001 100009 100367 100372) (-104 "CABMON.spad" 99556 99564 99991 99996) (-103 "BYTEORD.spad" 99231 99239 99546 99551) (-102 "BYTEBUF.spad" 97198 97206 98484 98511) (-101 "BYTE.spad" 96673 96681 97188 97193) (-100 "BTREE.spad" 95811 95821 96345 96372) (-99 "BTOURN.spad" 94882 94891 95483 95510) (-98 "BTCAT.spad" 94275 94284 94850 94877) 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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 f328d030..a06fcaf6 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,279 +1,279 @@
 
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197892) ((-1196 . -557) 197841) ((-1196 . -952) 197818) ((-1196 . -584) 197788) ((-1196 . -656) 197758) ((-1196 . -592) 197732) ((-1196 . -590) 197691) ((-1196 . -104) T) ((-1196 . -25) T) ((-1196 . -72) T) ((-1196 . -13) T) ((-1196 . -1130) T) ((-1196 . -554) 197673) ((-1196 . -1015) T) ((-1196 . -23) T) ((-1196 . -21) T) ((-1196 . -970) 197657) ((-1196 . -965) 197641) ((-1196 . -82) 197620) ((-1196 . -1203) 197599) ((-1196 . -963) T) ((-1196 . -665) T) ((-1196 . -1062) T) ((-1196 . -1027) T) ((-1196 . -972) T) ((-1196 . -1195) 197583) ((-1196 . -38) 197553) ((-1196 . -1200) 197532) ((-1194 . -1125) 197501) ((-1194 . -554) 197463) ((-1194 . -124) 197447) ((-1194 . -34) T) ((-1194 . -13) T) ((-1194 . -1130) T) ((-1194 . -72) T) ((-1194 . -260) 197385) ((-1194 . -454) 197318) ((-1194 . -1015) T) ((-1194 . -427) 197302) ((-1194 . -555) 197263) ((-1194 . -891) 197232) ((-1193 . -963) T) ((-1193 . -665) T) ((-1193 . -1062) T) ((-1193 . -1027) T) ((-1193 . -972) T) ((-1193 . -21) T) ((-1193 . -590) 197177) ((-1193 . -23) T) ((-1193 . -1015) T) ((-1193 . -554) 197146) ((-1193 . -1130) T) ((-1193 . -13) T) ((-1193 . -72) T) ((-1193 . -25) T) ((-1193 . -104) T) ((-1193 . -592) 197106) ((-1193 . -557) 197048) ((-1193 . -428) 197032) ((-1193 . -38) 197002) ((-1193 . -82) 196967) ((-1193 . -965) 196937) ((-1193 . -970) 196907) ((-1193 . -584) 196877) ((-1193 . -656) 196847) ((-1192 . -997) T) ((-1192 . -428) 196828) ((-1192 . -554) 196794) ((-1192 . -557) 196775) ((-1192 . -1015) T) ((-1192 . -1130) T) ((-1192 . -13) T) ((-1192 . -72) T) ((-1192 . -64) T) ((-1191 . -997) T) ((-1191 . -428) 196756) ((-1191 . -554) 196722) ((-1191 . -557) 196703) ((-1191 . -1015) T) ((-1191 . -1130) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -64) T) ((-1186 . -554) 196685) ((-1184 . -1015) T) ((-1184 . -554) 196667) ((-1184 . -1130) T) ((-1184 . -13) T) ((-1184 . -72) T) ((-1183 . -1015) T) ((-1183 . -554) 196649) ((-1183 . -1130) T) ((-1183 . -13) T) ((-1183 . -72) T) ((-1180 . -1179) 196633) ((-1180 . -322) 196617) ((-1180 . -761) 196596) ((-1180 . -758) 196575) ((-1180 . -124) 196559) ((-1180 . -34) T) ((-1180 . -13) T) ((-1180 . -1130) T) ((-1180 . -72) 196493) ((-1180 . -554) 196408) ((-1180 . -260) 196346) ((-1180 . -454) 196279) ((-1180 . -1015) 196232) ((-1180 . -427) 196216) ((-1180 . -555) 196177) ((-1180 . -241) 196129) ((-1180 . -540) 196106) ((-1180 . -243) 196083) ((-1180 . -595) 196067) ((-1180 . -19) 196051) ((-1177 . -1015) T) ((-1177 . -554) 196017) ((-1177 . -1130) T) ((-1177 . -13) T) ((-1177 . -72) T) ((-1170 . -1173) 196001) ((-1170 . -190) 195960) ((-1170 . -557) 195842) ((-1170 . -592) 195767) ((-1170 . -590) 195677) ((-1170 . -104) T) ((-1170 . -25) T) ((-1170 . -72) T) ((-1170 . -554) 195659) ((-1170 . -1015) T) ((-1170 . -23) T) ((-1170 . -21) T) ((-1170 . -972) T) ((-1170 . -1027) T) ((-1170 . -1062) T) ((-1170 . -665) T) ((-1170 . -963) T) ((-1170 . -186) 195612) ((-1170 . -13) T) ((-1170 . -1130) T) ((-1170 . -189) 195571) ((-1170 . -241) 195536) ((-1170 . -811) 195449) ((-1170 . -808) 195337) ((-1170 . -813) 195250) ((-1170 . -888) 195220) ((-1170 . -38) 195117) ((-1170 . -82) 194982) ((-1170 . -965) 194868) ((-1170 . -970) 194754) ((-1170 . -584) 194651) ((-1170 . -656) 194548) ((-1170 . -118) 194527) ((-1170 . -120) 194506) ((-1170 . -146) 194460) ((-1170 . -496) 194439) ((-1170 . -246) 194418) ((-1170 . -47) 194395) ((-1170 . -1159) 194372) ((-1170 . -35) 194338) ((-1170 . -66) 194304) ((-1170 . -239) 194270) ((-1170 . -431) 194236) ((-1170 . -1119) 194202) ((-1170 . -1116) 194168) ((-1170 . -917) 194134) ((-1167 . -277) 194078) ((-1167 . -952) 194044) ((-1167 . -353) 194010) ((-1167 . -38) 193867) ((-1167 . -557) 193741) ((-1167 . -592) 193630) ((-1167 . -590) 193504) ((-1167 . -972) T) ((-1167 . -1027) T) ((-1167 . -1062) T) ((-1167 . -665) T) ((-1167 . -963) T) ((-1167 . -82) 193354) ((-1167 . -965) 193243) ((-1167 . -970) 193132) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1015) T) ((-1167 . -554) 193114) ((-1167 . -1130) T) ((-1167 . -13) T) ((-1167 . -72) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -584) 192971) ((-1167 . -656) 192828) ((-1167 . -118) 192789) ((-1167 . -120) 192750) ((-1167 . -146) T) ((-1167 . -496) T) ((-1167 . -246) T) ((-1167 . -47) 192694) ((-1166 . -1165) 192673) ((-1166 . -312) 192652) ((-1166 . -1135) 192631) ((-1166 . -834) 192610) ((-1166 . -496) 192564) ((-1166 . -146) 192498) ((-1166 . -557) 192317) ((-1166 . -656) 192164) ((-1166 . -584) 192011) ((-1166 . -38) 191858) ((-1166 . -390) 191837) ((-1166 . -258) 191816) ((-1166 . -592) 191716) ((-1166 . -590) 191601) ((-1166 . -972) T) ((-1166 . -1027) T) ((-1166 . -1062) T) ((-1166 . -665) T) ((-1166 . -963) T) ((-1166 . -82) 191421) ((-1166 . -965) 191262) ((-1166 . -970) 191103) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1015) T) ((-1166 . -554) 191085) ((-1166 . -1130) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -246) 191039) ((-1166 . -201) 191018) ((-1166 . -917) 190984) ((-1166 . -1116) 190950) ((-1166 . -1119) 190916) ((-1166 . -431) 190882) ((-1166 . -239) 190848) ((-1166 . -66) 190814) ((-1166 . -35) 190780) ((-1166 . -1159) 190750) ((-1166 . -47) 190720) ((-1166 . -120) 190699) ((-1166 . -118) 190678) ((-1166 . -888) 190641) ((-1166 . -813) 190547) ((-1166 . -808) 190451) ((-1166 . -811) 190357) ((-1166 . -241) 190315) ((-1166 . -189) 190267) ((-1166 . -186) 190213) ((-1166 . -190) 190165) ((-1166 . -1163) 190149) ((-1166 . -952) 190133) ((-1161 . -1165) 190094) ((-1161 . -312) 190073) ((-1161 . -1135) 190052) ((-1161 . -834) 190031) ((-1161 . -496) 189985) ((-1161 . -146) 189919) ((-1161 . -557) 189668) ((-1161 . -656) 189515) ((-1161 . -584) 189362) ((-1161 . -38) 189209) ((-1161 . -390) 189188) ((-1161 . -258) 189167) ((-1161 . -592) 189067) ((-1161 . -590) 188952) ((-1161 . -972) T) ((-1161 . -1027) T) ((-1161 . -1062) T) ((-1161 . -665) T) ((-1161 . -963) T) ((-1161 . -82) 188772) ((-1161 . -965) 188613) ((-1161 . -970) 188454) ((-1161 . -21) T) ((-1161 . -23) T) ((-1161 . -1015) T) ((-1161 . -554) 188436) ((-1161 . -1130) T) ((-1161 . -13) T) ((-1161 . -72) T) ((-1161 . -25) T) ((-1161 . -104) T) ((-1161 . -246) 188390) ((-1161 . -201) 188369) ((-1161 . -917) 188335) ((-1161 . -1116) 188301) ((-1161 . -1119) 188267) ((-1161 . -431) 188233) ((-1161 . -239) 188199) ((-1161 . -66) 188165) ((-1161 . -35) 188131) ((-1161 . -1159) 188101) ((-1161 . -47) 188071) ((-1161 . -120) 188050) ((-1161 . -118) 188029) ((-1161 . -888) 187992) ((-1161 . -813) 187898) ((-1161 . -808) 187779) ((-1161 . -811) 187685) ((-1161 . -241) 187643) ((-1161 . -189) 187595) ((-1161 . -186) 187541) ((-1161 . -190) 187493) ((-1161 . -1163) 187477) ((-1161 . -952) 187412) ((-1149 . -1156) 187396) ((-1149 . -1067) 187374) ((-1149 . -555) NIL) ((-1149 . -260) 187361) ((-1149 . -454) 187309) ((-1149 . -277) 187286) ((-1149 . -952) 187169) ((-1149 . -353) 187153) ((-1149 . -38) 186985) ((-1149 . -82) 186790) ((-1149 . -965) 186616) ((-1149 . -970) 186442) ((-1149 . -590) 186352) ((-1149 . -592) 186241) ((-1149 . -584) 186073) ((-1149 . -656) 185905) ((-1149 . -557) 185661) ((-1149 . -118) 185640) ((-1149 . -120) 185619) ((-1149 . -47) 185596) ((-1149 . -327) 185580) ((-1149 . -582) 185528) ((-1149 . -811) 185472) ((-1149 . -808) 185379) ((-1149 . -813) 185290) ((-1149 . -798) NIL) ((-1149 . -823) 185269) ((-1149 . -1135) 185248) ((-1149 . -863) 185218) ((-1149 . -834) 185197) ((-1149 . -496) 185111) ((-1149 . -246) 185025) ((-1149 . -146) 184919) ((-1149 . -390) 184853) ((-1149 . -258) 184832) ((-1149 . -241) 184759) ((-1149 . -190) T) ((-1149 . -104) T) ((-1149 . -25) T) ((-1149 . -72) T) ((-1149 . -554) 184741) ((-1149 . -1015) T) ((-1149 . -23) T) ((-1149 . -21) T) ((-1149 . -972) T) ((-1149 . -1027) T) ((-1149 . -1062) T) ((-1149 . -665) T) ((-1149 . -963) T) ((-1149 . -186) 184728) ((-1149 . -13) T) ((-1149 . -1130) T) ((-1149 . -189) T) ((-1149 . -225) 184712) ((-1149 . -184) 184696) ((-1147 . -1008) 184680) ((-1147 . -559) 184664) ((-1147 . -1015) 184642) ((-1147 . -554) 184609) ((-1147 . -1130) 184587) ((-1147 . -13) 184565) ((-1147 . -72) 184543) ((-1147 . -1009) 184500) ((-1145 . -1144) 184479) ((-1145 . -917) 184445) ((-1145 . -1116) 184411) ((-1145 . -1119) 184377) ((-1145 . -431) 184343) ((-1145 . -239) 184309) ((-1145 . -66) 184275) ((-1145 . -35) 184241) ((-1145 . -1159) 184218) ((-1145 . -47) 184195) ((-1145 . -557) 183950) ((-1145 . -656) 183770) ((-1145 . -584) 183590) ((-1145 . -592) 183401) ((-1145 . -590) 183259) ((-1145 . -970) 183073) ((-1145 . -965) 182887) ((-1145 . -82) 182675) ((-1145 . -38) 182495) ((-1145 . -888) 182465) ((-1145 . -241) 182365) ((-1145 . -1142) 182349) ((-1145 . -972) T) ((-1145 . -1027) T) ((-1145 . -1062) T) ((-1145 . -665) T) ((-1145 . -963) T) ((-1145 . -21) T) ((-1145 . -23) T) ((-1145 . -1015) T) ((-1145 . -554) 182331) ((-1145 . -1130) T) ((-1145 . -13) T) ((-1145 . -72) T) ((-1145 . -25) T) ((-1145 . -104) T) ((-1145 . -118) 182259) ((-1145 . -120) 182187) ((-1145 . -555) 181860) ((-1145 . -184) 181830) ((-1145 . -811) 181684) ((-1145 . -813) 181484) ((-1145 . -808) 181282) ((-1145 . -225) 181252) ((-1145 . -189) 181114) ((-1145 . -186) 180970) ((-1145 . -190) 180878) ((-1145 . -312) 180857) ((-1145 . -1135) 180836) ((-1145 . -834) 180815) ((-1145 . -496) 180769) ((-1145 . -146) 180703) ((-1145 . -390) 180682) ((-1145 . -258) 180661) ((-1145 . -246) 180615) ((-1145 . -201) 180594) ((-1145 . -288) 180564) ((-1145 . -454) 180424) ((-1145 . -260) 180363) ((-1145 . -327) 180333) ((-1145 . -582) 180241) ((-1145 . -341) 180211) ((-1145 . -798) 180084) ((-1145 . -742) 180037) ((-1145 . -716) 179990) ((-1145 . -718) 179943) ((-1145 . -758) 179845) ((-1145 . -761) 179747) ((-1145 . -720) 179700) ((-1145 . -723) 179653) ((-1145 . -757) 179606) ((-1145 . -796) 179576) ((-1145 . -823) 179529) ((-1145 . -935) 179482) ((-1145 . -952) 179271) ((-1145 . -1067) 179223) ((-1145 . -906) 179193) ((-1140 . -1144) 179154) ((-1140 . -917) 179120) ((-1140 . -1116) 179086) ((-1140 . -1119) 179052) ((-1140 . -431) 179018) ((-1140 . -239) 178984) ((-1140 . -66) 178950) ((-1140 . -35) 178916) ((-1140 . -1159) 178893) ((-1140 . -47) 178870) ((-1140 . -557) 178671) ((-1140 . -656) 178473) ((-1140 . -584) 178275) ((-1140 . -592) 178130) ((-1140 . -590) 177970) ((-1140 . -970) 177766) ((-1140 . -965) 177562) ((-1140 . -82) 177314) ((-1140 . -38) 177116) ((-1140 . -888) 177086) ((-1140 . -241) 176914) ((-1140 . -1142) 176898) ((-1140 . -972) T) ((-1140 . -1027) T) ((-1140 . -1062) T) ((-1140 . -665) T) ((-1140 . -963) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1015) T) ((-1140 . -554) 176880) ((-1140 . -1130) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -25) T) ((-1140 . -104) T) ((-1140 . -118) 176790) ((-1140 . -120) 176700) ((-1140 . -555) NIL) ((-1140 . -184) 176652) ((-1140 . -811) 176488) ((-1140 . -813) 176252) ((-1140 . -808) 175991) ((-1140 . -225) 175943) ((-1140 . -189) 175769) ((-1140 . -186) 175589) ((-1140 . -190) 175479) ((-1140 . -312) 175458) ((-1140 . -1135) 175437) ((-1140 . -834) 175416) ((-1140 . -496) 175370) ((-1140 . -146) 175304) ((-1140 . -390) 175283) ((-1140 . -258) 175262) ((-1140 . -246) 175216) ((-1140 . -201) 175195) ((-1140 . -288) 175147) ((-1140 . -454) 174881) ((-1140 . -260) 174766) ((-1140 . -327) 174718) ((-1140 . -582) 174670) ((-1140 . -341) 174622) ((-1140 . -798) NIL) ((-1140 . -742) NIL) ((-1140 . -716) NIL) ((-1140 . -718) NIL) ((-1140 . -758) NIL) ((-1140 . -761) NIL) ((-1140 . -720) NIL) ((-1140 . -723) NIL) ((-1140 . -757) NIL) ((-1140 . -796) 174574) ((-1140 . -823) NIL) ((-1140 . -935) NIL) ((-1140 . -952) 174540) ((-1140 . -1067) NIL) ((-1140 . -906) 174492) ((-1139 . -754) T) ((-1139 . -761) T) ((-1139 . -758) T) ((-1139 . -1015) T) ((-1139 . -554) 174474) ((-1139 . -1130) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -318) T) ((-1139 . -606) T) ((-1138 . -754) T) ((-1138 . -761) T) ((-1138 . -758) T) ((-1138 . -1015) T) ((-1138 . -554) 174456) ((-1138 . -1130) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -318) T) ((-1138 . -606) T) ((-1137 . -754) T) ((-1137 . -761) T) ((-1137 . -758) T) ((-1137 . -1015) T) ((-1137 . -554) 174438) ((-1137 . -1130) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -318) T) ((-1137 . -606) T) ((-1136 . -754) T) ((-1136 . -761) T) ((-1136 . -758) T) ((-1136 . -1015) T) ((-1136 . -554) 174420) ((-1136 . -1130) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -606) T) ((-1131 . -997) T) ((-1131 . -428) 174401) ((-1131 . -554) 174367) ((-1131 . -557) 174348) ((-1131 . -1015) T) ((-1131 . -1130) T) ((-1131 . -13) T) ((-1131 . -72) T) ((-1131 . -64) T) ((-1128 . -428) 174325) ((-1128 . -554) 174266) ((-1128 . -557) 174243) ((-1128 . -1015) 174221) ((-1128 . -1130) 174199) ((-1128 . -13) 174177) ((-1128 . -72) 174155) ((-1123 . -681) 174131) ((-1123 . -35) 174097) ((-1123 . -66) 174063) ((-1123 . -239) 174029) ((-1123 . -431) 173995) ((-1123 . -1119) 173961) ((-1123 . -1116) 173927) ((-1123 . -917) 173893) ((-1123 . -47) 173862) ((-1123 . -38) 173759) ((-1123 . -584) 173656) ((-1123 . -656) 173553) ((-1123 . -557) 173435) ((-1123 . -246) 173414) ((-1123 . -496) 173393) ((-1123 . -82) 173258) ((-1123 . -965) 173144) ((-1123 . -970) 173030) ((-1123 . -146) 172984) ((-1123 . -120) 172963) ((-1123 . -118) 172942) ((-1123 . -592) 172867) ((-1123 . -590) 172777) ((-1123 . -888) 172738) ((-1123 . -813) 172719) ((-1123 . -1130) T) ((-1123 . -13) T) ((-1123 . -808) 172698) ((-1123 . -963) T) ((-1123 . -665) T) ((-1123 . -1062) T) ((-1123 . -1027) T) ((-1123 . -972) T) ((-1123 . -21) T) ((-1123 . -23) T) ((-1123 . -1015) T) ((-1123 . -554) 172680) ((-1123 . -72) T) ((-1123 . -25) T) ((-1123 . -104) T) ((-1123 . -811) 172661) ((-1123 . -454) 172628) ((-1123 . -260) 172615) ((-1117 . -925) 172599) ((-1117 . -34) T) ((-1117 . -13) T) ((-1117 . -1130) T) ((-1117 . -72) 172553) ((-1117 . -554) 172488) ((-1117 . -260) 172426) ((-1117 . -454) 172359) ((-1117 . -1015) 172337) ((-1117 . -427) 172321) ((-1112 . -314) 172295) ((-1112 . -72) T) ((-1112 . -13) T) ((-1112 . -1130) T) ((-1112 . -554) 172277) ((-1112 . -1015) T) ((-1110 . -1015) T) ((-1110 . -554) 172259) ((-1110 . -1130) T) ((-1110 . -13) T) ((-1110 . -72) T) ((-1110 . -557) 172241) ((-1105 . -749) 172225) ((-1105 . -72) T) ((-1105 . -13) T) ((-1105 . -1130) T) ((-1105 . -554) 172207) ((-1105 . -1015) T) ((-1103 . -1108) 172186) ((-1103 . -183) 172134) ((-1103 . -76) 172082) ((-1103 . -260) 171880) ((-1103 . -454) 171632) ((-1103 . -427) 171567) ((-1103 . -124) 171515) ((-1103 . -555) NIL) ((-1103 . -193) 171463) ((-1103 . -551) 171442) ((-1103 . -243) 171421) ((-1103 . -1130) T) ((-1103 . -13) T) ((-1103 . -241) 171400) ((-1103 . -1015) T) ((-1103 . -554) 171382) ((-1103 . -72) T) ((-1103 . -34) T) ((-1103 . -540) 171361) ((-1099 . -1015) T) ((-1099 . -554) 171343) ((-1099 . -1130) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1098 . -754) T) ((-1098 . -761) T) ((-1098 . -758) T) ((-1098 . -1015) T) ((-1098 . -554) 171325) ((-1098 . -1130) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -318) T) ((-1098 . -606) T) ((-1097 . -754) T) ((-1097 . -761) T) ((-1097 . -758) T) ((-1097 . -1015) T) ((-1097 . -554) 171307) ((-1097 . -1130) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -318) T) ((-1096 . -1176) T) ((-1096 . -1015) T) ((-1096 . -554) 171274) ((-1096 . -1130) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -952) 171210) ((-1096 . -557) 171146) ((-1095 . -554) 171128) ((-1094 . -554) 171110) ((-1093 . -277) 171087) ((-1093 . -952) 170985) ((-1093 . -353) 170969) ((-1093 . -38) 170866) ((-1093 . -557) 170723) ((-1093 . -592) 170648) ((-1093 . -590) 170558) ((-1093 . -972) T) ((-1093 . -1027) T) ((-1093 . -1062) T) ((-1093 . -665) T) ((-1093 . -963) T) ((-1093 . -82) 170423) ((-1093 . -965) 170309) ((-1093 . -970) 170195) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1015) T) ((-1093 . -554) 170177) ((-1093 . -1130) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -25) T) ((-1093 . -104) T) ((-1093 . -584) 170074) ((-1093 . -656) 169971) ((-1093 . -118) 169950) ((-1093 . -120) 169929) ((-1093 . -146) 169883) ((-1093 . -496) 169862) ((-1093 . -246) 169841) ((-1093 . -47) 169818) ((-1091 . -758) T) ((-1091 . -554) 169800) ((-1091 . -1015) T) ((-1091 . -72) T) ((-1091 . -13) T) ((-1091 . -1130) T) ((-1091 . -761) T) ((-1091 . -555) 169722) ((-1091 . -557) 169688) ((-1091 . -952) 169670) ((-1091 . -798) 169637) ((-1090 . -1173) 169621) ((-1090 . -190) 169580) ((-1090 . -557) 169462) ((-1090 . -592) 169387) ((-1090 . -590) 169297) ((-1090 . -104) T) ((-1090 . -25) T) ((-1090 . -72) T) ((-1090 . -554) 169279) ((-1090 . -1015) T) ((-1090 . -23) T) ((-1090 . -21) T) ((-1090 . -972) T) ((-1090 . -1027) T) ((-1090 . -1062) T) ((-1090 . -665) T) ((-1090 . -963) T) ((-1090 . -186) 169232) ((-1090 . -13) T) ((-1090 . -1130) T) ((-1090 . -189) 169191) ((-1090 . -241) 169156) ((-1090 . -811) 169069) ((-1090 . -808) 168957) 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166234) ((-1089 . -970) 166075) ((-1089 . -21) T) ((-1089 . -23) T) ((-1089 . -1015) T) ((-1089 . -554) 166057) ((-1089 . -1130) T) ((-1089 . -13) T) ((-1089 . -72) T) ((-1089 . -25) T) ((-1089 . -104) T) ((-1089 . -246) 166011) ((-1089 . -201) 165990) ((-1089 . -917) 165956) ((-1089 . -1116) 165922) ((-1089 . -1119) 165888) ((-1089 . -431) 165854) ((-1089 . -239) 165820) ((-1089 . -66) 165786) ((-1089 . -35) 165752) ((-1089 . -1159) 165722) ((-1089 . -47) 165692) ((-1089 . -120) 165671) ((-1089 . -118) 165650) ((-1089 . -888) 165613) ((-1089 . -813) 165519) ((-1089 . -808) 165400) ((-1089 . -811) 165306) ((-1089 . -241) 165264) ((-1089 . -189) 165216) ((-1089 . -186) 165162) ((-1089 . -190) 165114) ((-1089 . -1163) 165098) ((-1089 . -952) 165033) ((-1086 . -1156) 165017) ((-1086 . -1067) 164995) ((-1086 . -555) NIL) ((-1086 . -260) 164982) ((-1086 . -454) 164930) ((-1086 . -277) 164907) ((-1086 . -952) 164790) ((-1086 . -353) 164774) ((-1086 . -38) 164606) ((-1086 . -82) 164411) 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. -618) 156408) ((-1070 . -595) 156392) ((-1070 . -243) 156369) ((-1070 . -241) 156321) ((-1070 . -540) 156298) ((-1070 . -555) 156259) ((-1070 . -427) 156243) ((-1070 . -1015) 156221) ((-1070 . -454) 156154) ((-1070 . -260) 156092) ((-1070 . -554) 156027) ((-1070 . -72) 155981) ((-1070 . -1130) T) ((-1070 . -13) T) ((-1070 . -34) T) ((-1070 . -124) 155965) ((-1070 . -1169) 155949) ((-1070 . -925) 155933) ((-1070 . -1065) 155917) ((-1070 . -557) 155894) ((-1068 . -997) T) ((-1068 . -428) 155875) ((-1068 . -554) 155841) ((-1068 . -557) 155822) ((-1068 . -1015) T) ((-1068 . -1130) T) ((-1068 . -13) T) ((-1068 . -72) T) ((-1068 . -64) T) ((-1066 . -1108) 155801) ((-1066 . -183) 155749) ((-1066 . -76) 155697) ((-1066 . -260) 155495) ((-1066 . -454) 155247) ((-1066 . -427) 155182) ((-1066 . -124) 155130) ((-1066 . -555) NIL) ((-1066 . -193) 155078) ((-1066 . -551) 155057) ((-1066 . -243) 155036) ((-1066 . -1130) T) ((-1066 . -13) T) ((-1066 . -241) 155015) ((-1066 . -1015) T) ((-1066 . 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T) ((-1028 . -540) 147668) ((-1028 . -952) 147497) ((-1028 . -557) 147301) ((-1028 . -353) 147270) ((-1028 . -582) 147178) ((-1028 . -592) 147017) ((-1028 . -327) 146987) ((-1028 . -318) 146966) ((-1028 . -190) 146919) ((-1028 . -590) 146707) ((-1028 . -972) 146686) ((-1028 . -1027) 146665) ((-1028 . -1062) 146644) ((-1028 . -665) 146623) ((-1028 . -963) 146602) ((-1028 . -186) 146498) ((-1028 . -189) 146400) ((-1028 . -225) 146370) ((-1028 . -808) 146242) ((-1028 . -813) 146116) ((-1028 . -811) 146049) ((-1028 . -184) 146019) ((-1028 . -554) 145716) ((-1028 . -970) 145641) ((-1028 . -965) 145546) ((-1028 . -82) 145466) ((-1028 . -104) 145341) ((-1028 . -25) 145178) ((-1028 . -72) 144915) ((-1028 . -13) T) ((-1028 . -1130) T) ((-1028 . -1015) 144671) ((-1028 . -23) 144527) ((-1028 . -21) 144442) ((-1024 . -1025) 144426) ((-1024 . |MappingCategory|) 144400) ((-1024 . -1130) T) ((-1024 . -80) 144384) ((-1024 . -1015) T) ((-1024 . -554) 144366) ((-1024 . -13) T) ((-1024 . -72) T) ((-1019 . -1018) 144330) ((-1019 . -72) T) ((-1019 . -554) 144312) ((-1019 . -1015) T) ((-1019 . -241) 144268) ((-1019 . -1130) T) ((-1019 . -13) T) ((-1019 . -559) 144183) ((-1017 . -1018) 144135) ((-1017 . -72) T) ((-1017 . -554) 144117) ((-1017 . -1015) T) ((-1017 . -241) 144073) ((-1017 . -1130) T) ((-1017 . -13) T) ((-1017 . -559) 143976) ((-1016 . -318) T) ((-1016 . -72) T) ((-1016 . -13) T) ((-1016 . -1130) T) ((-1016 . -554) 143958) ((-1016 . -1015) T) ((-1011 . -367) 143942) ((-1011 . -1013) 143926) ((-1011 . -318) 143905) ((-1011 . -193) 143889) ((-1011 . -555) 143850) ((-1011 . -124) 143834) ((-1011 . -427) 143818) ((-1011 . -1015) T) ((-1011 . -454) 143751) ((-1011 . -260) 143689) ((-1011 . -554) 143671) ((-1011 . -72) T) ((-1011 . -1130) T) ((-1011 . -13) T) ((-1011 . -34) T) ((-1011 . -76) 143655) ((-1011 . -183) 143639) ((-1010 . -997) T) ((-1010 . -428) 143620) ((-1010 . -554) 143586) ((-1010 . -557) 143567) ((-1010 . -1015) T) ((-1010 . -1130) T) ((-1010 . -13) T) ((-1010 . -72) T) ((-1010 . -64) T) ((-1006 . -1130) T) ((-1006 . -13) T) ((-1006 . -1015) 143537) ((-1006 . -554) 143496) ((-1006 . -72) 143466) ((-1005 . -997) T) ((-1005 . -428) 143447) ((-1005 . -554) 143413) ((-1005 . -557) 143394) ((-1005 . -1015) T) ((-1005 . -1130) T) ((-1005 . -13) T) ((-1005 . -72) T) ((-1005 . -64) T) ((-1003 . -1008) 143378) ((-1003 . -559) 143362) ((-1003 . -1015) 143340) ((-1003 . -554) 143307) ((-1003 . -1130) 143285) ((-1003 . -13) 143263) ((-1003 . -72) 143241) ((-1003 . -1009) 143199) ((-1002 . -228) 143183) ((-1002 . -557) 143167) ((-1002 . -952) 143151) ((-1002 . -761) T) ((-1002 . -72) T) ((-1002 . -1015) T) ((-1002 . -554) 143133) ((-1002 . -758) T) ((-1002 . -186) 143120) ((-1002 . -13) T) ((-1002 . -1130) T) ((-1002 . -189) T) ((-1001 . -213) 143057) ((-1001 . -557) 142800) ((-1001 . -952) 142629) ((-1001 . -555) NIL) ((-1001 . -277) 142590) ((-1001 . -353) 142574) ((-1001 . -38) 142426) ((-1001 . -82) 142251) ((-1001 . -965) 142097) ((-1001 . -970) 141943) ((-1001 . -590) 141853) ((-1001 . -592) 141742) ((-1001 . -584) 141594) ((-1001 . -656) 141446) ((-1001 . -118) 141425) ((-1001 . -120) 141404) ((-1001 . -146) 141318) ((-1001 . -496) 141252) ((-1001 . -246) 141186) ((-1001 . -47) 141147) ((-1001 . -327) 141131) ((-1001 . -582) 141079) ((-1001 . -390) 141033) ((-1001 . -454) 140896) ((-1001 . -811) 140831) ((-1001 . -808) 140729) ((-1001 . -813) 140631) ((-1001 . -798) NIL) ((-1001 . -823) 140610) ((-1001 . -1135) 140589) ((-1001 . -863) 140534) ((-1001 . -260) 140521) ((-1001 . -190) 140500) ((-1001 . -104) T) ((-1001 . -25) T) ((-1001 . -72) T) ((-1001 . -554) 140482) ((-1001 . -1015) T) ((-1001 . -23) T) ((-1001 . -21) T) ((-1001 . -972) T) ((-1001 . -1027) T) ((-1001 . -1062) T) ((-1001 . -665) T) ((-1001 . -963) T) ((-1001 . -186) 140430) ((-1001 . -13) T) ((-1001 . -1130) T) ((-1001 . -189) 140384) ((-1001 . -225) 140368) ((-1001 . -184) 140352) ((-999 . -554) 140334) ((-996 . -758) T) ((-996 . -554) 140316) ((-996 . 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-13) T) ((-980 . -72) T) ((-980 . -64) T) ((-977 . -484) T) ((-977 . -1135) T) ((-977 . -1067) T) ((-977 . -952) 137411) ((-977 . -555) 137326) ((-977 . -935) T) ((-977 . -798) 137308) ((-977 . -757) T) ((-977 . -723) T) ((-977 . -720) T) ((-977 . -761) T) ((-977 . -758) T) ((-977 . -718) T) ((-977 . -716) T) ((-977 . -742) T) ((-977 . -592) 137280) ((-977 . -582) 137262) ((-977 . -834) T) ((-977 . -496) T) ((-977 . -246) T) ((-977 . -146) T) ((-977 . -557) 137234) ((-977 . -656) 137221) ((-977 . -584) 137208) ((-977 . -970) 137195) ((-977 . -965) 137182) ((-977 . -82) 137167) ((-977 . -38) 137154) ((-977 . -390) T) ((-977 . -258) T) ((-977 . -189) T) ((-977 . -186) 137141) ((-977 . -190) T) ((-977 . -116) T) ((-977 . -963) T) ((-977 . -665) T) ((-977 . -1062) T) ((-977 . -1027) T) ((-977 . -972) T) ((-977 . -21) T) ((-977 . -590) 137113) ((-977 . -23) T) ((-977 . -1015) T) ((-977 . -554) 137095) ((-977 . -1130) T) ((-977 . -13) T) ((-977 . -72) T) ((-977 . -25) T) ((-977 . -104) T) 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. -124) 135903) ((-960 . -1125) 135832) ((-950 . -997) T) ((-950 . -428) 135813) ((-950 . -554) 135779) ((-950 . -557) 135760) ((-950 . -1015) T) ((-950 . -1130) T) ((-950 . -13) T) ((-950 . -72) T) ((-950 . -64) T) ((-949 . -146) T) ((-949 . -557) 135729) ((-949 . -972) T) ((-949 . -1027) T) ((-949 . -1062) T) ((-949 . -665) T) ((-949 . -963) T) ((-949 . -592) 135703) ((-949 . -590) 135662) ((-949 . -104) T) ((-949 . -25) T) ((-949 . -72) T) ((-949 . -13) T) ((-949 . -1130) T) ((-949 . -554) 135644) ((-949 . -1015) T) ((-949 . -23) T) ((-949 . -21) T) ((-949 . -970) 135618) ((-949 . -965) 135592) ((-949 . -82) 135559) ((-949 . -38) 135543) ((-949 . -584) 135527) ((-949 . -656) 135511) ((-942 . -985) 135480) ((-942 . -891) 135449) ((-942 . -555) 135410) ((-942 . -427) 135394) ((-942 . -1015) T) ((-942 . -454) 135327) ((-942 . -260) 135265) ((-942 . -554) 135227) ((-942 . -72) T) ((-942 . -1130) T) ((-942 . -13) T) ((-942 . -34) T) ((-942 . -124) 135211) ((-942 . -1125) 135180) ((-941 . -1015) T) ((-941 . -554) 135162) ((-941 . -1130) T) ((-941 . -13) T) ((-941 . -72) T) ((-939 . -927) T) ((-939 . -917) T) ((-939 . -716) T) ((-939 . -718) T) ((-939 . -758) T) ((-939 . -761) T) ((-939 . -720) T) ((-939 . -723) T) ((-939 . -757) T) ((-939 . -952) 135047) ((-939 . -353) 135009) ((-939 . -201) T) ((-939 . -246) T) ((-939 . -258) T) ((-939 . -390) T) ((-939 . -38) 134946) ((-939 . -584) 134883) ((-939 . -656) 134820) ((-939 . -557) 134757) ((-939 . -496) T) ((-939 . -834) T) ((-939 . -1135) T) ((-939 . -312) T) ((-939 . -82) 134666) ((-939 . -965) 134603) ((-939 . -970) 134540) ((-939 . -146) T) ((-939 . -120) T) ((-939 . -592) 134477) ((-939 . -590) 134414) ((-939 . -104) T) ((-939 . -25) T) ((-939 . -72) T) ((-939 . -13) T) ((-939 . -1130) T) ((-939 . -554) 134396) ((-939 . -1015) T) ((-939 . -23) T) ((-939 . -21) T) ((-939 . -963) T) ((-939 . -665) T) ((-939 . -1062) T) ((-939 . -1027) T) ((-939 . -972) T) ((-934 . -997) T) ((-934 . -428) 134377) ((-934 . -554) 134343) 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-189) T) ((-919 . -225) 133584) ((-919 . -808) NIL) ((-919 . -813) NIL) ((-919 . -811) NIL) ((-919 . -184) 133566) ((-919 . -120) T) ((-919 . -118) NIL) ((-919 . -104) T) ((-919 . -25) T) ((-919 . -72) T) ((-919 . -13) T) ((-919 . -1130) T) ((-919 . -554) 133526) ((-919 . -1015) T) ((-919 . -23) T) ((-919 . -21) T) ((-919 . -963) T) ((-919 . -665) T) ((-919 . -1062) T) ((-919 . -1027) T) ((-919 . -972) T) ((-918 . -291) 133500) ((-918 . -146) T) ((-918 . -557) 133430) ((-918 . -972) T) ((-918 . -1027) T) ((-918 . -1062) T) ((-918 . -665) T) ((-918 . -963) T) ((-918 . -592) 133332) ((-918 . -590) 133262) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1130) T) ((-918 . -554) 133244) ((-918 . -1015) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -970) 133189) ((-918 . -965) 133134) ((-918 . -82) 133051) ((-918 . -555) 133035) ((-918 . -184) 133012) ((-918 . -811) 132964) ((-918 . -813) 132876) ((-918 . -808) 132786) ((-918 . -225) 132763) ((-918 . -189) 132703) ((-918 . -186) 132637) ((-918 . -190) 132609) ((-918 . -312) T) ((-918 . -1135) T) ((-918 . -834) T) ((-918 . -496) T) ((-918 . -656) 132554) ((-918 . -584) 132499) ((-918 . -38) 132444) ((-918 . -390) T) ((-918 . -258) T) ((-918 . -246) T) ((-918 . -201) T) ((-918 . -318) NIL) ((-918 . -299) NIL) ((-918 . -1067) NIL) ((-918 . -118) 132416) ((-918 . -343) NIL) ((-918 . -351) 132388) ((-918 . -120) 132360) ((-918 . -320) 132332) ((-918 . -327) 132309) ((-918 . -582) 132243) ((-918 . -353) 132220) ((-918 . -952) 132097) ((-918 . -663) 132069) ((-915 . -910) 132053) ((-915 . -427) 132037) ((-915 . -1015) 132015) ((-915 . -454) 131948) ((-915 . -260) 131886) ((-915 . -554) 131821) ((-915 . -72) 131775) ((-915 . -1130) T) ((-915 . -13) T) ((-915 . -34) T) ((-915 . -76) 131759) ((-911 . -913) 131743) ((-911 . -761) 131722) ((-911 . -758) 131701) ((-911 . -952) 131599) ((-911 . -353) 131583) ((-911 . -582) 131531) ((-911 . -592) 131433) ((-911 . -327) 131417) ((-911 . -241) 131375) 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((-908 . -590) 129975) ((-908 . -23) T) ((-908 . -1015) T) ((-908 . -554) 129957) ((-908 . -1130) T) ((-908 . -13) T) ((-908 . -72) T) ((-908 . -25) T) ((-908 . -104) T) ((-908 . -241) 129924) ((-904 . -554) 129906) ((-901 . -1015) T) ((-901 . -554) 129888) ((-901 . -1130) T) ((-901 . -13) T) ((-901 . -72) T) ((-886 . -723) T) ((-886 . -720) T) ((-886 . -761) T) ((-886 . -758) T) ((-886 . -718) T) ((-886 . -23) T) ((-886 . -1015) T) ((-886 . -554) 129848) ((-886 . -1130) T) ((-886 . -13) T) ((-886 . -72) T) ((-886 . -25) T) ((-886 . -104) T) ((-885 . -997) T) ((-885 . -428) 129829) ((-885 . -554) 129795) ((-885 . -557) 129776) ((-885 . -1015) T) ((-885 . -1130) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -64) T) ((-879 . -882) T) ((-879 . -72) T) ((-879 . -554) 129758) ((-879 . -1015) T) ((-879 . -606) T) ((-879 . -13) T) ((-879 . -1130) T) ((-879 . -84) T) ((-879 . -557) 129742) ((-878 . -554) 129724) ((-877 . -1015) T) ((-877 . -554) 129706) ((-877 . -1130) T) ((-877 . -13) T) 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125090) ((-859 . -82) 124915) ((-859 . -965) 124761) ((-859 . -970) 124607) ((-859 . -146) 124521) ((-859 . -120) 124500) ((-859 . -118) 124479) ((-859 . -590) 124389) ((-859 . -104) T) ((-859 . -25) T) ((-859 . -72) T) ((-859 . -13) T) ((-859 . -1130) T) ((-859 . -554) 124371) ((-859 . -1015) T) ((-859 . -23) T) ((-859 . -21) T) ((-859 . -963) T) ((-859 . -665) T) ((-859 . -1062) T) ((-859 . -1027) T) ((-859 . -972) T) ((-859 . -353) 124355) ((-859 . -277) 124324) ((-859 . -260) 124311) ((-859 . -555) 124172) ((-856 . -895) 124156) ((-856 . -19) 124140) ((-856 . -595) 124124) ((-856 . -243) 124101) ((-856 . -241) 124053) ((-856 . -540) 124030) ((-856 . -555) 123991) ((-856 . -427) 123975) ((-856 . -1015) 123928) ((-856 . -454) 123861) ((-856 . -260) 123799) ((-856 . -554) 123714) ((-856 . -72) 123648) ((-856 . -1130) T) ((-856 . -13) T) ((-856 . -34) T) ((-856 . -124) 123632) ((-856 . -758) 123611) ((-856 . -761) 123590) ((-856 . -322) 123574) ((-856 . -1179) 123558) ((-856 . -559) 123535) ((-840 . -889) T) ((-840 . -554) 123517) ((-838 . -868) T) ((-838 . -554) 123499) ((-832 . -720) T) ((-832 . -761) T) ((-832 . -758) T) ((-832 . -1015) T) ((-832 . -554) 123481) ((-832 . -1130) T) ((-832 . -13) T) ((-832 . -72) T) ((-832 . -25) T) ((-832 . -665) T) ((-832 . -1027) T) ((-827 . -312) T) ((-827 . -1135) T) ((-827 . -834) T) ((-827 . -496) T) ((-827 . -146) T) ((-827 . -557) 123418) ((-827 . -656) 123370) ((-827 . -584) 123322) ((-827 . -38) 123274) ((-827 . -390) T) ((-827 . -258) T) ((-827 . -592) 123226) ((-827 . -590) 123163) ((-827 . -972) T) ((-827 . -1027) T) ((-827 . -1062) T) ((-827 . -665) T) ((-827 . -963) T) ((-827 . -82) 123094) ((-827 . -965) 123046) ((-827 . -970) 122998) ((-827 . -21) T) ((-827 . -23) T) ((-827 . -1015) T) ((-827 . -554) 122980) ((-827 . -1130) T) ((-827 . -13) T) ((-827 . -72) T) ((-827 . -25) T) ((-827 . -104) T) ((-827 . -246) T) ((-827 . -201) T) ((-819 . -299) T) ((-819 . -1067) T) ((-819 . -318) T) ((-819 . -118) T) ((-819 . -312) T) ((-819 . -1135) T) ((-819 . -834) T) ((-819 . -496) T) ((-819 . -146) T) ((-819 . -557) 122930) ((-819 . -656) 122895) ((-819 . -584) 122860) ((-819 . -38) 122825) ((-819 . -390) T) ((-819 . -258) T) ((-819 . -82) 122774) ((-819 . -965) 122739) ((-819 . -970) 122704) ((-819 . -590) 122654) ((-819 . -592) 122619) ((-819 . -246) T) ((-819 . -201) T) ((-819 . -343) T) ((-819 . -189) T) ((-819 . -1130) T) ((-819 . -13) T) ((-819 . -186) 122606) ((-819 . -963) T) ((-819 . -665) T) ((-819 . -1062) T) ((-819 . -1027) T) ((-819 . -972) T) ((-819 . -21) T) ((-819 . -23) T) ((-819 . -1015) T) ((-819 . -554) 122588) ((-819 . -72) T) ((-819 . -25) T) ((-819 . -104) T) ((-819 . -190) T) ((-819 . -280) 122575) ((-819 . -120) 122557) ((-819 . -952) 122544) ((-819 . -1188) 122531) ((-819 . -1199) 122518) ((-819 . -555) 122500) ((-818 . -1015) T) ((-818 . -554) 122482) ((-818 . -1130) T) ((-818 . -13) T) ((-818 . -72) T) ((-815 . -817) 122466) ((-815 . -761) 122420) ((-815 . -758) 122374) 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121750) ((-787 . -1015) T) ((-787 . -1130) T) ((-787 . -13) T) ((-787 . -72) T) ((-787 . -64) T) ((-787 . -1176) T) ((-785 . -1015) T) ((-785 . -554) 121732) ((-785 . -1130) T) ((-785 . -13) T) ((-785 . -72) T) ((-785 . -557) 121714) ((-784 . -1130) T) ((-784 . -13) T) ((-784 . -554) 121589) ((-784 . -1015) 121540) ((-784 . -72) 121491) ((-783 . -906) 121475) ((-783 . -1067) 121453) ((-783 . -952) 121320) ((-783 . -557) 121219) ((-783 . -555) 121022) ((-783 . -935) 121001) ((-783 . -823) 120980) ((-783 . -796) 120964) ((-783 . -757) 120943) ((-783 . -723) 120922) ((-783 . -720) 120901) ((-783 . -761) 120855) ((-783 . -758) 120809) ((-783 . -718) 120788) ((-783 . -716) 120767) ((-783 . -742) 120746) ((-783 . -798) 120671) ((-783 . -341) 120655) ((-783 . -582) 120603) ((-783 . -592) 120519) ((-783 . -327) 120503) ((-783 . -241) 120461) ((-783 . -260) 120426) ((-783 . -454) 120338) ((-783 . -288) 120322) ((-783 . -201) T) ((-783 . -82) 120253) ((-783 . -965) 120205) ((-783 . -970) 120157) ((-783 . -246) T) ((-783 . -656) 120109) ((-783 . -584) 120061) ((-783 . -590) 119998) ((-783 . -38) 119950) ((-783 . -258) T) ((-783 . -390) T) ((-783 . -146) T) ((-783 . -496) T) ((-783 . -834) T) ((-783 . -1135) T) ((-783 . -312) T) ((-783 . -190) 119929) ((-783 . -186) 119877) ((-783 . -189) 119831) ((-783 . -225) 119815) ((-783 . -808) 119739) ((-783 . -813) 119665) ((-783 . -811) 119624) ((-783 . -184) 119608) ((-783 . -120) 119587) ((-783 . -118) 119566) ((-783 . -104) T) ((-783 . -25) T) ((-783 . -72) T) ((-783 . -13) T) ((-783 . -1130) T) ((-783 . -554) 119548) ((-783 . -1015) T) ((-783 . -23) T) ((-783 . -21) T) ((-783 . -963) T) ((-783 . -665) T) ((-783 . -1062) T) ((-783 . -1027) T) ((-783 . -972) T) ((-782 . -906) 119525) ((-782 . -1067) NIL) ((-782 . -952) 119502) ((-782 . -557) 119432) ((-782 . -555) NIL) ((-782 . -935) NIL) ((-782 . -823) NIL) ((-782 . -796) 119409) ((-782 . -757) NIL) ((-782 . -723) NIL) ((-782 . -720) NIL) ((-782 . -761) NIL) ((-782 . -758) NIL) 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-1062) T) ((-782 . -1027) T) ((-782 . -972) T) ((-780 . -781) 118491) ((-780 . -834) T) ((-780 . -496) T) ((-780 . -246) T) ((-780 . -146) T) ((-780 . -557) 118463) ((-780 . -656) 118450) ((-780 . -584) 118437) ((-780 . -970) 118424) ((-780 . -965) 118411) ((-780 . -82) 118396) ((-780 . -38) 118383) ((-780 . -390) T) ((-780 . -258) T) ((-780 . -963) T) ((-780 . -665) T) ((-780 . -1062) T) ((-780 . -1027) T) ((-780 . -972) T) ((-780 . -21) T) ((-780 . -590) 118355) ((-780 . -23) T) ((-780 . -1015) T) ((-780 . -554) 118337) ((-780 . -1130) T) ((-780 . -13) T) ((-780 . -72) T) ((-780 . -25) T) ((-780 . -104) T) ((-780 . -592) 118324) ((-780 . -120) T) ((-777 . -963) T) ((-777 . -665) T) ((-777 . -1062) T) ((-777 . -1027) T) ((-777 . -972) T) ((-777 . -21) T) ((-777 . -590) 118269) ((-777 . -23) T) ((-777 . -1015) T) ((-777 . -554) 118231) ((-777 . -1130) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -25) T) ((-777 . -104) T) ((-777 . -592) 118191) ((-777 . -557) 118126) ((-777 . -428) 118103) ((-777 . -38) 118073) ((-777 . -82) 118038) ((-777 . -965) 118008) ((-777 . -970) 117978) ((-777 . -584) 117948) ((-777 . -656) 117918) ((-776 . -1015) T) ((-776 . -554) 117900) ((-776 . -1130) T) ((-776 . -13) T) ((-776 . -72) T) ((-775 . -754) T) ((-775 . -761) T) ((-775 . -758) T) ((-775 . -1015) T) ((-775 . -554) 117882) ((-775 . -1130) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -318) T) ((-775 . -555) 117804) ((-774 . -1015) T) ((-774 . -554) 117786) ((-774 . -1130) T) ((-774 . -13) T) ((-774 . -72) T) ((-773 . -772) T) ((-773 . -147) T) ((-773 . -554) 117768) ((-769 . -758) T) ((-769 . -554) 117750) ((-769 . -1015) T) ((-769 . -72) T) ((-769 . -13) T) ((-769 . -1130) T) ((-769 . -761) T) ((-766 . -763) 117734) ((-766 . -952) 117632) ((-766 . -557) 117530) ((-766 . -353) 117514) ((-766 . -656) 117484) ((-766 . -584) 117454) ((-766 . -592) 117428) ((-766 . -590) 117387) ((-766 . -104) T) ((-766 . -25) T) ((-766 . -72) T) ((-766 . -13) T) ((-766 . -1130) T) ((-766 . -554) 117369) ((-766 . -1015) T) ((-766 . -23) T) ((-766 . -21) T) ((-766 . -970) 117353) ((-766 . -965) 117337) ((-766 . -82) 117316) ((-766 . -963) T) ((-766 . -665) T) ((-766 . -1062) T) ((-766 . -1027) T) ((-766 . -972) T) ((-766 . -38) 117286) ((-765 . -763) 117270) ((-765 . -952) 117168) ((-765 . -557) 117087) ((-765 . -353) 117071) ((-765 . -656) 117041) ((-765 . -584) 117011) ((-765 . -592) 116985) ((-765 . -590) 116944) ((-765 . -104) T) ((-765 . -25) T) ((-765 . -72) T) ((-765 . -13) T) ((-765 . -1130) T) ((-765 . -554) 116926) ((-765 . -1015) T) ((-765 . -23) T) ((-765 . -21) T) ((-765 . -970) 116910) ((-765 . -965) 116894) ((-765 . -82) 116873) ((-765 . -963) T) ((-765 . -665) T) ((-765 . -1062) T) ((-765 . -1027) T) ((-765 . -972) T) ((-765 . -38) 116843) ((-759 . -761) T) ((-759 . -1130) T) ((-759 . -13) T) ((-759 . -72) T) ((-759 . -428) 116827) ((-759 . -554) 116775) ((-759 . -557) 116759) ((-752 . -1015) T) ((-752 . -554) 116741) ((-752 . -1130) T) ((-752 . -13) T) ((-752 . -72) T) ((-752 . -353) 116725) ((-752 . -557) 116598) ((-752 . -952) 116496) ((-752 . -21) 116451) ((-752 . -590) 116371) ((-752 . -23) 116326) ((-752 . -25) 116281) ((-752 . -104) 116236) ((-752 . -757) 116215) ((-752 . -592) 116188) ((-752 . -972) 116167) ((-752 . -1062) 116146) ((-752 . -963) 116125) ((-752 . -723) 116104) ((-752 . -720) 116083) ((-752 . -761) 116062) ((-752 . -758) 116041) ((-752 . -718) 116020) ((-752 . -716) 115999) ((-752 . -1027) 115978) ((-752 . -665) 115957) ((-751 . -749) 115939) ((-751 . -72) T) ((-751 . -13) T) ((-751 . -1130) T) ((-751 . -554) 115921) ((-751 . -1015) T) ((-747 . -963) T) ((-747 . -665) T) ((-747 . -1062) T) ((-747 . -1027) T) ((-747 . -972) T) ((-747 . -21) T) ((-747 . -590) 115866) ((-747 . -23) T) ((-747 . -1015) T) ((-747 . -554) 115848) ((-747 . -1130) T) ((-747 . -13) T) ((-747 . -72) T) ((-747 . -25) T) ((-747 . -104) T) ((-747 . -592) 115808) ((-747 . -557) 115763) ((-747 . -952) 115733) ((-747 . -241) 115712) ((-747 . -120) 115691) ((-747 . -118) 115670) ((-747 . -38) 115640) ((-747 . -82) 115605) ((-747 . -965) 115575) ((-747 . -970) 115545) ((-747 . -584) 115515) ((-747 . -656) 115485) ((-745 . -1015) T) ((-745 . -554) 115467) ((-745 . -1130) T) ((-745 . -13) T) ((-745 . -72) T) ((-745 . -353) 115451) ((-745 . -557) 115324) ((-745 . -952) 115222) ((-745 . -21) 115177) ((-745 . -590) 115097) ((-745 . -23) 115052) ((-745 . -25) 115007) ((-745 . -104) 114962) ((-745 . -757) 114941) ((-745 . -592) 114914) ((-745 . -972) 114893) ((-745 . -1062) 114872) ((-745 . -963) 114851) ((-745 . -723) 114830) ((-745 . -720) 114809) ((-745 . -761) 114788) ((-745 . -758) 114767) ((-745 . -718) 114746) ((-745 . -716) 114725) ((-745 . -1027) 114704) ((-745 . -665) 114683) ((-743 . -647) 114667) ((-743 . -557) 114622) ((-743 . -656) 114592) ((-743 . -584) 114562) ((-743 . -592) 114536) ((-743 . -590) 114495) ((-743 . -104) T) ((-743 . -25) T) ((-743 . -72) T) ((-743 . -13) T) ((-743 . -1130) T) ((-743 . -554) 114477) ((-743 . -1015) T) ((-743 . -23) T) ((-743 . -21) T) ((-743 . -970) 114461) ((-743 . -965) 114445) ((-743 . -82) 114424) ((-743 . -963) T) ((-743 . -665) T) ((-743 . -1062) T) ((-743 . -1027) T) ((-743 . -972) T) ((-743 . -38) 114394) ((-743 . -190) 114373) ((-743 . -186) 114346) ((-743 . -189) 114325) ((-741 . -334) 114309) ((-741 . -557) 114293) ((-741 . -952) 114277) ((-741 . -761) T) ((-741 . -758) T) ((-741 . -1027) T) ((-741 . -72) T) ((-741 . -13) T) ((-741 . -1130) T) ((-741 . -554) 114259) ((-741 . -1015) T) ((-741 . -665) T) ((-741 . -756) T) ((-741 . -768) T) ((-740 . -228) 114243) ((-740 . -557) 114227) ((-740 . -952) 114211) ((-740 . -761) T) ((-740 . -72) T) ((-740 . -1015) T) ((-740 . -554) 114193) ((-740 . -758) T) ((-740 . -186) 114180) ((-740 . -13) T) ((-740 . -1130) T) ((-740 . -189) T) ((-739 . -82) 114115) ((-739 . -965) 114066) ((-739 . -970) 114017) ((-739 . -21) T) ((-739 . -590) 113953) ((-739 . -23) T) ((-739 . -1015) T) ((-739 . -554) 113922) ((-739 . -1130) T) ((-739 . -13) T) ((-739 . -72) T) ((-739 . -25) T) ((-739 . -104) T) ((-739 . -592) 113873) ((-739 . -190) T) ((-739 . -557) 113782) ((-739 . -972) T) ((-739 . -1027) T) ((-739 . -1062) T) ((-739 . -665) T) ((-739 . -963) T) ((-739 . -186) 113769) ((-739 . -189) T) ((-739 . -428) 113753) ((-739 . -312) 113732) ((-739 . -1135) 113711) ((-739 . -834) 113690) ((-739 . -496) 113669) ((-739 . -146) 113648) ((-739 . -656) 113585) ((-739 . -584) 113522) ((-739 . -38) 113459) ((-739 . -390) 113438) ((-739 . -258) 113417) ((-739 . -246) 113396) ((-739 . -201) 113375) ((-738 . -213) 113314) ((-738 . -557) 113058) ((-738 . -952) 112888) ((-738 . -555) NIL) ((-738 . -277) 112850) ((-738 . -353) 112834) ((-738 . -38) 112686) ((-738 . -82) 112511) ((-738 . -965) 112357) ((-738 . -970) 112203) ((-738 . -590) 112113) ((-738 . -592) 112002) ((-738 . -584) 111854) ((-738 . -656) 111706) ((-738 . -118) 111685) ((-738 . -120) 111664) ((-738 . -146) 111578) ((-738 . -496) 111512) ((-738 . -246) 111446) 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. -1130) T) ((-619 . -13) T) ((-619 . -72) T) ((-619 . -64) T) ((-616 . -758) T) ((-616 . -554) 92677) ((-616 . -1015) T) ((-616 . -72) T) ((-616 . -13) T) ((-616 . -1130) T) ((-616 . -761) T) ((-616 . -952) 92661) ((-616 . -557) 92645) ((-615 . -997) T) ((-615 . -428) 92626) ((-615 . -554) 92592) ((-615 . -557) 92573) ((-615 . -1015) T) ((-615 . -1130) T) ((-615 . -13) T) ((-615 . -72) T) ((-615 . -64) T) ((-614 . -1038) 92518) ((-614 . -427) 92502) ((-614 . -454) 92435) ((-614 . -260) 92373) ((-614 . -34) T) ((-614 . -967) 92313) ((-614 . -952) 92211) ((-614 . -557) 92130) ((-614 . -353) 92114) ((-614 . -582) 92062) ((-614 . -592) 92000) ((-614 . -327) 91984) ((-614 . -190) 91963) ((-614 . -186) 91911) ((-614 . -189) 91865) ((-614 . -225) 91849) ((-614 . -808) 91773) ((-614 . -813) 91699) ((-614 . -811) 91658) ((-614 . -184) 91642) ((-614 . -656) 91626) ((-614 . -584) 91610) ((-614 . -590) 91569) ((-614 . -104) T) ((-614 . -25) T) ((-614 . -72) T) ((-614 . -13) T) ((-614 . -1130) T) 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. -834) 85642) ((-560 . -38) 85626) ((-560 . -557) 85595) ((-560 . -592) 85569) ((-560 . -590) 85528) ((-560 . -972) T) ((-560 . -1027) T) ((-560 . -1062) T) ((-560 . -665) T) ((-560 . -963) T) ((-560 . -82) 85507) ((-560 . -965) 85491) ((-560 . -970) 85475) ((-560 . -21) T) ((-560 . -23) T) ((-560 . -1015) T) ((-560 . -554) 85457) ((-560 . -1130) T) ((-560 . -13) T) ((-560 . -72) T) ((-560 . -25) T) ((-560 . -104) T) ((-560 . -584) 85441) ((-560 . -656) 85425) ((-560 . -757) 85404) ((-560 . -723) 85383) ((-560 . -720) 85362) ((-560 . -761) 85341) ((-560 . -758) 85320) ((-560 . -718) 85299) ((-560 . -716) 85278) ((-558 . -882) T) ((-558 . -72) T) ((-558 . -554) 85260) ((-558 . -1015) T) ((-558 . -606) T) ((-558 . -13) T) ((-558 . -1130) T) ((-558 . -84) T) ((-558 . -318) T) ((-552 . -105) T) ((-552 . -72) T) ((-552 . -13) T) ((-552 . -1130) T) ((-552 . -554) 85242) ((-552 . -1015) T) ((-552 . -758) T) ((-552 . -761) T) ((-552 . -796) 85226) ((-552 . -555) 85087) ((-549 . -314) 85025) 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83894) ((-543 . -1130) T) ((-543 . -13) T) ((-543 . -72) T) ((-543 . -428) 83876) ((-543 . -557) 83858) ((-542 . -685) 83842) ((-542 . -659) T) ((-542 . -687) T) ((-542 . -82) 83821) ((-542 . -965) 83805) ((-542 . -970) 83789) ((-542 . -21) T) ((-542 . -590) 83758) ((-542 . -23) T) ((-542 . -1015) T) ((-542 . -554) 83727) ((-542 . -1130) T) ((-542 . -13) T) ((-542 . -72) T) ((-542 . -25) T) ((-542 . -104) T) ((-542 . -592) 83711) ((-542 . -584) 83695) ((-542 . -656) 83679) ((-542 . -359) 83644) ((-542 . -316) 83579) ((-542 . -241) 83537) ((-541 . -997) T) ((-541 . -428) 83518) ((-541 . -554) 83468) ((-541 . -557) 83449) ((-541 . -1015) T) ((-541 . -1130) T) ((-541 . -13) T) ((-541 . -72) T) ((-541 . -64) T) ((-538 . -1179) 83433) ((-538 . -322) 83417) ((-538 . -761) 83396) ((-538 . -758) 83375) ((-538 . -124) 83359) ((-538 . -34) T) ((-538 . -13) T) ((-538 . -1130) T) ((-538 . -72) 83293) ((-538 . -554) 83208) ((-538 . -260) 83146) ((-538 . -454) 83079) ((-538 . -1015) 83032) ((-538 . 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78676) ((-490 . -243) 78655) ((-490 . -1130) T) ((-490 . -13) T) ((-490 . -241) 78634) ((-490 . -1015) T) ((-490 . -554) 78616) ((-490 . -72) T) ((-490 . -34) T) ((-490 . -540) 78595) ((-489 . -754) T) ((-489 . -761) T) ((-489 . -758) T) ((-489 . -1015) T) ((-489 . -554) 78577) ((-489 . -1130) T) ((-489 . -13) T) ((-489 . -72) T) ((-489 . -318) T) ((-488 . -754) T) ((-488 . -761) T) ((-488 . -758) T) ((-488 . -1015) T) ((-488 . -554) 78559) ((-488 . -1130) T) ((-488 . -13) T) ((-488 . -72) T) ((-488 . -318) T) ((-487 . -754) T) ((-487 . -761) T) ((-487 . -758) T) ((-487 . -1015) T) ((-487 . -554) 78541) ((-487 . -1130) T) ((-487 . -13) T) ((-487 . -72) T) ((-487 . -318) T) ((-486 . -754) T) ((-486 . -761) T) ((-486 . -758) T) ((-486 . -1015) T) ((-486 . -554) 78523) ((-486 . -1130) T) ((-486 . -13) T) ((-486 . -72) T) ((-486 . -318) T) ((-485 . -484) T) ((-485 . -1135) T) ((-485 . -1067) T) ((-485 . -952) 78505) ((-485 . -555) 78420) ((-485 . -935) T) ((-485 . -798) 78402) ((-485 . -757) T) ((-485 . -723) T) ((-485 . -720) T) ((-485 . -761) T) ((-485 . -758) T) ((-485 . -718) T) ((-485 . -716) T) ((-485 . -742) T) ((-485 . -592) 78374) ((-485 . -582) 78356) ((-485 . -834) T) ((-485 . -496) T) ((-485 . -246) T) ((-485 . -146) T) ((-485 . -557) 78328) ((-485 . -656) 78315) ((-485 . -584) 78302) ((-485 . -970) 78289) ((-485 . -965) 78276) ((-485 . -82) 78261) ((-485 . -38) 78248) ((-485 . -390) T) ((-485 . -258) T) ((-485 . -189) T) ((-485 . -186) 78235) ((-485 . -190) T) ((-485 . -116) T) ((-485 . -963) T) ((-485 . -665) T) ((-485 . -1062) T) ((-485 . -1027) T) ((-485 . -972) T) ((-485 . -21) T) ((-485 . -590) 78207) ((-485 . -23) T) ((-485 . -1015) T) ((-485 . -554) 78189) ((-485 . -1130) T) ((-485 . -13) T) ((-485 . -72) T) ((-485 . -25) T) ((-485 . -104) T) ((-485 . -120) T) ((-474 . -1018) 78141) ((-474 . -72) T) ((-474 . -554) 78123) ((-474 . -1015) T) ((-474 . -241) 78079) ((-474 . -1130) T) ((-474 . -13) T) ((-474 . -559) 77982) ((-474 . -555) 77963) ((-472 . -693) 77945) ((-472 . -466) T) ((-472 . -147) T) ((-472 . -772) T) ((-472 . -513) T) ((-472 . -554) 77927) ((-470 . -719) T) ((-470 . -104) T) ((-470 . -25) T) ((-470 . -72) T) ((-470 . -13) T) ((-470 . -1130) T) ((-470 . -554) 77909) ((-470 . -1015) T) ((-470 . -23) T) ((-470 . -718) T) ((-470 . -758) T) ((-470 . -761) T) ((-470 . -720) T) ((-470 . -723) T) ((-470 . -448) 77886) ((-470 . -559) 77849) ((-468 . -466) T) ((-468 . -147) T) ((-468 . -554) 77831) ((-464 . -997) T) ((-464 . -428) 77812) ((-464 . -554) 77778) ((-464 . -557) 77759) ((-464 . -1015) T) ((-464 . -1130) T) ((-464 . -13) T) ((-464 . -72) T) ((-464 . -64) T) ((-463 . -997) T) ((-463 . -428) 77740) ((-463 . -554) 77706) ((-463 . -557) 77687) ((-463 . -1015) T) ((-463 . -1130) T) ((-463 . -13) T) ((-463 . -72) T) ((-463 . -64) T) ((-462 . -629) 77637) ((-462 . -427) 77621) ((-462 . -1015) 77599) ((-462 . -454) 77532) ((-462 . -260) 77470) ((-462 . -554) 77405) ((-462 . -72) 77359) ((-462 . -1130) T) ((-462 . -13) T) ((-462 . -34) T) ((-462 . -57) 77309) ((-459 . -57) 77283) ((-459 . -34) T) ((-459 . -13) T) ((-459 . -1130) T) ((-459 . -72) 77237) ((-459 . -554) 77172) ((-459 . -260) 77110) ((-459 . -454) 77043) ((-459 . -1015) 77021) ((-459 . -427) 77005) ((-458 . -280) 76982) ((-458 . -190) T) ((-458 . -186) 76969) ((-458 . -189) T) ((-458 . -318) T) ((-458 . -1067) T) ((-458 . -299) T) ((-458 . -120) 76951) ((-458 . -557) 76881) ((-458 . -592) 76826) ((-458 . -590) 76756) ((-458 . -104) T) ((-458 . -25) T) ((-458 . -72) T) ((-458 . -13) T) ((-458 . -1130) T) ((-458 . -554) 76738) ((-458 . -1015) T) ((-458 . -23) T) ((-458 . -21) T) ((-458 . -972) T) ((-458 . -1027) T) ((-458 . -1062) T) ((-458 . -665) T) ((-458 . -963) T) ((-458 . -312) T) ((-458 . -1135) T) ((-458 . -834) T) ((-458 . -496) T) ((-458 . -146) T) ((-458 . -656) 76683) ((-458 . -584) 76628) ((-458 . -38) 76593) ((-458 . -390) T) ((-458 . -258) T) ((-458 . -82) 76510) ((-458 . -965) 76455) ((-458 . -970) 76400) ((-458 . -246) T) 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72256) ((-422 . -454) 72189) ((-422 . -260) 72127) ((-422 . -554) 72062) ((-422 . -72) 72016) ((-422 . -1130) T) ((-422 . -13) T) ((-422 . -34) T) ((-422 . -76) 72000) ((-421 . -997) T) ((-421 . -428) 71981) ((-421 . -554) 71947) ((-421 . -557) 71928) ((-421 . -1015) T) ((-421 . -1130) T) ((-421 . -13) T) ((-421 . -72) T) ((-421 . -64) T) ((-420 . -196) 71907) ((-420 . -1188) 71877) ((-420 . -723) 71856) ((-420 . -720) 71835) ((-420 . -761) 71789) ((-420 . -758) 71743) ((-420 . -718) 71722) ((-420 . -719) 71701) ((-420 . -656) 71646) ((-420 . -584) 71571) ((-420 . -243) 71548) ((-420 . -241) 71525) ((-420 . -427) 71509) ((-420 . -454) 71442) ((-420 . -260) 71380) ((-420 . -34) T) ((-420 . -540) 71357) ((-420 . -952) 71186) ((-420 . -557) 70990) ((-420 . -353) 70959) ((-420 . -582) 70867) ((-420 . -592) 70706) ((-420 . -327) 70676) ((-420 . -318) 70655) ((-420 . -190) 70608) ((-420 . -590) 70396) ((-420 . -972) 70375) ((-420 . -1027) 70354) ((-420 . -1062) 70333) ((-420 . -665) 70312) 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. -965) 60178) ((-399 . -82) 60139) ((-392 . -863) 60106) ((-392 . -557) 59898) ((-392 . -952) 59776) ((-392 . -1135) 59755) ((-392 . -823) 59734) ((-392 . -798) NIL) ((-392 . -813) 59711) ((-392 . -808) 59686) ((-392 . -811) 59663) ((-392 . -454) 59601) ((-392 . -390) 59555) ((-392 . -582) 59503) ((-392 . -592) 59392) ((-392 . -327) 59376) ((-392 . -47) 59355) ((-392 . -38) 59207) ((-392 . -584) 59059) ((-392 . -656) 58911) ((-392 . -246) 58845) ((-392 . -496) 58779) ((-392 . -82) 58604) ((-392 . -965) 58450) ((-392 . -970) 58296) ((-392 . -146) 58210) ((-392 . -120) 58189) ((-392 . -118) 58168) ((-392 . -590) 58078) ((-392 . -104) T) ((-392 . -25) T) ((-392 . -72) T) ((-392 . -13) T) ((-392 . -1130) T) ((-392 . -554) 58060) ((-392 . -1015) T) ((-392 . -23) T) ((-392 . -21) T) ((-392 . -963) T) ((-392 . -665) T) ((-392 . -1062) T) ((-392 . -1027) T) ((-392 . -972) T) ((-392 . -353) 58044) ((-392 . -277) 58023) ((-392 . -260) 58010) ((-392 . -555) 57871) ((-391 . -359) 57841) ((-391 . 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T) ((-244 . -834) T) ((-244 . -241) 32396) ((-235 . -554) 32378) ((-234 . -554) 32360) ((-229 . -758) T) ((-229 . -554) 32342) ((-229 . -1015) T) ((-229 . -72) T) ((-229 . -13) T) ((-229 . -1130) T) ((-229 . -761) T) ((-226 . -213) 32304) ((-226 . -557) 32064) ((-226 . -952) 31910) ((-226 . -555) 31658) ((-226 . -277) 31630) ((-226 . -353) 31614) ((-226 . -38) 31466) ((-226 . -82) 31291) ((-226 . -965) 31137) ((-226 . -970) 30983) ((-226 . -590) 30893) ((-226 . -592) 30782) ((-226 . -584) 30634) ((-226 . -656) 30486) ((-226 . -118) 30465) ((-226 . -120) 30444) ((-226 . -146) 30358) ((-226 . -496) 30292) ((-226 . -246) 30226) ((-226 . -47) 30198) ((-226 . -327) 30182) ((-226 . -582) 30130) ((-226 . -390) 30084) ((-226 . -454) 29975) ((-226 . -811) 29921) ((-226 . -808) 29830) ((-226 . -813) 29743) ((-226 . -798) 29602) ((-226 . -823) 29581) ((-226 . -1135) 29560) ((-226 . -863) 29527) ((-226 . -260) 29514) ((-226 . -190) 29493) ((-226 . -104) T) ((-226 . -25) T) ((-226 . -72) T) ((-226 . -554) 29475) ((-226 . -1015) T) ((-226 . -23) T) ((-226 . -21) T) ((-226 . -972) T) ((-226 . -1027) T) ((-226 . -1062) T) ((-226 . -665) T) ((-226 . -963) T) ((-226 . -186) 29423) ((-226 . -13) T) ((-226 . -1130) T) ((-226 . -189) 29377) ((-226 . -225) 29361) ((-226 . -184) 29345) ((-221 . -1015) T) ((-221 . -554) 29327) ((-221 . -1130) T) ((-221 . -13) T) ((-221 . -72) T) ((-211 . -196) 29306) ((-211 . -1188) 29276) ((-211 . -723) 29255) ((-211 . -720) 29234) ((-211 . -761) 29188) ((-211 . -758) 29142) ((-211 . -718) 29121) ((-211 . -719) 29100) ((-211 . -656) 29045) ((-211 . -584) 28970) ((-211 . -243) 28947) ((-211 . -241) 28924) ((-211 . -427) 28908) ((-211 . -454) 28841) ((-211 . -260) 28779) ((-211 . -34) T) ((-211 . -540) 28756) ((-211 . -952) 28585) ((-211 . -557) 28389) ((-211 . -353) 28358) ((-211 . -582) 28266) ((-211 . -592) 28092) ((-211 . -327) 28062) ((-211 . -318) 28041) ((-211 . -190) 27994) ((-211 . -590) 27847) ((-211 . -972) 27826) ((-211 . -1027) 27805) ((-211 . 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25364) ((-210 . -972) 25343) ((-210 . -1027) 25322) ((-210 . -1062) 25301) ((-210 . -665) 25280) ((-210 . -963) 25259) ((-210 . -186) 25155) ((-210 . -189) 25057) ((-210 . -225) 25027) ((-210 . -808) 24899) ((-210 . -813) 24773) ((-210 . -811) 24706) ((-210 . -184) 24676) ((-210 . -554) 24637) ((-210 . -970) 24562) ((-210 . -965) 24467) ((-210 . -82) 24387) ((-210 . -104) T) ((-210 . -25) T) ((-210 . -72) T) ((-210 . -13) T) ((-210 . -1130) T) ((-210 . -1015) T) ((-210 . -23) T) ((-210 . -21) T) ((-209 . -1015) T) ((-209 . -554) 24369) ((-209 . -1130) T) ((-209 . -13) T) ((-209 . -72) T) ((-209 . -241) 24343) ((-208 . -160) T) ((-208 . -1015) T) ((-208 . -554) 24310) ((-208 . -1130) T) ((-208 . -13) T) ((-208 . -72) T) ((-208 . -749) 24292) ((-207 . -1015) T) ((-207 . -554) 24274) ((-207 . -1130) T) ((-207 . -13) T) ((-207 . -72) T) ((-206 . -863) 24219) ((-206 . -557) 24011) ((-206 . -952) 23889) ((-206 . -1135) 23868) ((-206 . -823) 23847) ((-206 . -798) NIL) ((-206 . -813) 23824) 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21731) ((-203 . -540) 21708) ((-203 . -555) 21669) ((-203 . -427) 21653) ((-203 . -1015) 21606) ((-203 . -454) 21539) ((-203 . -260) 21477) ((-203 . -554) 21372) ((-203 . -72) 21306) ((-203 . -1130) T) ((-203 . -13) T) ((-203 . -34) T) ((-203 . -124) 21290) ((-203 . -237) 21274) ((-203 . -428) 21251) ((-203 . -557) 21228) ((-197 . -196) 21207) ((-197 . -1188) 21177) ((-197 . -723) 21156) ((-197 . -720) 21135) ((-197 . -761) 21089) ((-197 . -758) 21043) ((-197 . -718) 21022) ((-197 . -719) 21001) ((-197 . -656) 20946) ((-197 . -584) 20871) ((-197 . -243) 20848) ((-197 . -241) 20825) ((-197 . -427) 20809) ((-197 . -454) 20742) ((-197 . -260) 20680) ((-197 . -34) T) ((-197 . -540) 20657) ((-197 . -952) 20486) ((-197 . -557) 20290) ((-197 . -353) 20259) ((-197 . -582) 20167) ((-197 . -592) 20006) ((-197 . -327) 19976) ((-197 . -318) 19955) ((-197 . -190) 19908) ((-197 . -590) 19696) ((-197 . -972) 19675) ((-197 . -1027) 19654) ((-197 . -1062) 19633) ((-197 . -665) 19612) ((-197 . -963) 19591) ((-197 . -186) 19487) ((-197 . -189) 19389) ((-197 . -225) 19359) ((-197 . -808) 19231) ((-197 . -813) 19105) ((-197 . -811) 19038) ((-197 . -184) 19008) ((-197 . -554) 18705) ((-197 . -970) 18630) ((-197 . -965) 18535) ((-197 . -82) 18455) ((-197 . -104) 18330) ((-197 . -25) 18167) ((-197 . -72) 17904) ((-197 . -13) T) ((-197 . -1130) T) ((-197 . -1015) 17660) ((-197 . -23) 17516) ((-197 . -21) 17431) ((-181 . -629) 17389) ((-181 . -427) 17373) ((-181 . -1015) 17351) ((-181 . -454) 17284) ((-181 . -260) 17222) ((-181 . -554) 17157) ((-181 . -72) 17111) ((-181 . -1130) T) ((-181 . -13) T) ((-181 . -34) T) ((-181 . -57) 17069) ((-179 . -345) T) ((-179 . -120) T) ((-179 . -557) 17019) ((-179 . -592) 16984) ((-179 . -590) 16934) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1130) T) ((-179 . -554) 16916) ((-179 . -1015) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -972) T) ((-179 . -1027) T) ((-179 . -1062) T) ((-179 . -665) T) ((-179 . -963) T) ((-179 . -555) 16846) ((-179 . -312) T) ((-179 . -1135) T) ((-179 . -834) T) ((-179 . -496) T) ((-179 . -146) T) ((-179 . -656) 16811) ((-179 . -584) 16776) ((-179 . -38) 16741) ((-179 . -390) T) ((-179 . -258) T) ((-179 . -82) 16690) ((-179 . -965) 16655) ((-179 . -970) 16620) ((-179 . -246) T) ((-179 . -201) T) ((-179 . -757) T) ((-179 . -723) T) ((-179 . -720) T) ((-179 . -761) T) ((-179 . -758) T) ((-179 . -718) T) ((-179 . -716) T) ((-179 . -798) 16602) ((-179 . -917) T) ((-179 . -935) T) ((-179 . -952) 16562) ((-179 . -975) T) ((-179 . -190) T) ((-179 . -186) 16549) ((-179 . -189) T) ((-179 . -1116) T) ((-179 . -1119) T) ((-179 . -431) T) ((-179 . -239) T) ((-179 . -66) T) ((-179 . -35) T) ((-177 . -562) 16526) ((-177 . -557) 16488) ((-177 . -592) 16455) ((-177 . -590) 16407) ((-177 . -972) T) ((-177 . -1027) T) ((-177 . -1062) T) ((-177 . -665) T) ((-177 . -963) T) ((-177 . -21) T) ((-177 . -23) T) ((-177 . -1015) T) ((-177 . -554) 16389) ((-177 . -1130) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -952) 16366) ((-176 . -214) 16350) ((-176 . -1036) 16334) ((-176 . -76) 16318) ((-176 . -34) T) ((-176 . -13) T) ((-176 . -1130) T) ((-176 . -72) 16272) ((-176 . -554) 16207) ((-176 . -260) 16145) ((-176 . -454) 16078) ((-176 . -1015) 16056) ((-176 . -427) 16040) ((-176 . -910) 16024) ((-172 . -997) T) ((-172 . -428) 16005) ((-172 . -554) 15971) ((-172 . -557) 15952) ((-172 . -1015) T) ((-172 . -1130) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -906) 15934) ((-171 . -1067) T) ((-171 . -557) 15884) ((-171 . -952) 15844) ((-171 . -555) 15774) ((-171 . -935) T) ((-171 . -823) NIL) ((-171 . -796) 15756) ((-171 . -757) T) ((-171 . -723) T) ((-171 . -720) T) ((-171 . -761) T) ((-171 . -758) T) ((-171 . -718) T) ((-171 . -716) T) ((-171 . -742) T) ((-171 . -798) 15738) ((-171 . -341) 15720) ((-171 . -582) 15702) ((-171 . -327) 15684) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -454) NIL) ((-171 . -288) 15666) ((-171 . -201) T) ((-171 . -82) 15593) ((-171 . -965) 15543) ((-171 . -970) 15493) ((-171 . -246) T) ((-171 . -656) 15443) ((-171 . -584) 15393) ((-171 . -592) 15343) ((-171 . -590) 15293) ((-171 . -38) 15243) ((-171 . -258) T) ((-171 . -390) T) ((-171 . -146) T) ((-171 . -496) T) ((-171 . -834) T) ((-171 . -1135) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15230) ((-171 . -189) T) ((-171 . -225) 15212) ((-171 . -808) NIL) ((-171 . -813) NIL) ((-171 . -811) NIL) ((-171 . -184) 15194) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1130) T) ((-171 . -554) 15136) ((-171 . -1015) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -963) T) ((-171 . -665) T) ((-171 . -1062) T) ((-171 . -1027) T) ((-171 . -972) T) ((-168 . -754) T) ((-168 . -761) T) ((-168 . -758) T) ((-168 . -1015) T) ((-168 . -554) 15118) ((-168 . -1130) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -318) T) ((-167 . -1015) T) ((-167 . -554) 15100) ((-167 . -1130) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -557) 15077) ((-166 . -1015) T) ((-166 . -554) 15059) ((-166 . -1130) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1015) T) ((-161 . -554) 15041) ((-161 . -1130) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1015) T) ((-158 . -554) 15023) ((-158 . -1130) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1015) T) ((-157 . -554) 15005) ((-157 . -1130) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -749) 14987) ((-154 . -997) T) ((-154 . -428) 14968) ((-154 . -554) 14934) ((-154 . -557) 14915) ((-154 . -1015) T) ((-154 . -1130) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -554) 14897) ((-148 . -38) 14829) ((-148 . -557) 14746) ((-148 . -592) 14678) ((-148 . -590) 14595) ((-148 . -972) T) ((-148 . -1027) T) ((-148 . -1062) T) ((-148 . -665) T) ((-148 . -963) T) ((-148 . -82) 14494) ((-148 . -965) 14426) ((-148 . -970) 14358) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1015) T) ((-148 . -554) 14340) ((-148 . -1130) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . -584) 14272) ((-148 . -656) 14204) ((-148 . -312) T) ((-148 . -1135) T) ((-148 . -834) T) ((-148 . -496) T) ((-148 . -146) T) ((-148 . -390) T) ((-148 . -258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1015) T) ((-145 . -554) 14186) ((-145 . -1130) T) ((-145 . -13) T) ((-145 . -72) T) ((-142 . -139) 14170) ((-142 . -35) 14148) ((-142 . -66) 14126) ((-142 . -239) 14104) ((-142 . -431) 14082) ((-142 . -1119) 14060) ((-142 . -1116) 14038) ((-142 . -917) 13990) ((-142 . -823) 13943) ((-142 . -555) 13711) ((-142 . -796) 13695) ((-142 . -318) 13649) ((-142 . -299) 13628) ((-142 . -1067) 13607) ((-142 . -343) 13586) ((-142 . -351) 13557) ((-142 . -38) 13391) ((-142 . -82) 13283) ((-142 . -965) 13196) ((-142 . -970) 13109) ((-142 . -584) 12943) ((-142 . -656) 12777) ((-142 . -320) 12748) ((-142 . -663) 12719) ((-142 . -952) 12617) ((-142 . -557) 12402) ((-142 . -353) 12386) ((-142 . 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T) ((-135 . -13) T) ((-135 . -72) T) ((-135 . -64) T) ((-134 . -1015) T) ((-134 . -554) 10685) ((-134 . -1130) T) ((-134 . -13) T) ((-134 . -72) T) ((-130 . -25) T) ((-130 . -72) T) ((-130 . -13) T) ((-130 . -1130) T) ((-130 . -554) 10667) ((-130 . -1015) T) ((-129 . -997) T) ((-129 . -428) 10648) ((-129 . -554) 10614) ((-129 . -557) 10595) ((-129 . -1015) T) ((-129 . -1130) T) ((-129 . -13) T) ((-129 . -72) T) ((-129 . -64) T) ((-127 . -997) T) ((-127 . -428) 10576) ((-127 . -554) 10542) ((-127 . -557) 10523) ((-127 . -1015) T) ((-127 . -1130) T) ((-127 . -13) T) ((-127 . -72) T) ((-127 . -64) T) ((-125 . -963) T) ((-125 . -665) T) ((-125 . -1062) T) ((-125 . -1027) T) ((-125 . -972) T) ((-125 . -21) T) ((-125 . -590) 10482) ((-125 . -23) T) ((-125 . -1015) T) ((-125 . -554) 10464) ((-125 . -1130) T) ((-125 . -13) T) ((-125 . -72) T) ((-125 . -25) T) ((-125 . -104) T) ((-125 . -592) 10438) ((-125 . -557) 10407) ((-125 . -38) 10391) ((-125 . -82) 10370) ((-125 . -965) 10354) ((-125 . 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\ No newline at end of file
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((-1201 . -23) T) ((-1201 . -1014) T) ((-1201 . -553) 198179) ((-1201 . -1129) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -591) 198153) ((-1201 . -1194) 198137) ((-1201 . -655) 198107) ((-1201 . -583) 198077) ((-1201 . -969) 198061) ((-1201 . -964) 198045) ((-1201 . -82) 198024) ((-1201 . -38) 197994) ((-1201 . -1199) 197970) ((-1200 . -1202) 197949) ((-1200 . -951) 197906) ((-1200 . -556) 197835) ((-1200 . -962) T) ((-1200 . -664) T) ((-1200 . -1061) T) ((-1200 . -1026) T) ((-1200 . -971) T) ((-1200 . -21) T) ((-1200 . -589) 197794) ((-1200 . -23) T) ((-1200 . -1014) T) ((-1200 . -553) 197776) ((-1200 . -1129) T) ((-1200 . -13) T) ((-1200 . -72) T) ((-1200 . -25) T) ((-1200 . -104) T) ((-1200 . -591) 197750) ((-1200 . -1194) 197734) ((-1200 . -655) 197704) ((-1200 . -583) 197674) ((-1200 . -969) 197658) ((-1200 . -964) 197642) ((-1200 . -82) 197621) ((-1200 . -38) 197591) ((-1200 . -1199) 197570) ((-1200 . -333) 197542) ((-1195 . -333) 197514) ((-1195 . -556) 197463) ((-1195 . -951) 197440) ((-1195 . -583) 197410) ((-1195 . -655) 197380) ((-1195 . -591) 197354) ((-1195 . -589) 197313) ((-1195 . -104) T) ((-1195 . -25) T) ((-1195 . -72) T) ((-1195 . -13) T) ((-1195 . -1129) T) ((-1195 . -553) 197295) ((-1195 . -1014) T) ((-1195 . -23) T) ((-1195 . -21) T) ((-1195 . -969) 197279) ((-1195 . -964) 197263) ((-1195 . -82) 197242) ((-1195 . -1202) 197221) ((-1195 . -962) T) ((-1195 . -664) T) ((-1195 . -1061) T) ((-1195 . -1026) T) ((-1195 . -971) T) ((-1195 . -1194) 197205) ((-1195 . -38) 197175) ((-1195 . -1199) 197154) ((-1193 . -1124) 197123) ((-1193 . -553) 197085) ((-1193 . -124) 197069) ((-1193 . -34) T) ((-1193 . -13) T) ((-1193 . -1129) T) ((-1193 . -72) T) ((-1193 . -260) 197007) ((-1193 . -454) 196940) ((-1193 . -1014) T) ((-1193 . -427) 196924) ((-1193 . -554) 196885) ((-1193 . -890) 196854) ((-1192 . -962) T) ((-1192 . -664) T) ((-1192 . -1061) T) ((-1192 . -1026) T) ((-1192 . -971) T) ((-1192 . -21) T) ((-1192 . -589) 196799) ((-1192 . -23) T) ((-1192 . -1014) T) ((-1192 . -553) 196768) ((-1192 . -1129) T) ((-1192 . -13) T) ((-1192 . -72) T) ((-1192 . -25) T) ((-1192 . -104) T) ((-1192 . -591) 196728) ((-1192 . -556) 196670) ((-1192 . -428) 196654) ((-1192 . -38) 196624) ((-1192 . -82) 196589) ((-1192 . -964) 196559) ((-1192 . -969) 196529) ((-1192 . -583) 196499) ((-1192 . -655) 196469) ((-1191 . -996) T) ((-1191 . -428) 196450) ((-1191 . -553) 196416) ((-1191 . -556) 196397) ((-1191 . -1014) T) ((-1191 . -1129) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -64) T) ((-1190 . -996) T) ((-1190 . -428) 196378) ((-1190 . -553) 196344) ((-1190 . -556) 196325) ((-1190 . -1014) T) ((-1190 . -1129) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -64) T) ((-1185 . -553) 196307) ((-1183 . -1014) T) ((-1183 . -553) 196289) ((-1183 . -1129) T) ((-1183 . -13) T) ((-1183 . -72) T) ((-1182 . -1014) T) ((-1182 . -553) 196271) ((-1182 . -1129) T) ((-1182 . -13) T) ((-1182 . -72) T) ((-1179 . -1178) 196255) ((-1179 . -322) 196239) ((-1179 . -760) 196218) ((-1179 . -757) 196197) ((-1179 . -124) 196181) ((-1179 . -34) T) ((-1179 . -13) T) ((-1179 . -1129) T) ((-1179 . -72) 196115) ((-1179 . -553) 196030) ((-1179 . -260) 195968) ((-1179 . -454) 195901) ((-1179 . -1014) 195854) ((-1179 . -427) 195838) ((-1179 . -554) 195799) ((-1179 . -241) 195751) ((-1179 . -539) 195728) ((-1179 . -243) 195705) ((-1179 . -594) 195689) ((-1179 . -19) 195673) ((-1176 . -1014) T) ((-1176 . -553) 195639) ((-1176 . -1129) T) ((-1176 . -13) T) ((-1176 . -72) T) ((-1169 . -1172) 195623) ((-1169 . -190) 195582) ((-1169 . -556) 195464) ((-1169 . -591) 195389) ((-1169 . -589) 195299) ((-1169 . -104) T) ((-1169 . -25) T) ((-1169 . -72) T) ((-1169 . -553) 195281) ((-1169 . -1014) T) ((-1169 . -23) T) ((-1169 . -21) T) ((-1169 . -971) T) ((-1169 . -1026) T) ((-1169 . -1061) T) ((-1169 . -664) T) ((-1169 . -962) T) ((-1169 . -186) 195234) ((-1169 . -13) T) ((-1169 . -1129) T) ((-1169 . -189) 195193) ((-1169 . -241) 195158) ((-1169 . -810) 195071) ((-1169 . -807) 194959) ((-1169 . -812) 194872) ((-1169 . -887) 194842) ((-1169 . -38) 194739) ((-1169 . -82) 194604) ((-1169 . -964) 194490) ((-1169 . -969) 194376) ((-1169 . -583) 194273) ((-1169 . -655) 194170) ((-1169 . -118) 194149) ((-1169 . -120) 194128) ((-1169 . -146) 194082) ((-1169 . -495) 194061) ((-1169 . -246) 194040) ((-1169 . -47) 194017) ((-1169 . -1158) 193994) ((-1169 . -35) 193960) ((-1169 . -66) 193926) ((-1169 . -239) 193892) ((-1169 . -431) 193858) ((-1169 . -1118) 193824) ((-1169 . -1115) 193790) ((-1169 . -916) 193756) ((-1166 . -277) 193700) ((-1166 . -951) 193666) ((-1166 . -353) 193632) ((-1166 . -38) 193489) ((-1166 . -556) 193363) ((-1166 . -591) 193252) ((-1166 . -589) 193126) ((-1166 . -971) T) ((-1166 . -1026) T) ((-1166 . -1061) T) ((-1166 . -664) T) ((-1166 . -962) T) ((-1166 . -82) 192976) ((-1166 . -964) 192865) ((-1166 . -969) 192754) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1014) T) ((-1166 . -553) 192736) ((-1166 . -1129) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -583) 192593) ((-1166 . -655) 192450) ((-1166 . -118) 192411) ((-1166 . -120) 192372) ((-1166 . -146) T) ((-1166 . -495) T) ((-1166 . -246) T) ((-1166 . -47) 192316) ((-1165 . -1164) 192295) ((-1165 . -312) 192274) ((-1165 . -1134) 192253) ((-1165 . -833) 192232) ((-1165 . -495) 192186) ((-1165 . -146) 192120) ((-1165 . -556) 191939) ((-1165 . -655) 191786) ((-1165 . -583) 191633) ((-1165 . -38) 191480) ((-1165 . -390) 191459) ((-1165 . -258) 191438) ((-1165 . -591) 191338) ((-1165 . -589) 191223) ((-1165 . -971) T) ((-1165 . -1026) T) ((-1165 . -1061) T) ((-1165 . -664) T) ((-1165 . -962) T) ((-1165 . -82) 191043) ((-1165 . -964) 190884) ((-1165 . -969) 190725) ((-1165 . -21) T) ((-1165 . -23) T) ((-1165 . -1014) T) ((-1165 . -553) 190707) ((-1165 . -1129) T) ((-1165 . -13) T) ((-1165 . -72) T) ((-1165 . -25) T) ((-1165 . -104) T) ((-1165 . -246) 190661) ((-1165 . -201) 190640) ((-1165 . -916) 190606) ((-1165 . -1115) 190572) ((-1165 . -1118) 190538) ((-1165 . -431) 190504) ((-1165 . -239) 190470) ((-1165 . -66) 190436) ((-1165 . -35) 190402) ((-1165 . -1158) 190372) ((-1165 . -47) 190342) ((-1165 . -120) 190321) ((-1165 . -118) 190300) ((-1165 . -887) 190263) ((-1165 . -812) 190169) ((-1165 . -807) 190073) ((-1165 . -810) 189979) ((-1165 . -241) 189937) ((-1165 . -189) 189889) ((-1165 . -186) 189835) ((-1165 . -190) 189787) ((-1165 . -1162) 189771) ((-1165 . -951) 189755) ((-1160 . -1164) 189716) ((-1160 . -312) 189695) ((-1160 . -1134) 189674) ((-1160 . -833) 189653) ((-1160 . -495) 189607) ((-1160 . -146) 189541) ((-1160 . -556) 189290) ((-1160 . -655) 189137) ((-1160 . -583) 188984) ((-1160 . -38) 188831) ((-1160 . -390) 188810) ((-1160 . -258) 188789) ((-1160 . -591) 188689) ((-1160 . -589) 188574) ((-1160 . -971) T) ((-1160 . -1026) T) ((-1160 . -1061) T) ((-1160 . -664) T) ((-1160 . -962) T) ((-1160 . -82) 188394) ((-1160 . -964) 188235) ((-1160 . -969) 188076) ((-1160 . -21) T) ((-1160 . -23) T) ((-1160 . -1014) T) ((-1160 . -553) 188058) ((-1160 . -1129) T) ((-1160 . -13) T) ((-1160 . -72) T) ((-1160 . -25) T) ((-1160 . -104) T) ((-1160 . -246) 188012) ((-1160 . -201) 187991) ((-1160 . -916) 187957) ((-1160 . -1115) 187923) ((-1160 . -1118) 187889) ((-1160 . -431) 187855) ((-1160 . -239) 187821) ((-1160 . -66) 187787) ((-1160 . -35) 187753) ((-1160 . -1158) 187723) ((-1160 . -47) 187693) ((-1160 . -120) 187672) ((-1160 . -118) 187651) ((-1160 . -887) 187614) ((-1160 . -812) 187520) ((-1160 . -807) 187401) ((-1160 . -810) 187307) ((-1160 . -241) 187265) ((-1160 . -189) 187217) ((-1160 . -186) 187163) ((-1160 . -190) 187115) ((-1160 . -1162) 187099) ((-1160 . -951) 187034) ((-1148 . -1155) 187018) ((-1148 . -1066) 186996) ((-1148 . -554) NIL) ((-1148 . -260) 186983) ((-1148 . -454) 186931) ((-1148 . -277) 186908) ((-1148 . -951) 186791) ((-1148 . -353) 186775) ((-1148 . -38) 186607) ((-1148 . -82) 186412) ((-1148 . -964) 186238) ((-1148 . -969) 186064) ((-1148 . -589) 185974) ((-1148 . -591) 185863) ((-1148 . -583) 185695) ((-1148 . -655) 185527) ((-1148 . -556) 185283) ((-1148 . -118) 185262) ((-1148 . -120) 185241) ((-1148 . -47) 185218) ((-1148 . -327) 185202) ((-1148 . -581) 185150) ((-1148 . -810) 185094) ((-1148 . -807) 185001) ((-1148 . -812) 184912) ((-1148 . -797) NIL) ((-1148 . -822) 184891) ((-1148 . -1134) 184870) ((-1148 . -862) 184840) ((-1148 . -833) 184819) ((-1148 . -495) 184733) ((-1148 . -246) 184647) ((-1148 . -146) 184541) ((-1148 . -390) 184475) ((-1148 . -258) 184454) ((-1148 . -241) 184381) ((-1148 . -190) T) ((-1148 . -104) T) ((-1148 . -25) T) ((-1148 . -72) T) ((-1148 . -553) 184363) ((-1148 . -1014) T) ((-1148 . -23) T) ((-1148 . -21) T) ((-1148 . -971) T) ((-1148 . -1026) T) ((-1148 . -1061) T) ((-1148 . -664) T) ((-1148 . -962) T) ((-1148 . -186) 184350) ((-1148 . -13) T) ((-1148 . -1129) T) ((-1148 . -189) T) ((-1148 . -225) 184334) ((-1148 . -184) 184318) ((-1146 . -1007) 184302) ((-1146 . -558) 184286) ((-1146 . -1014) 184264) ((-1146 . -553) 184231) ((-1146 . -1129) 184209) ((-1146 . -13) 184187) ((-1146 . -72) 184165) ((-1146 . -1008) 184122) ((-1144 . -1143) 184101) ((-1144 . -916) 184067) ((-1144 . -1115) 184033) ((-1144 . -1118) 183999) ((-1144 . -431) 183965) ((-1144 . -239) 183931) ((-1144 . -66) 183897) ((-1144 . -35) 183863) ((-1144 . -1158) 183840) ((-1144 . -47) 183817) ((-1144 . -556) 183572) ((-1144 . -655) 183392) ((-1144 . -583) 183212) ((-1144 . -591) 183023) ((-1144 . -589) 182881) ((-1144 . -969) 182695) ((-1144 . -964) 182509) ((-1144 . -82) 182297) ((-1144 . -38) 182117) ((-1144 . -887) 182087) ((-1144 . -241) 181987) ((-1144 . -1141) 181971) ((-1144 . -971) T) ((-1144 . -1026) T) ((-1144 . -1061) T) ((-1144 . -664) T) ((-1144 . -962) T) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1014) T) ((-1144 . -553) 181953) ((-1144 . -1129) T) ((-1144 . -13) T) ((-1144 . -72) T) ((-1144 . -25) T) ((-1144 . -104) T) ((-1144 . -118) 181881) ((-1144 . -120) 181809) ((-1144 . -554) 181482) ((-1144 . -184) 181452) ((-1144 . -810) 181306) ((-1144 . -812) 181106) ((-1144 . -807) 180904) ((-1144 . -225) 180874) ((-1144 . -189) 180736) ((-1144 . -186) 180592) ((-1144 . -190) 180500) ((-1144 . -312) 180479) ((-1144 . -1134) 180458) ((-1144 . -833) 180437) ((-1144 . -495) 180391) ((-1144 . -146) 180325) ((-1144 . -390) 180304) ((-1144 . -258) 180283) ((-1144 . -246) 180237) ((-1144 . -201) 180216) ((-1144 . -288) 180186) ((-1144 . -454) 180046) ((-1144 . -260) 179985) ((-1144 . -327) 179955) ((-1144 . -581) 179863) ((-1144 . -341) 179833) ((-1144 . -797) 179706) ((-1144 . -741) 179659) ((-1144 . -715) 179612) ((-1144 . -717) 179565) ((-1144 . -757) 179467) ((-1144 . -760) 179369) ((-1144 . -719) 179322) ((-1144 . -722) 179275) ((-1144 . -756) 179228) ((-1144 . -795) 179198) ((-1144 . -822) 179151) ((-1144 . -934) 179104) ((-1144 . -951) 178893) ((-1144 . -1066) 178845) ((-1144 . -905) 178815) ((-1139 . -1143) 178776) ((-1139 . -916) 178742) ((-1139 . -1115) 178708) ((-1139 . -1118) 178674) ((-1139 . -431) 178640) ((-1139 . -239) 178606) ((-1139 . -66) 178572) ((-1139 . -35) 178538) ((-1139 . -1158) 178515) ((-1139 . -47) 178492) ((-1139 . -556) 178293) ((-1139 . -655) 178095) ((-1139 . -583) 177897) ((-1139 . -591) 177752) ((-1139 . -589) 177592) ((-1139 . -969) 177388) ((-1139 . -964) 177184) ((-1139 . -82) 176936) ((-1139 . -38) 176738) ((-1139 . -887) 176708) ((-1139 . -241) 176536) ((-1139 . -1141) 176520) ((-1139 . -971) T) ((-1139 . -1026) T) ((-1139 . -1061) T) ((-1139 . -664) T) ((-1139 . -962) T) ((-1139 . -21) T) ((-1139 . -23) T) ((-1139 . -1014) T) ((-1139 . -553) 176502) ((-1139 . -1129) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -25) T) ((-1139 . -104) T) ((-1139 . -118) 176412) ((-1139 . -120) 176322) ((-1139 . -554) NIL) ((-1139 . -184) 176274) ((-1139 . -810) 176110) ((-1139 . -812) 175874) ((-1139 . -807) 175613) ((-1139 . -225) 175565) ((-1139 . -189) 175391) ((-1139 . -186) 175211) ((-1139 . -190) 175101) ((-1139 . -312) 175080) ((-1139 . -1134) 175059) ((-1139 . -833) 175038) ((-1139 . -495) 174992) ((-1139 . -146) 174926) ((-1139 . -390) 174905) ((-1139 . -258) 174884) ((-1139 . -246) 174838) ((-1139 . -201) 174817) ((-1139 . -288) 174769) ((-1139 . -454) 174503) ((-1139 . -260) 174388) ((-1139 . -327) 174340) ((-1139 . -581) 174292) ((-1139 . -341) 174244) ((-1139 . -797) NIL) ((-1139 . -741) NIL) ((-1139 . -715) NIL) ((-1139 . -717) NIL) ((-1139 . -757) NIL) ((-1139 . -760) NIL) ((-1139 . -719) NIL) ((-1139 . -722) NIL) ((-1139 . -756) NIL) ((-1139 . -795) 174196) ((-1139 . -822) NIL) ((-1139 . -934) NIL) ((-1139 . -951) 174162) ((-1139 . -1066) NIL) ((-1139 . -905) 174114) ((-1138 . -753) T) ((-1138 . -760) T) ((-1138 . -757) T) ((-1138 . -1014) T) ((-1138 . -553) 174096) ((-1138 . -1129) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -318) T) ((-1138 . -605) T) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1014) T) ((-1137 . -553) 174078) ((-1137 . -1129) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -318) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1014) T) ((-1136 . -553) 174060) ((-1136 . -1129) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -605) T) ((-1135 . -753) T) ((-1135 . -760) T) ((-1135 . -757) T) ((-1135 . -1014) T) ((-1135 . -553) 174042) ((-1135 . -1129) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -318) T) ((-1135 . -605) T) ((-1130 . -996) T) ((-1130 . -428) 174023) ((-1130 . -553) 173989) ((-1130 . -556) 173970) ((-1130 . -1014) T) ((-1130 . -1129) T) ((-1130 . -13) T) ((-1130 . -72) T) ((-1130 . -64) T) ((-1127 . -428) 173947) ((-1127 . -553) 173888) ((-1127 . -556) 173865) ((-1127 . -1014) 173843) ((-1127 . -1129) 173821) ((-1127 . -13) 173799) ((-1127 . -72) 173777) ((-1122 . -680) 173753) ((-1122 . -35) 173719) ((-1122 . -66) 173685) ((-1122 . -239) 173651) ((-1122 . -431) 173617) ((-1122 . -1118) 173583) ((-1122 . -1115) 173549) ((-1122 . -916) 173515) ((-1122 . -47) 173484) ((-1122 . -38) 173381) ((-1122 . -583) 173278) ((-1122 . -655) 173175) ((-1122 . -556) 173057) ((-1122 . -246) 173036) ((-1122 . -495) 173015) ((-1122 . -82) 172880) ((-1122 . -964) 172766) ((-1122 . -969) 172652) ((-1122 . -146) 172606) ((-1122 . -120) 172585) ((-1122 . -118) 172564) ((-1122 . -591) 172489) ((-1122 . -589) 172399) ((-1122 . -887) 172360) ((-1122 . -812) 172341) ((-1122 . -1129) T) ((-1122 . -13) T) ((-1122 . -807) 172320) ((-1122 . -962) T) ((-1122 . -664) T) ((-1122 . -1061) T) ((-1122 . -1026) T) ((-1122 . -971) T) ((-1122 . -21) T) ((-1122 . -23) T) ((-1122 . -1014) T) ((-1122 . -553) 172302) ((-1122 . -72) T) ((-1122 . -25) T) ((-1122 . -104) T) ((-1122 . -810) 172283) ((-1122 . -454) 172250) ((-1122 . -260) 172237) ((-1116 . -924) 172221) ((-1116 . -34) T) ((-1116 . -13) T) ((-1116 . -1129) T) ((-1116 . -72) 172175) ((-1116 . -553) 172110) ((-1116 . -260) 172048) ((-1116 . -454) 171981) ((-1116 . -1014) 171959) ((-1116 . -427) 171943) ((-1111 . -314) 171917) ((-1111 . -72) T) ((-1111 . -13) T) ((-1111 . -1129) T) ((-1111 . -553) 171899) ((-1111 . -1014) T) ((-1109 . -1014) T) ((-1109 . -553) 171881) ((-1109 . -1129) T) ((-1109 . -13) T) ((-1109 . -72) T) ((-1109 . -556) 171863) ((-1104 . -748) 171847) ((-1104 . -72) T) ((-1104 . -13) T) ((-1104 . -1129) T) ((-1104 . -553) 171829) ((-1104 . -1014) T) ((-1102 . -1107) 171808) ((-1102 . -183) 171756) ((-1102 . -76) 171704) ((-1102 . -260) 171502) ((-1102 . -454) 171254) ((-1102 . -427) 171189) ((-1102 . -124) 171137) ((-1102 . -554) NIL) ((-1102 . -193) 171085) ((-1102 . -550) 171064) ((-1102 . -243) 171043) ((-1102 . -1129) T) ((-1102 . -13) T) ((-1102 . -241) 171022) ((-1102 . -1014) T) ((-1102 . -553) 171004) ((-1102 . -72) T) ((-1102 . -34) T) ((-1102 . -539) 170983) ((-1098 . -1014) T) ((-1098 . -553) 170965) ((-1098 . -1129) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1097 . -753) T) ((-1097 . -760) T) ((-1097 . -757) T) ((-1097 . -1014) T) ((-1097 . -553) 170947) ((-1097 . -1129) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -318) T) ((-1097 . -605) T) ((-1096 . -753) T) ((-1096 . -760) T) ((-1096 . -757) T) ((-1096 . -1014) T) ((-1096 . -553) 170929) ((-1096 . -1129) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -318) T) ((-1095 . -1175) T) ((-1095 . -1014) T) ((-1095 . -553) 170896) ((-1095 . -1129) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -951) 170832) ((-1095 . -556) 170768) ((-1094 . -553) 170750) ((-1093 . -553) 170732) ((-1092 . -277) 170709) ((-1092 . -951) 170607) ((-1092 . -353) 170591) ((-1092 . -38) 170488) ((-1092 . -556) 170345) ((-1092 . -591) 170270) ((-1092 . -589) 170180) ((-1092 . -971) T) ((-1092 . -1026) T) ((-1092 . -1061) T) ((-1092 . -664) T) ((-1092 . -962) T) ((-1092 . -82) 170045) ((-1092 . -964) 169931) ((-1092 . -969) 169817) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1014) T) ((-1092 . -553) 169799) ((-1092 . -1129) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -583) 169696) ((-1092 . -655) 169593) ((-1092 . -118) 169572) ((-1092 . -120) 169551) ((-1092 . -146) 169505) ((-1092 . -495) 169484) ((-1092 . -246) 169463) ((-1092 . -47) 169440) ((-1090 . -757) T) ((-1090 . -553) 169422) ((-1090 . -1014) T) ((-1090 . -72) T) ((-1090 . -13) T) ((-1090 . -1129) T) ((-1090 . -760) T) ((-1090 . -554) 169344) ((-1090 . -556) 169310) ((-1090 . -951) 169292) ((-1090 . -797) 169259) ((-1089 . -1172) 169243) ((-1089 . -190) 169202) ((-1089 . -556) 169084) ((-1089 . -591) 169009) ((-1089 . -589) 168919) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -553) 168901) ((-1089 . -1014) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -971) T) ((-1089 . -1026) T) ((-1089 . -1061) T) ((-1089 . -664) T) ((-1089 . -962) T) ((-1089 . -186) 168854) ((-1089 . -13) T) ((-1089 . -1129) T) ((-1089 . -189) 168813) ((-1089 . -241) 168778) ((-1089 . -810) 168691) ((-1089 . -807) 168579) 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165856) ((-1088 . -969) 165697) ((-1088 . -21) T) ((-1088 . -23) T) ((-1088 . -1014) T) ((-1088 . -553) 165679) ((-1088 . -1129) T) ((-1088 . -13) T) ((-1088 . -72) T) ((-1088 . -25) T) ((-1088 . -104) T) ((-1088 . -246) 165633) ((-1088 . -201) 165612) ((-1088 . -916) 165578) ((-1088 . -1115) 165544) ((-1088 . -1118) 165510) ((-1088 . -431) 165476) ((-1088 . -239) 165442) ((-1088 . -66) 165408) ((-1088 . -35) 165374) ((-1088 . -1158) 165344) ((-1088 . -47) 165314) ((-1088 . -120) 165293) ((-1088 . -118) 165272) ((-1088 . -887) 165235) ((-1088 . -812) 165141) ((-1088 . -807) 165022) ((-1088 . -810) 164928) ((-1088 . -241) 164886) ((-1088 . -189) 164838) ((-1088 . -186) 164784) ((-1088 . -190) 164736) ((-1088 . -1162) 164720) ((-1088 . -951) 164655) ((-1085 . -1155) 164639) ((-1085 . -1066) 164617) ((-1085 . -554) NIL) ((-1085 . -260) 164604) ((-1085 . -454) 164552) ((-1085 . -277) 164529) ((-1085 . -951) 164412) ((-1085 . -353) 164396) ((-1085 . -38) 164228) ((-1085 . -82) 164033) 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-189) 158536) ((-1082 . -186) 158356) ((-1082 . -190) 158246) ((-1082 . -312) 158225) ((-1082 . -1134) 158204) ((-1082 . -833) 158183) ((-1082 . -495) 158137) ((-1082 . -146) 158071) ((-1082 . -390) 158050) ((-1082 . -258) 158029) ((-1082 . -246) 157983) ((-1082 . -201) 157962) ((-1082 . -288) 157914) ((-1082 . -454) 157648) ((-1082 . -260) 157533) ((-1082 . -327) 157485) ((-1082 . -581) 157437) ((-1082 . -341) 157389) ((-1082 . -797) NIL) ((-1082 . -741) NIL) ((-1082 . -715) NIL) ((-1082 . -717) NIL) ((-1082 . -757) NIL) ((-1082 . -760) NIL) ((-1082 . -719) NIL) ((-1082 . -722) NIL) ((-1082 . -756) NIL) ((-1082 . -795) 157341) ((-1082 . -822) NIL) ((-1082 . -934) NIL) ((-1082 . -951) 157307) ((-1082 . -1066) NIL) ((-1082 . -905) 157259) ((-1081 . -996) T) ((-1081 . -428) 157240) ((-1081 . -553) 157206) ((-1081 . -556) 157187) ((-1081 . -1014) T) ((-1081 . -1129) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -64) T) ((-1080 . -1014) T) ((-1080 . -553) 157169) ((-1080 . -1129) T) 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. -617) 156030) ((-1069 . -594) 156014) ((-1069 . -243) 155991) ((-1069 . -241) 155943) ((-1069 . -539) 155920) ((-1069 . -554) 155881) ((-1069 . -427) 155865) ((-1069 . -1014) 155843) ((-1069 . -454) 155776) ((-1069 . -260) 155714) ((-1069 . -553) 155649) ((-1069 . -72) 155603) ((-1069 . -1129) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -124) 155587) ((-1069 . -1168) 155571) ((-1069 . -924) 155555) ((-1069 . -1064) 155539) ((-1069 . -556) 155516) ((-1067 . -996) T) ((-1067 . -428) 155497) ((-1067 . -553) 155463) ((-1067 . -556) 155444) ((-1067 . -1014) T) ((-1067 . -1129) T) ((-1067 . -13) T) ((-1067 . -72) T) ((-1067 . -64) T) ((-1065 . -1107) 155423) ((-1065 . -183) 155371) ((-1065 . -76) 155319) ((-1065 . -260) 155117) ((-1065 . -454) 154869) ((-1065 . -427) 154804) ((-1065 . -124) 154752) ((-1065 . -554) NIL) ((-1065 . -193) 154700) ((-1065 . -550) 154679) ((-1065 . -243) 154658) ((-1065 . -1129) T) ((-1065 . -13) T) ((-1065 . -241) 154637) ((-1065 . -1014) T) ((-1065 . 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T) ((-1049 . -1129) T) ((-1049 . -553) 152360) ((-1049 . -1014) T) ((-1049 . -556) 152341) ((-1049 . -428) 152322) ((-1049 . -996) T) ((-1047 . -1048) 152306) ((-1047 . -72) T) ((-1047 . -13) T) ((-1047 . -1129) T) ((-1047 . -553) 152288) ((-1047 . -1014) T) ((-1040 . -680) 152267) ((-1040 . -35) 152233) ((-1040 . -66) 152199) ((-1040 . -239) 152165) ((-1040 . -431) 152131) ((-1040 . -1118) 152097) ((-1040 . -1115) 152063) ((-1040 . -916) 152029) ((-1040 . -47) 152001) ((-1040 . -38) 151898) ((-1040 . -583) 151795) ((-1040 . -655) 151692) ((-1040 . -556) 151574) ((-1040 . -246) 151553) ((-1040 . -495) 151532) ((-1040 . -82) 151397) ((-1040 . -964) 151283) ((-1040 . -969) 151169) ((-1040 . -146) 151123) ((-1040 . -120) 151102) ((-1040 . -118) 151081) ((-1040 . -591) 151006) ((-1040 . -589) 150916) ((-1040 . -887) 150883) ((-1040 . -812) 150867) ((-1040 . -1129) T) ((-1040 . -13) T) ((-1040 . -807) 150849) ((-1040 . -962) T) ((-1040 . -664) T) ((-1040 . -1061) T) ((-1040 . -1026) T) 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-1061) T) ((-1034 . -1026) T) ((-1034 . -971) T) ((-1034 . -21) T) ((-1034 . -589) 147969) ((-1034 . -23) T) ((-1034 . -1014) T) ((-1034 . -553) 147951) ((-1034 . -1129) T) ((-1034 . -13) T) ((-1034 . -72) T) ((-1034 . -25) T) ((-1034 . -104) T) ((-1034 . -120) T) ((-1034 . -753) T) ((-1034 . -318) T) ((-1034 . -84) T) ((-1034 . -605) T) ((-1030 . -996) T) ((-1030 . -428) 147932) ((-1030 . -553) 147898) ((-1030 . -556) 147879) ((-1030 . -1014) T) ((-1030 . -1129) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1030 . -64) T) ((-1029 . -1014) T) ((-1029 . -553) 147861) ((-1029 . -1129) T) ((-1029 . -13) T) ((-1029 . -72) T) ((-1027 . -196) 147840) ((-1027 . -1187) 147810) ((-1027 . -722) 147789) ((-1027 . -719) 147768) ((-1027 . -760) 147722) ((-1027 . -757) 147676) ((-1027 . -717) 147655) ((-1027 . -718) 147634) ((-1027 . -655) 147579) ((-1027 . -583) 147504) ((-1027 . -243) 147481) ((-1027 . -241) 147458) ((-1027 . -427) 147442) ((-1027 . -454) 147375) ((-1027 . -260) 147313) ((-1027 . -34) T) ((-1027 . -539) 147290) ((-1027 . -951) 147119) ((-1027 . -556) 146923) ((-1027 . -353) 146892) ((-1027 . -581) 146800) ((-1027 . -591) 146639) ((-1027 . -327) 146609) ((-1027 . -318) 146588) ((-1027 . -190) 146541) ((-1027 . -589) 146329) ((-1027 . -971) 146308) ((-1027 . -1026) 146287) ((-1027 . -1061) 146266) ((-1027 . -664) 146245) ((-1027 . -962) 146224) ((-1027 . -186) 146120) ((-1027 . -189) 146022) ((-1027 . -225) 145992) ((-1027 . -807) 145864) ((-1027 . -812) 145738) ((-1027 . -810) 145671) ((-1027 . -184) 145641) ((-1027 . -553) 145338) ((-1027 . -969) 145263) ((-1027 . -964) 145168) ((-1027 . -82) 145088) ((-1027 . -104) 144963) ((-1027 . -25) 144800) ((-1027 . -72) 144537) ((-1027 . -13) T) ((-1027 . -1129) T) ((-1027 . -1014) 144293) ((-1027 . -23) 144149) ((-1027 . -21) 144064) ((-1023 . -1024) 144048) ((-1023 . |MappingCategory|) 144022) ((-1023 . -1129) T) ((-1023 . -80) 144006) ((-1023 . -1014) T) ((-1023 . -553) 143988) ((-1023 . -13) T) ((-1023 . -72) T) ((-1018 . -1017) 143952) ((-1018 . -72) T) ((-1018 . -553) 143934) ((-1018 . -1014) T) ((-1018 . -241) 143890) ((-1018 . -1129) T) ((-1018 . -13) T) ((-1018 . -558) 143805) ((-1016 . -1017) 143757) ((-1016 . -72) T) ((-1016 . -553) 143739) ((-1016 . -1014) T) ((-1016 . -241) 143695) ((-1016 . -1129) T) ((-1016 . -13) T) ((-1016 . -558) 143598) ((-1015 . -318) T) ((-1015 . -72) T) ((-1015 . -13) T) ((-1015 . -1129) T) ((-1015 . -553) 143580) ((-1015 . -1014) T) ((-1010 . -367) 143564) ((-1010 . -1012) 143548) ((-1010 . -318) 143527) ((-1010 . -193) 143511) ((-1010 . -554) 143472) ((-1010 . -124) 143456) ((-1010 . -427) 143440) ((-1010 . -1014) T) ((-1010 . -454) 143373) ((-1010 . -260) 143311) ((-1010 . -553) 143293) ((-1010 . -72) T) ((-1010 . -1129) T) ((-1010 . -13) T) ((-1010 . -34) T) ((-1010 . -76) 143277) ((-1010 . -183) 143261) ((-1009 . -996) T) ((-1009 . -428) 143242) ((-1009 . -553) 143208) ((-1009 . -556) 143189) ((-1009 . -1014) T) ((-1009 . -1129) T) ((-1009 . -13) T) ((-1009 . 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141565) ((-1000 . -589) 141475) ((-1000 . -591) 141364) ((-1000 . -583) 141216) ((-1000 . -655) 141068) ((-1000 . -118) 141047) ((-1000 . -120) 141026) ((-1000 . -146) 140940) ((-1000 . -495) 140874) ((-1000 . -246) 140808) ((-1000 . -47) 140769) ((-1000 . -327) 140753) ((-1000 . -581) 140701) ((-1000 . -390) 140655) ((-1000 . -454) 140518) ((-1000 . -810) 140453) ((-1000 . -807) 140351) ((-1000 . -812) 140253) ((-1000 . -797) NIL) ((-1000 . -822) 140232) ((-1000 . -1134) 140211) ((-1000 . -862) 140156) ((-1000 . -260) 140143) ((-1000 . -190) 140122) ((-1000 . -104) T) ((-1000 . -25) T) ((-1000 . -72) T) ((-1000 . -553) 140104) ((-1000 . -1014) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -971) T) ((-1000 . -1026) T) ((-1000 . -1061) T) ((-1000 . -664) T) ((-1000 . -962) T) ((-1000 . -186) 140052) ((-1000 . -13) T) ((-1000 . -1129) T) ((-1000 . -189) 140006) ((-1000 . -225) 139990) ((-1000 . -184) 139974) ((-998 . -553) 139956) ((-995 . -757) T) ((-995 . -553) 139938) ((-995 . -1014) T) ((-995 . -72) T) ((-995 . -13) T) ((-995 . -1129) T) ((-995 . -760) T) ((-995 . -554) 139919) ((-992 . -662) 139898) ((-992 . -951) 139796) ((-992 . -353) 139780) ((-992 . -581) 139728) ((-992 . -591) 139605) ((-992 . -327) 139589) ((-992 . -320) 139568) ((-992 . -120) 139547) ((-992 . -556) 139372) ((-992 . -655) 139246) ((-992 . -583) 139120) ((-992 . -589) 139018) ((-992 . -969) 138931) ((-992 . -964) 138844) ((-992 . -82) 138736) ((-992 . -38) 138610) ((-992 . -351) 138589) ((-992 . -343) 138568) ((-992 . -118) 138522) ((-992 . -1066) 138501) ((-992 . -299) 138480) ((-992 . -318) 138434) ((-992 . -201) 138388) ((-992 . -246) 138342) ((-992 . -258) 138296) ((-992 . -390) 138250) ((-992 . -495) 138204) ((-992 . -833) 138158) ((-992 . -1134) 138112) ((-992 . -312) 138066) ((-992 . -190) 137994) ((-992 . -186) 137870) ((-992 . -189) 137752) ((-992 . -225) 137722) ((-992 . -807) 137594) ((-992 . -812) 137468) ((-992 . -810) 137401) ((-992 . -184) 137371) ((-992 . -554) 137355) 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-13) T) ((-979 . -72) T) ((-979 . -64) T) ((-976 . -483) T) ((-976 . -1134) T) ((-976 . -1066) T) ((-976 . -951) 137033) ((-976 . -554) 136948) ((-976 . -934) T) ((-976 . -797) 136930) ((-976 . -756) T) ((-976 . -722) T) ((-976 . -719) T) ((-976 . -760) T) ((-976 . -757) T) ((-976 . -717) T) ((-976 . -715) T) ((-976 . -741) T) ((-976 . -591) 136902) ((-976 . -581) 136884) ((-976 . -833) T) ((-976 . -495) T) ((-976 . -246) T) ((-976 . -146) T) ((-976 . -556) 136856) ((-976 . -655) 136843) ((-976 . -583) 136830) ((-976 . -969) 136817) ((-976 . -964) 136804) ((-976 . -82) 136789) ((-976 . -38) 136776) ((-976 . -390) T) ((-976 . -258) T) ((-976 . -189) T) ((-976 . -186) 136763) ((-976 . -190) T) ((-976 . -116) T) ((-976 . -962) T) ((-976 . -664) T) ((-976 . -1061) T) ((-976 . -1026) T) ((-976 . -971) T) ((-976 . -21) T) ((-976 . -589) 136735) ((-976 . -23) T) ((-976 . -1014) T) ((-976 . -553) 136717) ((-976 . -1129) T) ((-976 . -13) T) ((-976 . -72) T) ((-976 . -25) T) ((-976 . -104) T) ((-976 . -120) T) ((-976 . -558) 136698) ((-975 . -981) 136677) ((-975 . -72) T) ((-975 . -13) T) ((-975 . -1129) T) ((-975 . -553) 136659) ((-975 . -1014) T) ((-972 . -1129) T) ((-972 . -13) T) ((-972 . -1014) 136637) ((-972 . -553) 136604) ((-972 . -72) 136582) ((-967 . -966) 136522) ((-967 . -583) 136467) ((-967 . -655) 136412) ((-967 . -34) T) ((-967 . -260) 136350) ((-967 . -454) 136283) ((-967 . -427) 136267) ((-967 . -591) 136251) ((-967 . -589) 136220) ((-967 . -104) T) ((-967 . -25) T) ((-967 . -72) T) ((-967 . -13) T) ((-967 . -1129) T) ((-967 . -553) 136182) ((-967 . -1014) T) ((-967 . -23) T) ((-967 . -21) T) ((-967 . -969) 136166) ((-967 . -964) 136150) ((-967 . -82) 136129) ((-967 . -1187) 136099) ((-967 . -554) 136060) ((-959 . -984) 135989) ((-959 . -890) 135918) ((-959 . -554) 135860) ((-959 . -427) 135825) ((-959 . -1014) T) ((-959 . -454) 135709) ((-959 . -260) 135617) ((-959 . -553) 135560) ((-959 . -72) T) ((-959 . -1129) T) ((-959 . -13) T) ((-959 . -34) T) ((-959 . -124) 135525) ((-959 . -1124) 135454) ((-949 . -996) T) ((-949 . -428) 135435) ((-949 . -553) 135401) ((-949 . -556) 135382) ((-949 . -1014) T) ((-949 . -1129) T) ((-949 . -13) T) ((-949 . -72) T) ((-949 . -64) T) ((-948 . -146) T) ((-948 . -556) 135351) ((-948 . -971) T) ((-948 . -1026) T) ((-948 . -1061) T) ((-948 . -664) T) ((-948 . -962) T) ((-948 . -591) 135325) ((-948 . -589) 135284) ((-948 . -104) T) ((-948 . -25) T) ((-948 . -72) T) ((-948 . -13) T) ((-948 . -1129) T) ((-948 . -553) 135266) ((-948 . -1014) T) ((-948 . -23) T) ((-948 . -21) T) ((-948 . -969) 135240) ((-948 . -964) 135214) ((-948 . -82) 135181) ((-948 . -38) 135165) ((-948 . -583) 135149) ((-948 . -655) 135133) ((-941 . -984) 135102) ((-941 . -890) 135071) ((-941 . -554) 135032) ((-941 . -427) 135016) ((-941 . -1014) T) ((-941 . -454) 134949) ((-941 . -260) 134887) ((-941 . -553) 134849) ((-941 . -72) T) ((-941 . -1129) T) ((-941 . -13) T) ((-941 . -34) T) ((-941 . -124) 134833) ((-941 . -1124) 134802) ((-940 . -1014) T) ((-940 . -553) 134784) ((-940 . -1129) T) ((-940 . -13) T) ((-940 . -72) T) ((-938 . -926) T) ((-938 . -916) T) ((-938 . -715) T) ((-938 . -717) T) ((-938 . -757) T) ((-938 . -760) T) ((-938 . -719) T) ((-938 . -722) T) ((-938 . -756) T) ((-938 . -951) 134669) ((-938 . -353) 134631) ((-938 . -201) T) ((-938 . -246) T) ((-938 . -258) T) ((-938 . -390) T) ((-938 . -38) 134568) ((-938 . -583) 134505) ((-938 . -655) 134442) ((-938 . -556) 134379) ((-938 . -495) T) ((-938 . -833) T) ((-938 . -1134) T) ((-938 . -312) T) ((-938 . -82) 134288) ((-938 . -964) 134225) ((-938 . -969) 134162) ((-938 . -146) T) ((-938 . -120) T) ((-938 . -591) 134099) ((-938 . -589) 134036) ((-938 . -104) T) ((-938 . -25) T) ((-938 . -72) T) ((-938 . -13) T) ((-938 . -1129) T) ((-938 . -553) 134018) ((-938 . -1014) T) ((-938 . -23) T) ((-938 . -21) T) ((-938 . -962) T) ((-938 . -664) T) ((-938 . -1061) T) ((-938 . -1026) T) ((-938 . -971) T) ((-933 . -996) T) ((-933 . -428) 133999) ((-933 . -553) 133965) ((-933 . -556) 133946) ((-933 . -1014) T) ((-933 . -1129) T) ((-933 . -13) T) ((-933 . -72) T) ((-933 . -64) T) ((-918 . -905) 133928) ((-918 . -1066) T) ((-918 . -556) 133878) ((-918 . -951) 133838) ((-918 . -554) 133768) ((-918 . -934) T) ((-918 . -822) NIL) ((-918 . -795) 133750) ((-918 . -756) T) ((-918 . -722) T) ((-918 . -719) T) ((-918 . -760) T) ((-918 . -757) T) ((-918 . -717) T) ((-918 . -715) T) ((-918 . -741) T) ((-918 . -797) 133732) ((-918 . -341) 133714) ((-918 . -581) 133696) ((-918 . -327) 133678) ((-918 . -241) NIL) ((-918 . -260) NIL) ((-918 . -454) NIL) ((-918 . -288) 133660) ((-918 . -201) T) ((-918 . -82) 133587) ((-918 . -964) 133537) ((-918 . -969) 133487) ((-918 . -246) T) ((-918 . -655) 133437) ((-918 . -583) 133387) ((-918 . -591) 133337) ((-918 . -589) 133287) ((-918 . -38) 133237) ((-918 . -258) T) ((-918 . -390) T) ((-918 . -146) T) ((-918 . -495) T) ((-918 . -833) T) ((-918 . -1134) T) ((-918 . -312) T) ((-918 . -190) T) ((-918 . -186) 133224) ((-918 . -189) T) ((-918 . -225) 133206) ((-918 . -807) NIL) ((-918 . -812) NIL) ((-918 . -810) NIL) ((-918 . -184) 133188) ((-918 . -120) T) ((-918 . -118) NIL) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1129) T) ((-918 . -553) 133148) ((-918 . -1014) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -962) T) ((-918 . -664) T) ((-918 . -1061) T) ((-918 . -1026) T) ((-918 . -971) T) ((-917 . -291) 133122) ((-917 . -146) T) ((-917 . -556) 133052) ((-917 . -971) T) ((-917 . -1026) T) ((-917 . -1061) T) ((-917 . -664) T) ((-917 . -962) T) ((-917 . -591) 132954) ((-917 . -589) 132884) ((-917 . -104) T) ((-917 . -25) T) ((-917 . -72) T) ((-917 . -13) T) ((-917 . -1129) T) ((-917 . -553) 132866) ((-917 . -1014) T) ((-917 . -23) T) ((-917 . -21) T) ((-917 . -969) 132811) ((-917 . -964) 132756) ((-917 . -82) 132673) ((-917 . -554) 132657) ((-917 . -184) 132634) ((-917 . -810) 132586) ((-917 . -812) 132498) ((-917 . -807) 132408) ((-917 . -225) 132385) ((-917 . -189) 132325) ((-917 . -186) 132259) ((-917 . -190) 132231) ((-917 . -312) T) ((-917 . -1134) T) ((-917 . -833) T) ((-917 . -495) T) ((-917 . -655) 132176) ((-917 . -583) 132121) ((-917 . -38) 132066) ((-917 . -390) T) ((-917 . -258) T) ((-917 . -246) T) ((-917 . -201) T) ((-917 . -318) NIL) ((-917 . -299) NIL) ((-917 . -1066) NIL) ((-917 . -118) 132038) ((-917 . -343) NIL) ((-917 . -351) 132010) ((-917 . -120) 131982) ((-917 . -320) 131954) ((-917 . -327) 131931) ((-917 . -581) 131865) ((-917 . -353) 131842) ((-917 . -951) 131719) ((-917 . -662) 131691) ((-914 . -909) 131675) ((-914 . -427) 131659) ((-914 . -1014) 131637) ((-914 . -454) 131570) ((-914 . -260) 131508) ((-914 . -553) 131443) ((-914 . -72) 131397) ((-914 . -1129) T) ((-914 . -13) T) ((-914 . -34) T) ((-914 . -76) 131381) ((-910 . -912) 131365) ((-910 . -760) 131344) ((-910 . -757) 131323) ((-910 . -951) 131221) ((-910 . -353) 131205) ((-910 . -581) 131153) ((-910 . -591) 131055) ((-910 . -327) 131039) ((-910 . -241) 130997) ((-910 . -260) 130962) ((-910 . -454) 130874) ((-910 . -288) 130858) ((-910 . -38) 130806) ((-910 . -82) 130684) ((-910 . -964) 130583) ((-910 . -969) 130482) ((-910 . -589) 130405) ((-910 . -583) 130353) ((-910 . -655) 130301) ((-910 . -556) 130195) ((-910 . -246) 130149) ((-910 . -201) 130128) ((-910 . -190) 130107) ((-910 . -186) 130055) ((-910 . -189) 130009) ((-910 . -225) 129993) ((-910 . -807) 129917) ((-910 . -812) 129843) ((-910 . -810) 129802) ((-910 . -184) 129786) ((-910 . -554) 129747) ((-910 . -120) 129726) ((-910 . -118) 129705) ((-910 . -104) T) ((-910 . -25) T) ((-910 . -72) T) ((-910 . -13) T) ((-910 . -1129) T) ((-910 . -553) 129687) ((-910 . -1014) T) ((-910 . -23) T) ((-910 . -21) T) ((-910 . -962) T) ((-910 . -664) T) ((-910 . -1061) T) ((-910 . -1026) T) ((-910 . -971) T) ((-908 . -996) T) ((-908 . -428) 129668) ((-908 . -553) 129634) ((-908 . -556) 129615) ((-908 . -1014) T) ((-908 . -1129) T) ((-908 . -13) T) ((-908 . -72) T) ((-908 . -64) T) ((-907 . -21) T) ((-907 . -589) 129597) ((-907 . -23) T) ((-907 . -1014) T) ((-907 . -553) 129579) ((-907 . -1129) T) ((-907 . -13) T) ((-907 . -72) T) ((-907 . -25) T) ((-907 . -104) T) ((-907 . -241) 129546) ((-903 . -553) 129528) ((-900 . -1014) T) ((-900 . -553) 129510) ((-900 . -1129) T) ((-900 . -13) T) ((-900 . -72) T) ((-885 . -722) T) ((-885 . -719) T) ((-885 . -760) T) ((-885 . -757) T) ((-885 . -717) T) ((-885 . -23) T) ((-885 . -1014) T) ((-885 . -553) 129470) ((-885 . -1129) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -25) T) ((-885 . -104) T) ((-884 . -996) T) ((-884 . -428) 129451) ((-884 . -553) 129417) ((-884 . -556) 129398) ((-884 . -1014) T) ((-884 . -1129) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -64) T) ((-878 . -881) T) ((-878 . -72) T) ((-878 . -553) 129380) ((-878 . -1014) T) ((-878 . -605) T) ((-878 . -13) T) ((-878 . -1129) T) ((-878 . -84) T) ((-878 . -556) 129364) ((-877 . -553) 129346) ((-876 . -1014) T) ((-876 . -553) 129328) ((-876 . -1129) T) ((-876 . -13) T) 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123157) ((-839 . -888) T) ((-839 . -553) 123139) ((-837 . -867) T) ((-837 . -553) 123121) ((-831 . -719) T) ((-831 . -760) T) ((-831 . -757) T) ((-831 . -1014) T) ((-831 . -553) 123103) ((-831 . -1129) T) ((-831 . -13) T) ((-831 . -72) T) ((-831 . -25) T) ((-831 . -664) T) ((-831 . -1026) T) ((-826 . -312) T) ((-826 . -1134) T) ((-826 . -833) T) ((-826 . -495) T) ((-826 . -146) T) ((-826 . -556) 123040) ((-826 . -655) 122992) ((-826 . -583) 122944) ((-826 . -38) 122896) ((-826 . -390) T) ((-826 . -258) T) ((-826 . -591) 122848) ((-826 . -589) 122785) ((-826 . -971) T) ((-826 . -1026) T) ((-826 . -1061) T) ((-826 . -664) T) ((-826 . -962) T) ((-826 . -82) 122716) ((-826 . -964) 122668) ((-826 . -969) 122620) ((-826 . -21) T) ((-826 . -23) T) ((-826 . -1014) T) ((-826 . -553) 122602) ((-826 . -1129) T) ((-826 . -13) T) ((-826 . -72) T) ((-826 . -25) T) ((-826 . -104) T) ((-826 . -246) T) ((-826 . -201) T) ((-818 . -299) T) ((-818 . -1066) T) ((-818 . -318) T) ((-818 . -118) T) ((-818 . 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121372) ((-786 . -1014) T) ((-786 . -1129) T) ((-786 . -13) T) ((-786 . -72) T) ((-786 . -64) T) ((-786 . -1175) T) ((-784 . -1014) T) ((-784 . -553) 121354) ((-784 . -1129) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -556) 121336) ((-783 . -1129) T) ((-783 . -13) T) ((-783 . -553) 121211) ((-783 . -1014) 121162) ((-783 . -72) 121113) ((-782 . -905) 121097) ((-782 . -1066) 121075) ((-782 . -951) 120942) ((-782 . -556) 120841) ((-782 . -554) 120644) ((-782 . -934) 120623) ((-782 . -822) 120602) ((-782 . -795) 120586) ((-782 . -756) 120565) ((-782 . -722) 120544) ((-782 . -719) 120523) ((-782 . -760) 120477) ((-782 . -757) 120431) ((-782 . -717) 120410) ((-782 . -715) 120389) ((-782 . -741) 120368) ((-782 . -797) 120293) ((-782 . -341) 120277) ((-782 . -581) 120225) ((-782 . -591) 120141) ((-782 . -327) 120125) ((-782 . -241) 120083) ((-782 . -260) 120048) ((-782 . -454) 119960) ((-782 . -288) 119944) ((-782 . -201) T) ((-782 . -82) 119875) ((-782 . -964) 119827) ((-782 . -969) 119779) 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-1061) T) ((-781 . -1026) T) ((-781 . -971) T) ((-779 . -780) 118113) ((-779 . -833) T) ((-779 . -495) T) ((-779 . -246) T) ((-779 . -146) T) ((-779 . -556) 118085) ((-779 . -655) 118072) ((-779 . -583) 118059) ((-779 . -969) 118046) ((-779 . -964) 118033) ((-779 . -82) 118018) ((-779 . -38) 118005) ((-779 . -390) T) ((-779 . -258) T) ((-779 . -962) T) ((-779 . -664) T) ((-779 . -1061) T) ((-779 . -1026) T) ((-779 . -971) T) ((-779 . -21) T) ((-779 . -589) 117977) ((-779 . -23) T) ((-779 . -1014) T) ((-779 . -553) 117959) ((-779 . -1129) T) ((-779 . -13) T) ((-779 . -72) T) ((-779 . -25) T) ((-779 . -104) T) ((-779 . -591) 117946) ((-779 . -120) T) ((-776 . -962) T) ((-776 . -664) T) ((-776 . -1061) T) ((-776 . -1026) T) ((-776 . -971) T) ((-776 . -21) T) ((-776 . -589) 117891) ((-776 . -23) T) ((-776 . -1014) T) ((-776 . -553) 117853) ((-776 . -1129) T) ((-776 . -13) T) ((-776 . -72) T) ((-776 . -25) T) ((-776 . -104) T) ((-776 . -591) 117813) ((-776 . -556) 117748) ((-776 . -428) 117725) ((-776 . -38) 117695) ((-776 . -82) 117660) ((-776 . -964) 117630) ((-776 . -969) 117600) ((-776 . -583) 117570) ((-776 . -655) 117540) ((-775 . -1014) T) ((-775 . -553) 117522) ((-775 . -1129) T) ((-775 . -13) T) ((-775 . -72) T) ((-774 . -753) T) ((-774 . -760) T) ((-774 . -757) T) ((-774 . -1014) T) ((-774 . -553) 117504) ((-774 . -1129) T) ((-774 . -13) T) ((-774 . -72) T) ((-774 . -318) T) ((-774 . -554) 117426) ((-773 . -1014) T) ((-773 . -553) 117408) ((-773 . -1129) T) ((-773 . -13) T) ((-773 . -72) T) ((-772 . -771) T) ((-772 . -147) T) ((-772 . -553) 117390) ((-768 . -757) T) ((-768 . -553) 117372) ((-768 . -1014) T) ((-768 . -72) T) ((-768 . -13) T) ((-768 . -1129) T) ((-768 . -760) T) ((-765 . -762) 117356) ((-765 . -951) 117254) ((-765 . -556) 117152) ((-765 . -353) 117136) ((-765 . -655) 117106) ((-765 . -583) 117076) ((-765 . -591) 117050) ((-765 . -589) 117009) ((-765 . -104) T) ((-765 . -25) T) ((-765 . -72) T) ((-765 . -13) T) ((-765 . -1129) T) ((-765 . -553) 116991) ((-765 . -1014) T) ((-765 . -23) T) ((-765 . -21) T) ((-765 . -969) 116975) ((-765 . -964) 116959) ((-765 . -82) 116938) ((-765 . -962) T) ((-765 . -664) T) ((-765 . -1061) T) ((-765 . -1026) T) ((-765 . -971) T) ((-765 . -38) 116908) ((-764 . -762) 116892) ((-764 . -951) 116790) ((-764 . -556) 116709) ((-764 . -353) 116693) ((-764 . -655) 116663) ((-764 . -583) 116633) ((-764 . -591) 116607) ((-764 . -589) 116566) ((-764 . -104) T) ((-764 . -25) T) ((-764 . -72) T) ((-764 . -13) T) ((-764 . -1129) T) ((-764 . -553) 116548) ((-764 . -1014) T) ((-764 . -23) T) ((-764 . -21) T) ((-764 . -969) 116532) ((-764 . -964) 116516) ((-764 . -82) 116495) ((-764 . -962) T) ((-764 . -664) T) ((-764 . -1061) T) ((-764 . -1026) T) ((-764 . -971) T) ((-764 . -38) 116465) ((-758 . -760) T) ((-758 . -1129) T) ((-758 . -13) T) ((-758 . -72) T) ((-758 . -428) 116449) ((-758 . -553) 116397) ((-758 . -556) 116381) ((-751 . -1014) T) ((-751 . -553) 116363) ((-751 . -1129) T) ((-751 . -13) T) ((-751 . -72) T) ((-751 . -353) 116347) ((-751 . -556) 116220) ((-751 . -951) 116118) ((-751 . -21) 116073) ((-751 . -589) 115993) ((-751 . -23) 115948) ((-751 . -25) 115903) ((-751 . -104) 115858) ((-751 . -756) 115837) ((-751 . -591) 115810) ((-751 . -971) 115789) ((-751 . -1061) 115768) ((-751 . -962) 115747) ((-751 . -722) 115726) ((-751 . -719) 115705) ((-751 . -760) 115684) ((-751 . -757) 115663) ((-751 . -717) 115642) ((-751 . -715) 115621) ((-751 . -1026) 115600) ((-751 . -664) 115579) ((-750 . -748) 115561) ((-750 . -72) T) ((-750 . -13) T) ((-750 . -1129) T) ((-750 . -553) 115543) ((-750 . -1014) T) ((-746 . -962) T) ((-746 . -664) T) ((-746 . -1061) T) ((-746 . -1026) T) ((-746 . -971) T) ((-746 . -21) T) ((-746 . -589) 115488) ((-746 . -23) T) ((-746 . -1014) T) ((-746 . -553) 115470) ((-746 . -1129) T) ((-746 . -13) T) ((-746 . -72) T) ((-746 . -25) T) ((-746 . -104) T) ((-746 . -591) 115430) ((-746 . -556) 115385) ((-746 . -951) 115355) ((-746 . -241) 115334) ((-746 . -120) 115313) ((-746 . -118) 115292) ((-746 . -38) 115262) ((-746 . -82) 115227) ((-746 . -964) 115197) ((-746 . -969) 115167) ((-746 . -583) 115137) ((-746 . -655) 115107) ((-744 . -1014) T) ((-744 . -553) 115089) ((-744 . -1129) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -353) 115073) ((-744 . -556) 114946) ((-744 . -951) 114844) ((-744 . -21) 114799) ((-744 . -589) 114719) ((-744 . -23) 114674) ((-744 . -25) 114629) ((-744 . -104) 114584) ((-744 . -756) 114563) ((-744 . -591) 114536) ((-744 . -971) 114515) ((-744 . -1061) 114494) ((-744 . -962) 114473) ((-744 . -722) 114452) ((-744 . -719) 114431) ((-744 . -760) 114410) ((-744 . -757) 114389) ((-744 . -717) 114368) ((-744 . -715) 114347) ((-744 . -1026) 114326) ((-744 . -664) 114305) ((-742 . -646) 114289) ((-742 . -556) 114244) ((-742 . -655) 114214) ((-742 . -583) 114184) ((-742 . -591) 114158) ((-742 . -589) 114117) ((-742 . -104) T) ((-742 . -25) T) ((-742 . -72) T) ((-742 . -13) T) ((-742 . -1129) T) ((-742 . -553) 114099) ((-742 . -1014) T) ((-742 . -23) T) ((-742 . -21) T) ((-742 . -969) 114083) ((-742 . -964) 114067) ((-742 . -82) 114046) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1061) T) ((-742 . -1026) T) ((-742 . -971) T) ((-742 . -38) 114016) ((-742 . -190) 113995) ((-742 . -186) 113968) ((-742 . -189) 113947) ((-740 . -334) 113931) ((-740 . -556) 113915) ((-740 . -951) 113899) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1026) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1129) T) ((-740 . -553) 113881) ((-740 . -1014) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -228) 113865) ((-739 . -556) 113849) ((-739 . -951) 113833) ((-739 . -760) T) ((-739 . -72) T) ((-739 . -1014) T) ((-739 . -553) 113815) ((-739 . -757) T) ((-739 . -186) 113802) ((-739 . -13) T) ((-739 . -1129) T) ((-739 . -189) T) ((-738 . -82) 113737) ((-738 . -964) 113688) ((-738 . -969) 113639) ((-738 . -21) T) ((-738 . -589) 113575) ((-738 . -23) T) ((-738 . -1014) T) ((-738 . -553) 113544) ((-738 . -1129) T) 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T) ((-618 . -13) T) ((-618 . -72) T) ((-618 . -64) T) ((-615 . -757) T) ((-615 . -553) 92299) ((-615 . -1014) T) ((-615 . -72) T) ((-615 . -13) T) ((-615 . -1129) T) ((-615 . -760) T) ((-615 . -951) 92283) ((-615 . -556) 92267) ((-614 . -996) T) ((-614 . -428) 92248) ((-614 . -553) 92214) ((-614 . -556) 92195) ((-614 . -1014) T) ((-614 . -1129) T) ((-614 . -13) T) ((-614 . -72) T) ((-614 . -64) T) ((-613 . -1037) 92140) ((-613 . -427) 92124) ((-613 . -454) 92057) ((-613 . -260) 91995) ((-613 . -34) T) ((-613 . -966) 91935) ((-613 . -951) 91833) ((-613 . -556) 91752) ((-613 . -353) 91736) ((-613 . -581) 91684) ((-613 . -591) 91622) ((-613 . -327) 91606) ((-613 . -190) 91585) ((-613 . -186) 91533) ((-613 . -189) 91487) ((-613 . -225) 91471) ((-613 . -807) 91395) ((-613 . -812) 91321) ((-613 . -810) 91280) ((-613 . -184) 91264) ((-613 . -655) 91248) ((-613 . -583) 91232) ((-613 . -589) 91191) ((-613 . -104) T) ((-613 . -25) T) ((-613 . -72) T) ((-613 . -13) T) ((-613 . -1129) T) ((-613 . 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. -147) T) ((-513 . -465) T) ((-513 . -553) 79264) ((-507 . -493) 79248) ((-507 . -35) T) ((-507 . -66) T) ((-507 . -239) T) ((-507 . -431) T) ((-507 . -1118) T) ((-507 . -1115) T) ((-507 . -951) 79230) ((-507 . -916) T) ((-507 . -760) T) ((-507 . -757) T) ((-507 . -495) T) ((-507 . -246) T) ((-507 . -146) T) ((-507 . -556) 79202) ((-507 . -655) 79189) ((-507 . -583) 79176) ((-507 . -591) 79163) ((-507 . -589) 79135) ((-507 . -104) T) ((-507 . -25) T) ((-507 . -72) T) ((-507 . -13) T) ((-507 . -1129) T) ((-507 . -553) 79117) ((-507 . -1014) T) ((-507 . -23) T) ((-507 . -21) T) ((-507 . -969) 79104) ((-507 . -964) 79091) ((-507 . -82) 79076) ((-507 . -962) T) ((-507 . -664) T) ((-507 . -1061) T) ((-507 . -1026) T) ((-507 . -971) T) ((-507 . -38) 79063) ((-507 . -390) T) ((-489 . -1107) 79042) ((-489 . -183) 78990) ((-489 . -76) 78938) ((-489 . -260) 78736) ((-489 . -454) 78488) ((-489 . -427) 78423) ((-489 . -124) 78371) ((-489 . -554) NIL) ((-489 . -193) 78319) ((-489 . -550) 78298) 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77567) ((-471 . -465) T) ((-471 . -147) T) ((-471 . -771) T) ((-471 . -512) T) ((-471 . -553) 77549) ((-469 . -718) T) ((-469 . -104) T) ((-469 . -25) T) ((-469 . -72) T) ((-469 . -13) T) ((-469 . -1129) T) ((-469 . -553) 77531) ((-469 . -1014) T) ((-469 . -23) T) ((-469 . -717) T) ((-469 . -757) T) ((-469 . -760) T) ((-469 . -719) T) ((-469 . -722) T) ((-469 . -448) 77508) ((-469 . -558) 77471) ((-467 . -465) T) ((-467 . -147) T) ((-467 . -553) 77453) ((-463 . -996) T) ((-463 . -428) 77434) ((-463 . -553) 77400) ((-463 . -556) 77381) ((-463 . -1014) T) ((-463 . -1129) T) ((-463 . -13) T) ((-463 . -72) T) ((-463 . -64) T) ((-462 . -996) T) ((-462 . -428) 77362) ((-462 . -553) 77328) ((-462 . -556) 77309) ((-462 . -1014) T) ((-462 . -1129) T) ((-462 . -13) T) ((-462 . -72) T) ((-462 . -64) T) ((-459 . -57) 77283) ((-459 . -34) T) ((-459 . -13) T) ((-459 . -1129) T) ((-459 . -72) 77237) ((-459 . -553) 77172) ((-459 . -260) 77110) ((-459 . -454) 77043) ((-459 . -1014) 77021) ((-459 . 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. -1129) T) ((-442 . -13) T) ((-442 . -72) T) ((-440 . -757) T) ((-440 . -553) 75029) ((-440 . -1014) T) ((-440 . -72) T) ((-440 . -13) T) ((-440 . -1129) T) ((-440 . -760) T) ((-440 . -556) 75010) ((-438 . -96) T) ((-438 . -322) 74993) ((-438 . -760) T) ((-438 . -757) T) ((-438 . -124) 74976) ((-438 . -34) T) ((-438 . -72) T) ((-438 . -553) 74958) ((-438 . -260) NIL) ((-438 . -454) NIL) ((-438 . -1014) T) ((-438 . -427) 74941) ((-438 . -554) 74923) ((-438 . -241) 74874) ((-438 . -539) 74850) ((-438 . -243) 74826) ((-438 . -594) 74809) ((-438 . -19) 74792) ((-438 . -605) T) ((-438 . -13) T) ((-438 . -1129) T) ((-438 . -84) T) ((-435 . -57) 74742) ((-435 . -34) T) ((-435 . -13) T) ((-435 . -1129) T) ((-435 . -72) 74696) ((-435 . -553) 74631) ((-435 . -260) 74569) ((-435 . -454) 74502) ((-435 . -1014) 74480) ((-435 . -427) 74464) ((-434 . -19) 74448) ((-434 . -594) 74432) ((-434 . -243) 74409) ((-434 . -241) 74361) ((-434 . -539) 74338) ((-434 . -554) 74299) ((-434 . -427) 74283) ((-434 . -1014) 74236) ((-434 . -454) 74169) ((-434 . -260) 74107) ((-434 . -553) 74022) ((-434 . -72) 73956) ((-434 . -1129) T) ((-434 . -13) T) ((-434 . -34) T) ((-434 . -124) 73940) ((-434 . -757) 73919) ((-434 . -760) 73898) ((-434 . -322) 73882) ((-433 . -254) T) ((-433 . -72) T) ((-433 . -13) T) ((-433 . -1129) T) ((-433 . -553) 73864) ((-433 . -1014) T) ((-433 . -556) 73765) ((-433 . -951) 73708) ((-433 . -454) 73674) ((-433 . -260) 73661) ((-433 . -27) T) ((-433 . -916) T) ((-433 . -201) T) ((-433 . -82) 73610) ((-433 . -964) 73575) ((-433 . -969) 73540) ((-433 . -246) T) ((-433 . -655) 73505) ((-433 . -583) 73470) ((-433 . -591) 73420) ((-433 . -589) 73370) ((-433 . -104) T) ((-433 . -25) T) ((-433 . -23) T) ((-433 . -21) T) ((-433 . -962) T) ((-433 . -664) T) ((-433 . -1061) T) ((-433 . -1026) T) ((-433 . -971) T) ((-433 . -38) 73335) ((-433 . -258) T) ((-433 . -390) T) ((-433 . -146) T) ((-433 . -495) T) ((-433 . -833) T) ((-433 . -1134) T) ((-433 . -312) T) ((-433 . -581) 73295) 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71928) ((-421 . -1014) T) ((-421 . -1129) T) ((-421 . -13) T) ((-421 . -72) T) ((-421 . -64) T) ((-420 . -196) 71907) ((-420 . -1187) 71877) ((-420 . -722) 71856) ((-420 . -719) 71835) ((-420 . -760) 71789) ((-420 . -757) 71743) ((-420 . -717) 71722) ((-420 . -718) 71701) ((-420 . -655) 71646) ((-420 . -583) 71571) ((-420 . -243) 71548) ((-420 . -241) 71525) ((-420 . -427) 71509) ((-420 . -454) 71442) ((-420 . -260) 71380) ((-420 . -34) T) ((-420 . -539) 71357) ((-420 . -951) 71186) ((-420 . -556) 70990) ((-420 . -353) 70959) ((-420 . -581) 70867) ((-420 . -591) 70706) ((-420 . -327) 70676) ((-420 . -318) 70655) ((-420 . -190) 70608) ((-420 . -589) 70396) ((-420 . -971) 70375) ((-420 . -1026) 70354) ((-420 . -1061) 70333) ((-420 . -664) 70312) ((-420 . -962) 70291) ((-420 . -186) 70187) ((-420 . -189) 70089) ((-420 . -225) 70059) ((-420 . -807) 69931) ((-420 . -812) 69805) ((-420 . -810) 69738) ((-420 . -184) 69708) ((-420 . -553) 69405) ((-420 . -969) 69330) ((-420 . -964) 69235) 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. -1026) T) ((-419 . -971) T) ((-419 . -353) 65992) ((-419 . -277) 65949) ((-419 . -260) 65936) ((-419 . -554) 65797) ((-417 . -1107) 65776) ((-417 . -183) 65724) ((-417 . -76) 65672) ((-417 . -260) 65470) ((-417 . -454) 65222) ((-417 . -427) 65157) ((-417 . -124) 65105) ((-417 . -554) NIL) ((-417 . -193) 65053) ((-417 . -550) 65032) ((-417 . -243) 65011) ((-417 . -1129) T) ((-417 . -13) T) ((-417 . -241) 64990) ((-417 . -1014) T) ((-417 . -553) 64972) ((-417 . -72) T) ((-417 . -34) T) ((-417 . -539) 64951) ((-416 . -996) T) ((-416 . -428) 64932) ((-416 . -553) 64898) ((-416 . -556) 64879) ((-416 . -1014) T) ((-416 . -1129) T) ((-416 . -13) T) ((-416 . -72) T) ((-416 . -64) T) ((-415 . -312) T) ((-415 . -1134) T) ((-415 . -833) T) ((-415 . -495) T) ((-415 . -146) T) ((-415 . -556) 64829) ((-415 . -655) 64794) ((-415 . -583) 64759) ((-415 . -38) 64724) ((-415 . -390) T) ((-415 . -258) T) ((-415 . -591) 64689) ((-415 . -589) 64639) ((-415 . -971) T) ((-415 . -1026) T) ((-415 . -1061) T) 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T) ((-413 . -34) T) ((-413 . -539) 63206) ((-412 . -1162) 63190) ((-412 . -190) 63142) ((-412 . -186) 63088) ((-412 . -189) 63040) ((-412 . -241) 62998) ((-412 . -810) 62904) ((-412 . -807) 62785) ((-412 . -812) 62691) ((-412 . -887) 62654) ((-412 . -38) 62501) ((-412 . -82) 62321) ((-412 . -964) 62162) ((-412 . -969) 62003) ((-412 . -589) 61888) ((-412 . -591) 61788) ((-412 . -583) 61635) ((-412 . -655) 61482) ((-412 . -556) 61314) ((-412 . -118) 61293) ((-412 . -120) 61272) ((-412 . -47) 61242) ((-412 . -1158) 61212) ((-412 . -35) 61178) ((-412 . -66) 61144) ((-412 . -239) 61110) ((-412 . -431) 61076) ((-412 . -1118) 61042) ((-412 . -1115) 61008) ((-412 . -916) 60974) ((-412 . -201) 60953) ((-412 . -246) 60907) ((-412 . -104) T) ((-412 . -25) T) ((-412 . -72) T) ((-412 . -13) T) ((-412 . -1129) T) ((-412 . -553) 60889) ((-412 . -1014) T) ((-412 . -23) T) ((-412 . -21) T) ((-412 . -962) T) ((-412 . -664) T) ((-412 . -1061) T) ((-412 . -1026) T) ((-412 . -971) T) ((-412 . -258) 60868) 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59601) ((-392 . -390) 59555) ((-392 . -581) 59503) ((-392 . -591) 59392) ((-392 . -327) 59376) ((-392 . -47) 59355) ((-392 . -38) 59207) ((-392 . -583) 59059) ((-392 . -655) 58911) ((-392 . -246) 58845) ((-392 . -495) 58779) ((-392 . -82) 58604) ((-392 . -964) 58450) ((-392 . -969) 58296) ((-392 . -146) 58210) ((-392 . -120) 58189) ((-392 . -118) 58168) ((-392 . -589) 58078) ((-392 . -104) T) ((-392 . -25) T) ((-392 . -72) T) ((-392 . -13) T) ((-392 . -1129) T) ((-392 . -553) 58060) ((-392 . -1014) T) ((-392 . -23) T) ((-392 . -21) T) ((-392 . -962) T) ((-392 . -664) T) ((-392 . -1061) T) ((-392 . -1026) T) ((-392 . -971) T) ((-392 . -353) 58044) ((-392 . -277) 58023) ((-392 . -260) 58010) ((-392 . -554) 57871) ((-391 . -359) 57841) ((-391 . -684) 57811) ((-391 . -658) T) ((-391 . -686) T) ((-391 . -82) 57762) ((-391 . -964) 57732) ((-391 . -969) 57702) ((-391 . -21) T) ((-391 . -589) 57617) ((-391 . -23) T) ((-391 . -1014) T) ((-391 . -553) 57599) ((-391 . -72) T) ((-391 . -25) T) 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21290) ((-203 . -237) 21274) ((-203 . -428) 21251) ((-203 . -556) 21228) ((-197 . -196) 21207) ((-197 . -1187) 21177) ((-197 . -722) 21156) ((-197 . -719) 21135) ((-197 . -760) 21089) ((-197 . -757) 21043) ((-197 . -717) 21022) ((-197 . -718) 21001) ((-197 . -655) 20946) ((-197 . -583) 20871) ((-197 . -243) 20848) ((-197 . -241) 20825) ((-197 . -427) 20809) ((-197 . -454) 20742) ((-197 . -260) 20680) ((-197 . -34) T) ((-197 . -539) 20657) ((-197 . -951) 20486) ((-197 . -556) 20290) ((-197 . -353) 20259) ((-197 . -581) 20167) ((-197 . -591) 20006) ((-197 . -327) 19976) ((-197 . -318) 19955) ((-197 . -190) 19908) ((-197 . -589) 19696) ((-197 . -971) 19675) ((-197 . -1026) 19654) ((-197 . -1061) 19633) ((-197 . -664) 19612) ((-197 . -962) 19591) ((-197 . -186) 19487) ((-197 . -189) 19389) ((-197 . -225) 19359) ((-197 . -807) 19231) ((-197 . -812) 19105) ((-197 . -810) 19038) ((-197 . -184) 19008) ((-197 . -553) 18705) ((-197 . -969) 18630) ((-197 . -964) 18535) ((-197 . -82) 18455) ((-197 . -104) 18330) ((-197 . -25) 18167) ((-197 . -72) 17904) ((-197 . -13) T) ((-197 . -1129) T) ((-197 . -1014) 17660) ((-197 . -23) 17516) ((-197 . -21) 17431) ((-181 . -628) 17389) ((-181 . -427) 17373) ((-181 . -1014) 17351) ((-181 . -454) 17284) ((-181 . -260) 17222) ((-181 . -553) 17157) ((-181 . -72) 17111) ((-181 . -1129) T) ((-181 . -13) T) ((-181 . -34) T) ((-181 . -57) 17069) ((-179 . -345) T) ((-179 . -120) T) ((-179 . -556) 17019) ((-179 . -591) 16984) ((-179 . -589) 16934) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1129) T) ((-179 . -553) 16916) ((-179 . -1014) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -971) T) ((-179 . -1026) T) ((-179 . -1061) T) ((-179 . -664) T) ((-179 . -962) T) ((-179 . -554) 16846) ((-179 . -312) T) ((-179 . -1134) T) ((-179 . -833) T) ((-179 . -495) T) ((-179 . -146) T) ((-179 . -655) 16811) ((-179 . -583) 16776) ((-179 . -38) 16741) ((-179 . -390) T) ((-179 . -258) T) ((-179 . -82) 16690) ((-179 . -964) 16655) 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-258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1014) T) ((-145 . -553) 14186) ((-145 . -1129) T) ((-145 . -13) T) ((-145 . -72) T) ((-142 . -139) 14170) ((-142 . -35) 14148) ((-142 . -66) 14126) ((-142 . -239) 14104) ((-142 . -431) 14082) ((-142 . -1118) 14060) ((-142 . -1115) 14038) ((-142 . -916) 13990) ((-142 . -822) 13943) ((-142 . -554) 13711) ((-142 . -795) 13695) ((-142 . -318) 13649) ((-142 . -299) 13628) ((-142 . -1066) 13607) ((-142 . -343) 13586) ((-142 . -351) 13557) ((-142 . -38) 13391) ((-142 . -82) 13283) ((-142 . -964) 13196) ((-142 . -969) 13109) ((-142 . -583) 12943) ((-142 . -655) 12777) ((-142 . -320) 12748) ((-142 . -662) 12719) ((-142 . -951) 12617) ((-142 . -556) 12402) ((-142 . -353) 12386) ((-142 . -797) 12311) ((-142 . -341) 12295) ((-142 . -581) 12243) ((-142 . -591) 12120) ((-142 . -589) 12018) ((-142 . -327) 12002) ((-142 . -241) 11960) ((-142 . -260) 11925) ((-142 . -454) 11837) ((-142 . -288) 11821) ((-142 . -201) 11775) ((-142 . -1134) 11683) 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T) ((-129 . -996) T) ((-129 . -428) 10648) ((-129 . -553) 10614) ((-129 . -556) 10595) ((-129 . -1014) T) ((-129 . -1129) T) ((-129 . -13) T) ((-129 . -72) T) ((-129 . -64) T) ((-127 . -996) T) ((-127 . -428) 10576) ((-127 . -553) 10542) ((-127 . -556) 10523) ((-127 . -1014) T) ((-127 . -1129) T) ((-127 . -13) T) ((-127 . -72) T) ((-127 . -64) T) ((-125 . -962) T) ((-125 . -664) T) ((-125 . -1061) T) ((-125 . -1026) T) ((-125 . -971) T) ((-125 . -21) T) ((-125 . -589) 10482) ((-125 . -23) T) ((-125 . -1014) T) ((-125 . -553) 10464) ((-125 . -1129) T) ((-125 . -13) T) ((-125 . -72) T) ((-125 . -25) T) ((-125 . -104) T) ((-125 . -591) 10438) ((-125 . -556) 10407) ((-125 . -38) 10391) ((-125 . -82) 10370) ((-125 . -964) 10354) ((-125 . -969) 10338) ((-125 . -583) 10322) ((-125 . -655) 10306) ((-125 . -1187) 10290) ((-117 . -753) T) ((-117 . -760) T) ((-117 . -757) T) ((-117 . -1014) T) ((-117 . -553) 10272) ((-117 . -1129) T) ((-117 . -13) T) ((-117 . -72) T) ((-117 . -318) T) ((-114 . -1014) T) ((-114 . -553) 10254) ((-114 . -1129) T) ((-114 . -13) T) ((-114 . -72) T) ((-114 . -554) 10213) ((-114 . -367) 10195) ((-114 . -1012) 10177) ((-114 . -318) T) ((-114 . -193) 10159) ((-114 . -124) 10141) ((-114 . -427) 10123) ((-114 . -454) NIL) ((-114 . -260) NIL) ((-114 . -34) T) ((-114 . -76) 10105) ((-114 . -183) 10087) ((-113 . -553) 10069) ((-112 . -160) T) ((-112 . -1014) T) ((-112 . -553) 10036) ((-112 . -1129) T) ((-112 . -13) T) ((-112 . -72) T) ((-112 . -748) 10018) ((-111 . -996) T) ((-111 . -428) 9999) ((-111 . -553) 9965) ((-111 . -556) 9946) ((-111 . -1014) T) ((-111 . -1129) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -996) T) ((-110 . -428) 9927) ((-110 . -553) 9893) ((-110 . -556) 9874) ((-110 . -1014) T) ((-110 . -1129) T) ((-110 . -13) T) ((-110 . -72) T) ((-110 . -64) T) ((-108 . -403) 9851) ((-108 . -556) 9747) ((-108 . -951) 9731) ((-108 . -1014) T) ((-108 . -553) 9713) ((-108 . -1129) T) ((-108 . -13) T) ((-108 . -72) T) ((-108 . -408) 9668) ((-108 . -241) 9645) ((-107 . -757) T) ((-107 . -553) 9627) ((-107 . -1014) T) ((-107 . -72) T) ((-107 . -13) T) ((-107 . -1129) T) ((-107 . -760) T) ((-107 . -23) T) ((-107 . -25) T) ((-107 . -664) T) ((-107 . -1026) T) ((-107 . -951) 9609) ((-107 . -556) 9591) ((-106 . -996) T) ((-106 . -428) 9572) ((-106 . -553) 9538) ((-106 . -556) 9519) ((-106 . -1014) T) ((-106 . -1129) T) ((-106 . -13) T) ((-106 . -72) T) ((-106 . -64) T) ((-103 . -1014) T) ((-103 . -553) 9501) ((-103 . -1129) T) ((-103 . -13) T) ((-103 . -72) T) ((-102 . -19) 9483) ((-102 . -594) 9465) ((-102 . -243) 9440) ((-102 . -241) 9390) ((-102 . -539) 9365) ((-102 . -554) NIL) ((-102 . -427) 9347) ((-102 . -1014) T) ((-102 . -454) NIL) ((-102 . -260) NIL) ((-102 . -553) 9291) ((-102 . -72) T) ((-102 . -1129) T) ((-102 . -13) T) ((-102 . -34) T) ((-102 . -124) 9273) ((-102 . -757) T) ((-102 . -760) T) ((-102 . -322) 9255) ((-101 . -753) T) ((-101 . -760) T) ((-101 . -757) T) ((-101 . -1014) T) ((-101 . -553) 9237) ((-101 . -1129) T) ((-101 . -13) T) ((-101 . -72) T) ((-101 . -318) T) ((-101 . -605) T) ((-100 . -98) 9221) ((-100 . -924) 9205) ((-100 . -34) T) ((-100 . -13) T) ((-100 . -1129) T) ((-100 . -72) 9159) ((-100 . -553) 9094) ((-100 . -260) 9032) ((-100 . -454) 8965) ((-100 . -1014) 8943) ((-100 . -427) 8927) ((-100 . -92) 8911) ((-99 . -98) 8895) ((-99 . -924) 8879) ((-99 . -34) T) ((-99 . -13) T) ((-99 . -1129) T) ((-99 . -72) 8833) ((-99 . -553) 8768) ((-99 . -260) 8706) ((-99 . -454) 8639) ((-99 . -1014) 8617) ((-99 . -427) 8601) ((-99 . -92) 8585) ((-94 . -98) 8569) ((-94 . -924) 8553) ((-94 . -34) T) ((-94 . -13) T) ((-94 . -1129) T) ((-94 . -72) 8507) ((-94 . -553) 8442) ((-94 . -260) 8380) ((-94 . -454) 8313) ((-94 . -1014) 8291) ((-94 . -427) 8275) ((-94 . -92) 8259) ((-90 . -905) 8237) ((-90 . -1066) NIL) ((-90 . -951) 8215) ((-90 . -556) 8146) ((-90 . -554) NIL) ((-90 . -934) NIL) ((-90 . -822) NIL) ((-90 . -795) 8124) ((-90 . -756) NIL) ((-90 . -722) NIL) ((-90 . -719) NIL) ((-90 . -760) NIL) ((-90 . -757) NIL) ((-90 . -717) NIL) ((-90 . -715) NIL) ((-90 . -741) NIL) ((-90 . -797) NIL) ((-90 . -341) 8102) ((-90 . -581) 8080) ((-90 . -591) 8026) ((-90 . -327) 8004) ((-90 . -241) 7938) ((-90 . -260) 7885) ((-90 . -454) 7755) ((-90 . -288) 7733) ((-90 . -201) T) ((-90 . -82) 7652) ((-90 . -964) 7598) ((-90 . -969) 7544) ((-90 . -246) T) ((-90 . -655) 7490) ((-90 . -583) 7436) ((-90 . -589) 7367) ((-90 . -38) 7313) ((-90 . -258) T) ((-90 . -390) T) ((-90 . -146) T) ((-90 . -495) T) ((-90 . -833) T) ((-90 . -1134) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7291) ((-90 . -807) NIL) ((-90 . -812) NIL) ((-90 . -810) NIL) ((-90 . -184) 7269) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1129) T) ((-90 . -553) 7251) ((-90 . -1014) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -962) T) ((-90 . -664) T) ((-90 . -1061) T) ((-90 . -1026) T) ((-90 . -971) T) ((-89 . -780) 7235) ((-89 . -833) T) ((-89 . -495) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -556) 7207) ((-89 . -655) 7194) ((-89 . -583) 7181) ((-89 . -969) 7168) ((-89 . -964) 7155) ((-89 . -82) 7140) ((-89 . -38) 7127) ((-89 . -390) T) ((-89 . -258) T) ((-89 . -962) T) ((-89 . -664) T) ((-89 . -1061) T) ((-89 . -1026) T) ((-89 . -971) T) ((-89 . -21) T) ((-89 . -589) 7099) ((-89 . -23) T) ((-89 . -1014) T) ((-89 . -553) 7081) ((-89 . -1129) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -591) 7068) ((-89 . -120) T) ((-86 . -757) T) ((-86 . -553) 7050) ((-86 . -1014) T) ((-86 . -72) T) ((-86 . -13) T) ((-86 . -1129) T) ((-86 . -760) T) ((-86 . -748) 7031) ((-85 . -753) T) ((-85 . -760) T) ((-85 . -757) T) ((-85 . -1014) T) ((-85 . -553) 7013) ((-85 . -1129) T) ((-85 . -13) T) ((-85 . -72) T) ((-85 . -318) T) ((-85 . -881) T) ((-85 . -605) T) ((-85 . -84) T) ((-85 . -554) 6995) ((-81 . -96) T) ((-81 . -322) 6978) ((-81 . -760) T) ((-81 . -757) T) ((-81 . -124) 6961) ((-81 . -34) T) ((-81 . -72) T) ((-81 . -553) 6943) ((-81 . -260) NIL) ((-81 . -454) NIL) ((-81 . -1014) T) ((-81 . -427) 6926) ((-81 . -554) 6908) ((-81 . -241) 6859) ((-81 . -539) 6835) ((-81 . -243) 6811) ((-81 . -594) 6794) ((-81 . -19) 6777) ((-81 . -605) T) ((-81 . -13) T) ((-81 . -1129) T) ((-81 . -84) T) ((-79 . -80) 6761) ((-79 . -1129) T) ((-79 . |MappingCategory|) 6735) ((-79 . -1014) T) ((-79 . -553) 6717) ((-79 . -13) T) ((-79 . -72) T) ((-78 . -553) 6699) ((-77 . -905) 6681) ((-77 . -1066) T) ((-77 . -556) 6631) ((-77 . -951) 6591) ((-77 . -554) 6521) ((-77 . -934) T) ((-77 . -822) NIL) ((-77 . -795) 6503) ((-77 . -756) T) ((-77 . -722) T) ((-77 . -719) T) ((-77 . -760) T) ((-77 . -757) T) ((-77 . -717) T) ((-77 . -715) T) ((-77 . -741) T) ((-77 . -797) 6485) ((-77 . -341) 6467) ((-77 . -581) 6449) ((-77 . -327) 6431) ((-77 . -241) NIL) ((-77 . -260) NIL) ((-77 . -454) NIL) ((-77 . -288) 6413) ((-77 . -201) T) ((-77 . -82) 6340) ((-77 . -964) 6290) ((-77 . -969) 6240) ((-77 . -246) T) ((-77 . -655) 6190) ((-77 . -583) 6140) ((-77 . -591) 6090) ((-77 . -589) 6040) ((-77 . -38) 5990) ((-77 . -258) T) ((-77 . -390) T) ((-77 . -146) T) ((-77 . -495) T) ((-77 . -833) T) ((-77 . -1134) T) ((-77 . -312) T) ((-77 . -190) T) ((-77 . -186) 5977) ((-77 . -189) T) ((-77 . -225) 5959) ((-77 . -807) NIL) ((-77 . -812) NIL) ((-77 . -810) NIL) ((-77 . -184) 5941) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1129) T) ((-77 . -553) 5884) ((-77 . -1014) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -962) T) ((-77 . -664) T) ((-77 . -1061) T) ((-77 . -1026) T) ((-77 . -971) T) ((-73 . -98) 5868) ((-73 . -924) 5852) ((-73 . -34) T) ((-73 . -13) T) ((-73 . -1129) T) ((-73 . -72) 5806) ((-73 . -553) 5741) ((-73 . -260) 5679) ((-73 . -454) 5612) ((-73 . -1014) 5590) ((-73 . -427) 5574) ((-73 . -92) 5558) ((-69 . -411) T) ((-69 . -1026) T) ((-69 . -72) T) ((-69 . -13) T) ((-69 . -1129) T) ((-69 . -553) 5540) ((-69 . -1014) T) ((-69 . -664) T) ((-69 . -241) 5519) ((-67 . -996) T) ((-67 . -428) 5500) ((-67 . -553) 5466) ((-67 . -556) 5447) ((-67 . -1014) T) ((-67 . -1129) T) ((-67 . -13) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1035) 5431) ((-62 . -427) 5415) ((-62 . -1014) 5393) ((-62 . -454) 5326) ((-62 . -260) 5264) ((-62 . -553) 5199) ((-62 . -72) 5153) ((-62 . -1129) T) ((-62 . -13) T) ((-62 . -34) T) ((-62 . -76) 5137) ((-60 . -57) 5099) ((-60 . -34) T) ((-60 . -13) T) ((-60 . -1129) T) ((-60 . -72) 5053) ((-60 . -553) 4988) ((-60 . -260) 4926) ((-60 . -454) 4859) ((-60 . -1014) 4837) ((-60 . -427) 4821) ((-58 . -19) 4805) ((-58 . -594) 4789) ((-58 . -243) 4766) ((-58 . -241) 4718) ((-58 . -539) 4695) ((-58 . -554) 4656) ((-58 . -427) 4640) ((-58 . -1014) 4593) ((-58 . -454) 4526) ((-58 . -260) 4464) ((-58 . -553) 4379) ((-58 . -72) 4313) ((-58 . -1129) T) ((-58 . -13) T) ((-58 . -34) T) ((-58 . -124) 4297) ((-58 . -757) 4276) ((-58 . -760) 4255) ((-58 . -322) 4239) ((-55 . -1014) T) ((-55 . -553) 4221) ((-55 . -1129) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -951) 4203) ((-55 . -556) 4185) ((-51 . -1014) T) ((-51 . -553) 4167) ((-51 . -1129) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -561) 4151) ((-50 . -556) 4120) ((-50 . -591) 4094) ((-50 . -589) 4053) ((-50 . -971) T) ((-50 . -1026) T) ((-50 . -1061) T) ((-50 . -664) T) ((-50 . -962) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1014) T) ((-50 . -553) 4035) ((-50 . -1129) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -951) 4019) ((-49 . -1014) T) ((-49 . -553) 4001) ((-49 . -1129) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -254) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1129) T) ((-48 . -553) 3983) ((-48 . -1014) T) ((-48 . -556) 3884) ((-48 . -951) 3827) ((-48 . -454) 3793) ((-48 . -260) 3780) ((-48 . -27) T) ((-48 . -916) T) ((-48 . -201) T) ((-48 . -82) 3729) ((-48 . -964) 3694) ((-48 . -969) 3659) ((-48 . -246) T) ((-48 . -655) 3624) ((-48 . -583) 3589) ((-48 . -591) 3539) ((-48 . -589) 3489) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -962) T) ((-48 . -664) T) ((-48 . -1061) T) ((-48 . -1026) T) ((-48 . -971) T) ((-48 . -38) 3454) ((-48 . -258) T) ((-48 . -390) T) ((-48 . -146) T) ((-48 . -495) T) ((-48 . -833) T) ((-48 . -1134) T) ((-48 . -312) T) ((-48 . -581) 3414) ((-48 . -934) T) ((-48 . -554) 3359) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3346) ((-48 . -189) T) ((-45 . -36) 3325) ((-45 . -539) 3248) ((-45 . -260) 3046) ((-45 . -454) 2798) ((-45 . -427) 2733) ((-45 . -241) 2631) ((-45 . -243) 2554) ((-45 . -550) 2533) ((-45 . -193) 2481) ((-45 . -76) 2429) ((-45 . -183) 2377) ((-45 . -1107) 2356) ((-45 . -237) 2304) ((-45 . -124) 2252) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1129) T) ((-45 . -72) T) ((-45 . -553) 2234) ((-45 . -1014) T) ((-45 . -554) NIL) ((-45 . -594) 2182) ((-45 . -322) 2130) ((-45 . -760) NIL) ((-45 . -757) NIL) ((-45 . -1064) 2078) ((-45 . -924) 2026) ((-45 . -1168) 1974) ((-45 . -609) 1922) ((-44 . -359) 1906) ((-44 . -684) 1890) ((-44 . -658) T) ((-44 . -686) T) ((-44 . -82) 1869) ((-44 . -964) 1853) ((-44 . -969) 1837) ((-44 . -21) T) ((-44 . -589) 1780) ((-44 . -23) T) ((-44 . -1014) T) ((-44 . -553) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -104) T) ((-44 . -591) 1720) ((-44 . -583) 1704) ((-44 . -655) 1688) ((-44 . -316) 1672) ((-44 . -1129) T) ((-44 . -13) T) ((-44 . -241) 1649) ((-40 . -291) 1623) ((-40 . -146) T) ((-40 . -556) 1553) ((-40 . -971) T) ((-40 . -1026) T) ((-40 . -1061) T) ((-40 . -664) T) ((-40 . -962) T) ((-40 . -591) 1455) ((-40 . -589) 1385) ((-40 . -104) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -13) T) ((-40 . -1129) T) ((-40 . -553) 1367) ((-40 . -1014) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -969) 1312) ((-40 . -964) 1257) ((-40 . -82) 1174) ((-40 . -554) 1158) ((-40 . -184) 1135) ((-40 . -810) 1087) ((-40 . -812) 999) ((-40 . -807) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -312) T) ((-40 . -1134) T) ((-40 . -833) T) ((-40 . -495) T) ((-40 . -655) 677) ((-40 . -583) 622) ((-40 . -38) 567) ((-40 . -390) T) ((-40 . -258) T) ((-40 . -246) T) ((-40 . -201) T) ((-40 . -318) NIL) ((-40 . -299) NIL) ((-40 . -1066) NIL) ((-40 . -118) 539) ((-40 . -343) NIL) ((-40 . -351) 511) ((-40 . -120) 483) ((-40 . -320) 455) ((-40 . -327) 432) ((-40 . -581) 366) ((-40 . -353) 343) ((-40 . -951) 220) ((-40 . -662) 192) ((-31 . -996) T) ((-31 . -428) 173) ((-31 . -553) 139) ((-31 . -556) 120) ((-31 . -1014) T) ((-31 . -1129) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -867) T) ((-30 . -553) 102) ((0 . |EnumerationCategory|) T) ((0 . -553) 84) ((0 . -1014) T) ((0 . -72) T) ((0 . -1129) T) ((-2 . |RecordCategory|) T) ((-2 . -553) 66) ((-2 . -1014) T) ((-2 . -72) T) ((-2 . -1129) T) ((-3 . |UnionCategory|) T) ((-3 . -553) 48) ((-3 . -1014) T) ((-3 . -72) T) ((-3 . -1129) T) ((-1 . -1014) T) ((-1 . -553) 30) ((-1 . -1129) T) ((-1 . -13) T) ((-1 . -72) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index ea14a7b6..7944b76a 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3577223100)            
-(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3577234981)            
+(3998 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -148,16 +148,16 @@
  |InnerEvalable&| |InnerEvalable| |InnerFreeAbelianMonoid|
  |IndexedFlexibleArray| |IfAst| |InnerFiniteField|
  |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions|
- |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| |InAst|
- |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions|
- |InputBinaryFile| |IncrementingMaps| |IndexedExponents|
- |InnerNumericEigenPackage| |InetClientStreamSocket| |Infinity| |InputForm|
- |InputFormFunctions1| |InfiniteProductCharacteristicZero|
- |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact|
- |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign|
- |IntegerNumberSystem&| |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64|
- |Int8| |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits|
- |IntervalCategory| |IntegralDomain&| |IntegralDomain| |ElementaryIntegration|
+ |InnerMatrixQuotientFieldFunctions| |ImportAst| |InAst| |InputByteConduit&|
+ |InputByteConduit| |InnerNormalBasisFieldFunctions| |InputBinaryFile|
+ |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage|
+ |InetClientStreamSocket| |Infinity| |InputForm| |InputFormFunctions1|
+ |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage|
+ |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField|
+ |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&|
+ |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64| |Int8| |InnerTable|
+ |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory|
+ |IntegralDomain&| |IntegralDomain| |ElementaryIntegration|
  |IntegerFactorizationPackage| |GenusZeroIntegration|
  |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration|
  |TranscendentalHermiteIntegration| |PureAlgebraicIntegration|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 4a6a72da..fbffe074 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4048 +1,4045 @@
 
-(2820676 . 3577223109)       
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+(-13 (-322 |t#1|) (-10 -7 (-6 -3996))) 
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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) ((-25) . T) ((-38 (-348 (-485))) . T) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) . T) ((-27) . T) ((-72) . T) ((-82 (-348 (-485)) (-348 (-485))) . T) ((-82 |#1| |#1|) |has| |#1| (-146)) ((-82 $ $) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-557 (-348 (-485))) . T) ((-557 (-348 (-859 |#1|))) |has| |#1| (-496)) ((-557 (-485)) . T) ((-557 (-552 $)) . T) ((-557 (-859 |#1|)) |has| |#1| (-963)) ((-557 (-1091)) . T) ((-557 |#1|) . T) ((-557 $) . T) ((-554 (-774)) . T) ((-146) . T) ((-555 (-474)) |has| |#1| (-555 (-474))) ((-555 (-802 (-328))) |has| |#1| (-555 (-802 (-328)))) ((-555 (-802 (-485))) |has| |#1| (-555 (-802 (-485)))) ((-201) . T) ((-246) . T) ((-258) . T) ((-260 $) . T) ((-254) . T) ((-312) . T) ((-327 |#1|) |has| |#1| (-963)) ((-341 |#1|) . T) ((-353 |#1|) . T) ((-362 |#1|) . T) ((-390) . T) ((-411) |has| |#1| (-411)) ((-454 (-552 $) $) . T) ((-454 $ $) . T) ((-496) . T) ((-13) . T) ((-590 (-348 (-485))) . T) ((-590 (-485)) . T) ((-590 |#1|) OR (|has| |#1| (-963)) (|has| |#1| (-146))) ((-590 $) . T) ((-592 (-348 (-485))) . T) ((-592 (-485)) -12 (|has| |#1| (-582 (-485))) (|has| |#1| (-963))) ((-592 |#1|) OR (|has| |#1| (-963)) (|has| |#1| (-146))) ((-592 $) . T) ((-584 (-348 (-485))) . T) ((-584 |#1|) |has| |#1| (-146)) ((-584 $) . T) ((-582 (-485)) -12 (|has| |#1| (-582 (-485))) (|has| |#1| (-963))) ((-582 |#1|) |has| |#1| (-963)) ((-656 (-348 (-485))) . T) ((-656 |#1|) |has| |#1| (-146)) ((-656 $) . T) ((-665) . T) ((-808 $ (-1091)) |has| |#1| (-963)) ((-811 (-1091)) |has| |#1| (-963)) ((-813 (-1091)) |has| |#1| (-963)) ((-798 (-328)) |has| |#1| (-798 (-328))) ((-798 (-485)) |has| |#1| (-798 (-485))) ((-796 |#1|) . T) ((-834) . T) ((-917) . T) ((-952 (-348 (-485))) OR (|has| |#1| (-952 (-348 (-485)))) (-12 (|has| |#1| (-496)) (|has| |#1| (-952 (-485))))) ((-952 (-348 (-859 |#1|))) |has| |#1| (-496)) ((-952 (-485)) |has| |#1| (-952 (-485))) ((-952 (-552 $)) . T) ((-952 (-859 |#1|)) |has| |#1| (-963)) ((-952 (-1091)) . T) ((-952 |#1|) . T) ((-965 (-348 (-485))) . T) ((-965 |#1|) |has| |#1| (-146)) ((-965 $) . T) ((-970 (-348 (-485))) . T) ((-970 |#1|) |has| |#1| (-146)) ((-970 $) . T) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1130) . T) ((-1135) . T)) 
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+((-1223 (*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014)) (-5 *2 (-2 (|:| -3860 *3) (|:| |entry| *4)))))) 
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+(((-34) . T) ((-76 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1014)) (|has| |#2| (-72))) ((-553 (-773)) OR (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-1014)) (|has| |#2| (-553 (-773)))) ((-124 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-554 (-473)) |has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-554 (-473))) ((-183 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-193 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-484) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-1146 (-484)) $) . T) ((-241 |#1| |#2|) . T) ((-243 (-484) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-237 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-322 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-427 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-427 |#2|) . T) ((-539 (-484) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-539 |#1| |#2|) . T) ((-454 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ((-454 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-550 |#1| |#2|) . T) ((-594 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-609 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-757) |has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-757)) ((-760) |has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-757)) ((-924 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-1014) OR (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-757)) (|has| |#2| (-1014))) ((-1064 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T) ((-1107 |#1| |#2|) . T) ((-1129) . T) ((-1168 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) . T)) 
+((-3946 (((-773) $) NIL T ELT) (($ (-484)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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+NIL 
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 (((-38 |#1|) (-113) (-146)) (T -38)) 
 NIL 
-(-13 (-963) (-656 |t#1|) (-557 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-557 (-485)) . T) ((-557 |#1|) . T) ((-554 (-774)) . T) ((-13) . T) ((-590 (-485)) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-592 |#1|) . T) ((-592 $) . T) ((-584 |#1|) . T) ((-656 |#1|) . T) ((-665) . T) ((-965 |#1|) . T) ((-970 |#1|) . T) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1130) . T)) 
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+NIL 
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+NIL 
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 (((-64) (-113)) (T -64)) 
 NIL 
-(-13 (-1015) (-428 (-1096))) 
-(((-72) . T) ((-557 (-1096)) . T) ((-554 (-774)) . T) ((-554 (-1096)) . T) ((-428 (-1096)) . T) ((-13) . T) ((-1015) . T) ((-1130) . T)) 
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+(((-72) . T) ((-556 (-1095)) . T) ((-553 (-773)) . T) ((-553 (-1095)) . T) ((-428 (-1095)) . T) ((-13) . T) ((-1014) . T) ((-1129) . T)) 
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 NIL 
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 (((-66) (-113)) (T -66)) 
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 NIL 
 (((-68) (-113)) (T -68)) 
 NIL 
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-NIL 
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 (((-146) (-113)) (T -146)) 
 NIL 
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+NIL 
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 NIL 
 (-13 (-193 |t#1|)) 
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-NIL 
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-NIL 
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-NIL 
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 (((-190) (-113)) (T -190)) 
 NIL 
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 (((-191) (-113)) (T -191)) 
 NIL 
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-NIL 
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(-962))) ELT) (($ $ (-584 (-1090))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-1946 (((-695) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3995)) ELT) (((-695) |#2| $) NIL (-12 (|has| $ (-6 -3995)) (|has| |#2| (-1014))) ELT)) (-3400 (($ $) NIL T ELT)) (-3946 (((-1179 |#2|) $) 9 T ELT) (($ (-484)) NIL (OR (-12 (|has| |#2| (-951 (-484))) (|has| |#2| (-1014))) (|has| |#2| (-962))) ELT) (($ (-348 (-484))) NIL (-12 (|has| |#2| (-951 (-348 (-484)))) (|has| |#2| (-1014))) ELT) (($ |#2|) 12 (|has| |#2| (-1014)) ELT) (((-773) $) NIL (|has| |#2| (-553 (-773))) ELT)) (-3127 (((-695)) NIL (|has| |#2| (-962)) CONST)) (-1265 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-1948 (((-85) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3995)) ELT)) (-3126 (((-85) $ $) NIL (|has| |#2| (-962)) ELT)) (-2661 (($) 37 (|has| |#2| (-23)) CONST)) (-2667 (($) 41 (|has| |#2| (-962)) CONST)) (-2670 (($ $ (-695)) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1090)) (-584 (-695))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090) (-695)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1090))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-2567 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2568 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-3057 (((-85) $ $) 28 (|has| |#2| (-72)) ELT)) (-2685 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2686 (((-85) $ $) 67 (|has| |#2| (-757)) ELT)) (-3949 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3837 (($ $ $) NIL (|has| |#2| (-21)) ELT) (($ $) NIL (|has| |#2| (-21)) ELT)) (-3839 (($ $ $) 35 (|has| |#2| (-25)) ELT)) (** (($ $ (-695)) NIL (|has| |#2| (-962)) ELT) (($ $ (-831)) NIL (|has| |#2| (-962)) ELT)) (* (($ $ $) 47 (|has| |#2| (-962)) ELT) (($ $ |#2|) 45 (|has| |#2| (-664)) ELT) (($ |#2| $) 46 (|has| |#2| (-664)) ELT) (($ (-484) $) NIL (|has| |#2| (-21)) ELT) (($ (-695) $) NIL (|has| |#2| (-23)) ELT) (($ (-831) $) NIL (|has| |#2| (-25)) ELT)) (-3957 (((-695) $) NIL (|has| $ (-6 -3995)) ELT))) 
+(((-197 |#1| |#2|) (-196 |#1| |#2|) (-695) (-1129)) (T -197)) 
+NIL 
+((-3841 (((-197 |#1| |#3|) (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|) 21 T ELT)) (-3842 ((|#3| (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|) 23 T ELT)) (-3958 (((-197 |#1| |#3|) (-1 |#3| |#2|) (-197 |#1| |#2|)) 18 T ELT))) 
+(((-198 |#1| |#2| |#3|) (-10 -7 (-15 -3841 ((-197 |#1| |#3|) (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|)) (-15 -3842 (|#3| (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|)) (-15 -3958 ((-197 |#1| |#3|) (-1 |#3| |#2|) (-197 |#1| |#2|)))) (-695) (-1129) (-1129)) (T -198)) 
+((-3958 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-197 *5 *6)) (-14 *5 (-695)) (-4 *6 (-1129)) (-4 *7 (-1129)) (-5 *2 (-197 *5 *7)) (-5 *1 (-198 *5 *6 *7)))) (-3842 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-197 *5 *6)) (-14 *5 (-695)) (-4 *6 (-1129)) (-4 *2 (-1129)) (-5 *1 (-198 *5 *6 *2)))) (-3841 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-197 *6 *7)) (-14 *6 (-695)) (-4 *7 (-1129)) (-4 *5 (-1129)) (-5 *2 (-197 *6 *5)) (-5 *1 (-198 *6 *7 *5))))) 
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+NIL 
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 (((-201) (-113)) (T -201)) 
-((** (*1 *1 *1 *2) (-12 (-4 *1 (-201)) (-5 *2 (-485)))) (-2486 (*1 *1 *1) (-4 *1 (-201)))) 
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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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ELT) (($ $ (-1 |#1| |#1|) (-695)) NIL T ELT) (($ $ (-1090)) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-584 (-1090))) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-1090) (-695)) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-584 (-1090)) (-584 (-695))) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-695)) NIL (|has| |#1| (-189)) ELT)) (-1489 (((-584 |#2|) $) NIL T ELT)) (-3948 (((-469 |#3|) $) NIL T ELT) (((-695) $ |#3|) NIL T ELT) (((-584 (-695)) $ (-584 |#3|)) NIL T ELT) (((-695) $ |#2|) NIL T ELT)) (-3972 (((-801 (-328)) $) NIL (-12 (|has| |#1| (-554 (-801 (-328)))) (|has| |#3| (-554 (-801 (-328))))) ELT) (((-801 (-484)) $) NIL (-12 (|has| |#1| (-554 (-801 (-484)))) (|has| |#3| (-554 (-801 (-484))))) ELT) (((-473) $) NIL (-12 (|has| |#1| (-554 (-473))) (|has| |#3| (-554 (-473)))) ELT)) (-2818 ((|#1| $) NIL (|has| |#1| (-390)) ELT) (($ $ |#3|) NIL (|has| |#1| (-390)) ELT)) (-2704 (((-3 (-1179 $) #1#) (-631 $)) NIL (-12 (|has| $ (-118)) (|has| |#1| 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ELT) (($ $ (-1090)) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-584 (-1090))) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-1090) (-695)) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $ (-584 (-1090)) (-584 (-695))) NIL (|has| |#1| (-812 (-1090))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-695)) NIL (|has| |#1| (-189)) ELT)) (-3057 (((-85) $ $) NIL T ELT)) (-3949 (($ $ |#1|) NIL (|has| |#1| (-312)) ELT)) (-3837 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3839 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-348 (-484))) NIL (|has| |#1| (-38 (-348 (-484)))) ELT) (($ (-348 (-484)) $) NIL (|has| |#1| (-38 (-348 (-484)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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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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 (((-246) (-113)) (T -246)) 
 NIL 
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+NIL 
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-((-3769 (($ $ (-585 |#2|) (-585 |#2|)) 14 T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ (-249 |#2|)) 11 T ELT) (($ $ (-585 (-249 |#2|))) NIL T ELT))) 
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-NIL 
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-(-13 (-454 |t#1| |t#1|) (-10 -8 (-15 -3769 ($ $ (-249 |t#1|))) (-15 -3769 ($ $ (-585 (-249 |t#1|)))))) 
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+NIL 
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 (((-454 |#1| |#1|) . T)) 
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-NIL 
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-((-2570 (((-85) $ $) NIL T ELT)) (-3190 (((-85) $) NIL T ELT)) (-3775 (((-585 (-2 (|:| |gen| |#1|) (|:| -3944 (-696)))) $) NIL T ELT)) (-1313 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3138 (((-696) $) NIL T ELT)) (-3725 (($) NIL T CONST)) (-3159 (((-3 |#1| #1#) $) NIL T ELT)) (-3158 ((|#1| $) NIL T ELT)) (-1215 (((-85) $ $) NIL T ELT)) (-2301 ((|#1| $ (-485)) NIL T ELT)) (-1623 (((-696) $ (-485)) NIL T ELT)) (-2292 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-1622 (($ (-1 (-696) (-696)) $) NIL T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-1621 (($ $ $) NIL (|has| (-696) (-718)) ELT)) (-3245 (((-1035) $) NIL T ELT)) (-3947 (((-774) $) NIL T ELT) (($ |#1|) NIL T ELT)) (-3678 (((-696) |#1| $) NIL T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-2662 (($) NIL T CONST)) (-3058 (((-85) $ $) NIL T ELT)) (-3840 (($ $ $) NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (-832) $) NIL T ELT) (($ (-696) $) NIL T ELT) (($ (-696) |#1|) NIL T ELT))) 
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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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(($ (-348 (-484)) $) NIL T ELT) (($ $ (-818 |#1|)) NIL T ELT) (($ (-818 |#1|) $) NIL T ELT))) 
+(((-289 |#1| |#2|) (-280 (-818 |#1|)) (-831) (-831)) (T -289)) 
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-NIL 
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-NIL 
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-NIL 
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-(((-335 |#1|) (-334 |#1|) (-1015)) (T -335)) 
-NIL 
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+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1014) . T) ((-1129) . T)) 
+((-1782 (((-631 |#2|) (-1179 $)) 45 T ELT)) (-1792 (($ (-1179 |#2|) (-1179 $)) 39 T ELT)) (-1781 (((-631 |#2|) $ (-1179 $)) 47 T ELT)) (-3757 ((|#2| (-1179 $)) 13 T ELT)) (-3225 (((-1179 |#2|) $ (-1179 $)) NIL T ELT) (((-631 |#2|) (-1179 $) (-1179 $)) 27 T ELT))) 
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+NIL 
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+(((-320 |#1| |#2|) (-113) (-146) (-1155 |t#1|)) (T -320)) 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1061) . T) ((-1014) . T) ((-1129) . T)) 
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+NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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+(((-351 |#1| |#2|) (-113) (-146) (-1155 |t#1|)) (T -351)) 
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+NIL 
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+(((-353 |#1|) (-113) (-1129)) (T -353)) 
+NIL 
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-NIL 
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+NIL 
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-NIL 
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+NIL 
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-NIL 
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-NIL 
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|#2|))))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-249 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) (-584 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-249 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-584 (-249 |#2|))) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT)) (-1222 (((-85) $ $) NIL T ELT)) (-2203 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3995)) (|has| |#2| (-1014))) ELT)) (-2206 (((-584 |#2|) $) NIL T ELT)) (-3403 (((-85) $) NIL T ELT)) (-3565 (($) NIL T ELT)) (-3800 ((|#2| $ |#1|) 13 T ELT) ((|#2| $ |#1| |#2|) NIL T ELT)) (-1466 (($) NIL T ELT) (($ (-584 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-1946 (((-695) (-1 (-85) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3995)) ELT) (((-695) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) $) NIL (-12 (|has| $ (-6 -3995)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (((-695) |#2| $) NIL (-12 (|has| $ (-6 -3995)) (|has| |#2| (-1014))) ELT) (((-695) (-1 (-85) |#2|) $) NIL (|has| $ (-6 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+NIL 
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+((-3627 (*1 *1) (-5 *1 (-415)))) 
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(|:| |entry| |#2|)) (-1014))) ELT) (($ (-1 (-85) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3995)) ELT)) (-3842 (((-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| $ (-6 -3995)) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (((-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) NIL (|has| $ (-6 -3995)) ELT) (((-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3995)) ELT)) (-1576 ((|#2| $ |#1| |#2|) NIL (|has| $ (-6 -3996)) ELT)) (-3113 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|#2|))))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-249 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|))) (-584 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) 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+NIL 
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ELT)) (-2818 ((|#2| $) NIL (|has| |#2| (-390)) ELT) (($ $ (-774 |#1|)) NIL (|has| |#2| (-390)) ELT)) (-2704 (((-3 (-1179 $) #1#) (-631 $)) NIL (-12 (|has| $ (-118)) (|has| |#2| (-822))) ELT)) (-3946 (((-773) $) NIL T ELT) (($ (-484)) NIL T ELT) (($ |#2|) NIL T ELT) (($ (-774 |#1|)) NIL T ELT) (($ (-348 (-484))) NIL (OR (|has| |#2| (-38 (-348 (-484)))) (|has| |#2| (-951 (-348 (-484))))) ELT) (($ $) NIL (|has| |#2| (-495)) ELT)) (-3817 (((-584 |#2|) $) NIL T ELT)) (-3677 ((|#2| $ (-420 (-3957 |#1|) (-695))) NIL T ELT) (($ $ (-774 |#1|) (-695)) NIL T ELT) (($ $ (-584 (-774 |#1|)) (-584 (-695))) NIL T ELT)) (-2703 (((-633 $) $) NIL (OR (-12 (|has| $ (-118)) (|has| |#2| (-822))) (|has| |#2| (-118))) ELT)) (-3127 (((-695)) NIL T CONST)) (-1623 (($ $ $ (-695)) NIL (|has| |#2| (-146)) ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-2063 (((-85) $ $) NIL (|has| |#2| (-495)) ELT)) (-3126 (((-85) $ $) NIL T ELT)) (-2661 (($) NIL T CONST)) (-2667 (($) NIL T CONST)) (-2670 (($ $ (-584 (-774 |#1|)) (-584 (-695))) NIL T ELT) (($ $ (-774 |#1|) (-695)) NIL T ELT) (($ $ (-584 (-774 |#1|))) NIL T ELT) (($ $ (-774 |#1|)) NIL T ELT)) (-3057 (((-85) $ $) NIL T ELT)) (-3949 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3837 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3839 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-348 (-484))) NIL (|has| |#2| (-38 (-348 (-484)))) ELT) (($ (-348 (-484)) $) NIL (|has| |#2| (-38 (-348 (-484)))) ELT) (($ |#2| $) NIL T ELT) (($ $ |#2|) NIL T ELT))) 
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+((-1937 (*1 *1 *1 *2) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-419 *3 *4)) (-14 *3 (-584 (-1090))) (-4 *4 (-962))))) 
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(((-2 (|:| |mat| (-631 (-484))) (|:| |vec| (-1179 (-484)))) (-631 $) (-1179 $)) NIL (-12 (|has| |#2| (-581 (-484))) (|has| |#2| (-962))) ELT) (((-2 (|:| |mat| (-631 |#2|)) (|:| |vec| (-1179 |#2|))) (-631 $) (-1179 $)) NIL (|has| |#2| (-962)) ELT) (((-631 |#2|) (-631 $)) NIL (|has| |#2| (-962)) ELT)) (-3467 (((-3 $ #1#) $) NIL (|has| |#2| (-962)) ELT)) (-2995 (($) NIL (|has| |#2| (-318)) ELT)) (-1576 ((|#2| $ (-484) |#2|) NIL (|has| $ (-6 -3996)) ELT)) (-3113 ((|#2| $ (-484)) 11 T ELT)) (-3187 (((-85) $) NIL (|has| |#2| (-718)) ELT)) (-2890 (((-584 |#2|) $) NIL (|has| $ (-6 -3995)) ELT)) (-1214 (((-85) $ $) NIL (|has| |#2| (-23)) ELT)) (-2411 (((-85) $) NIL (|has| |#2| (-962)) ELT)) (-2201 (((-484) $) NIL (|has| (-484) (-757)) ELT)) (-2532 (($ $ $) NIL (|has| |#2| (-757)) ELT)) (-2609 (((-584 |#2|) $) NIL (|has| $ (-6 -3995)) ELT)) (-3246 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3995)) (|has| |#2| (-1014))) ELT)) (-2202 (((-484) $) NIL (|has| (-484) (-757)) ELT)) (-2858 (($ $ $) NIL 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(|has| |#2| (-962))) ELT) (($ $ (-584 (-1090))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-1946 (((-695) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3995)) ELT) (((-695) |#2| $) NIL (-12 (|has| $ (-6 -3995)) (|has| |#2| (-1014))) ELT)) (-3400 (($ $) NIL T ELT)) (-3946 (((-1179 |#2|) $) NIL T ELT) (($ (-484)) NIL (OR (-12 (|has| |#2| (-951 (-484))) (|has| |#2| (-1014))) (|has| |#2| (-962))) ELT) (($ (-348 (-484))) NIL (-12 (|has| |#2| (-951 (-348 (-484)))) (|has| |#2| (-1014))) ELT) (($ |#2|) NIL (|has| |#2| (-1014)) ELT) (((-773) $) NIL (|has| |#2| (-553 (-773))) ELT)) (-3127 (((-695)) NIL (|has| |#2| (-962)) CONST)) (-1265 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-1948 (((-85) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3995)) ELT)) (-3126 (((-85) $ $) NIL (|has| |#2| (-962)) ELT)) (-2661 (($) NIL (|has| |#2| (-23)) CONST)) (-2667 (($) NIL (|has| |#2| (-962)) CONST)) (-2670 (($ $ (-695)) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1090)) (-584 (-695))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090) (-695)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1090))) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1090)) NIL (-12 (|has| |#2| (-812 (-1090))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-2567 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2568 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-3057 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-2685 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2686 (((-85) $ $) 17 (|has| |#2| (-757)) ELT)) (-3949 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3837 (($ $ $) NIL (|has| 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+(((-420 |#1| |#2|) (-196 |#1| |#2|) (-695) (-718)) (T -420)) 
+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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+(((-463) (-13 (-996) (-10 -8 (-15 -3450 ((-445) $)) (-15 -1995 ((-1049) $))))) (T -463)) 
+((-3450 (*1 *2 *1) (-12 (-5 *2 (-445)) (-5 *1 (-463)))) (-1995 (*1 *2 *1) (-12 (-5 *2 (-1049)) (-5 *1 (-463))))) 
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+NIL 
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 (((-147) . T)) 
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-(((-468) (-13 (-466) (-554 (-774)) (-10 -8 (-15 -2019 ($ (-336))) (-15 -2019 ($ (-1074))) (-15 -2018 ((-85) $)) (-15 -2560 ((-85) $)) (-15 -3420 ((-1035) $)) (-15 -2017 ((-1035) $ (-1035)))))) (T -468)) 
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-((-2021 (((-1 |#1| |#1|) |#1|) 11 T ELT)) (-2020 (((-1 |#1| |#1|)) 10 T ELT))) 
-(((-469 |#1|) (-10 -7 (-15 -2020 ((-1 |#1| |#1|))) (-15 -2021 ((-1 |#1| |#1|) |#1|))) (-13 (-665) (-25))) (T -469)) 
-((-2021 (*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-469 *3)) (-4 *3 (-13 (-665) (-25))))) (-2020 (*1 *2) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-469 *3)) (-4 *3 (-13 (-665) (-25)))))) 
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-NIL 
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-((-2557 (((-634 (-1139)) $ (-1139)) NIL T ELT)) (-2558 (((-634 (-489)) $ (-489)) NIL T ELT)) (-2556 (((-696) $ (-102)) 39 T ELT)) (-2559 (((-634 (-101)) $ (-101)) 40 T ELT)) (-2002 (((-634 (-1139)) $) NIL T ELT)) (-1998 (((-634 (-1137)) $) NIL T ELT)) (-2000 (((-634 (-1136)) $) NIL T ELT)) (-2003 (((-634 (-489)) $) NIL T ELT)) (-1999 (((-634 (-487)) $) NIL T ELT)) (-2001 (((-634 (-486)) $) NIL T ELT)) (-1997 (((-696) $ (-102)) 35 T ELT)) (-2004 (((-634 (-101)) $) 37 T ELT)) (-2441 (((-85) $) 27 T ELT)) (-2442 (((-634 $) (-516) (-867)) 18 T ELT) (((-634 $) (-429) (-867)) 24 T ELT)) (-3947 (((-774) $) 48 T ELT)) (-1701 (($ $) 42 T ELT))) 
-(((-472) (-13 (-693 (-516)) (-554 (-774)) (-10 -8 (-15 -2442 ((-634 $) (-429) (-867)))))) (T -472)) 
-((-2442 (*1 *2 *3 *4) (-12 (-5 *3 (-429)) (-5 *4 (-867)) (-5 *2 (-634 (-472))) (-5 *1 (-472))))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+((-3249 (*1 *2 *1) (-12 (-5 *2 (-584 (-1049))) (-5 *1 (-614))))) 
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+NIL 
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+(((-655 |#1|) (-113) (-146)) (T -655)) 
+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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-(((-742) (-113)) (T -742)) 
-NIL 
-(-13 (-496) (-757)) 
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-NIL 
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+(((-722) (-113)) (T -722)) 
+NIL 
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 (((-756) (-113)) (T -756)) 
 NIL 
-(-13 (-768) (-665)) 
-(((-72) . T) ((-554 (-774)) . T) ((-13) . T) ((-665) . T) ((-768) . T) ((-758) . T) ((-761) . T) ((-1027) . T) ((-1015) . T) ((-1130) . T)) 
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+(-13 (-715) (-962) (-664)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-556 (-484)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-715) . T) ((-717) . T) ((-719) . T) ((-722) . T) ((-757) . T) ((-760) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1061) . T) ((-1014) . T) ((-1129) . T)) 
+((-2569 (((-85) $ $) 7 T ELT)) (-2532 (($ $ $) 23 T ELT)) (-2858 (($ $ $) 22 T ELT)) (-3243 (((-1073) $) 11 T ELT)) (-3244 (((-1034) $) 12 T ELT)) (-3946 (((-773) $) 13 T ELT)) (-1265 (((-85) $ $) 6 T ELT)) (-2567 (((-85) $ $) 21 T ELT)) (-2568 (((-85) $ $) 19 T ELT)) (-3057 (((-85) $ $) 8 T ELT)) (-2685 (((-85) $ $) 20 T ELT)) (-2686 (((-85) $ $) 18 T ELT))) 
 (((-757) (-113)) (T -757)) 
 NIL 
-(-13 (-716) (-963) (-665)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-557 (-485)) . T) ((-554 (-774)) . T) ((-13) . T) ((-590 (-485)) . T) ((-590 $) . T) ((-592 $) . T) ((-665) . T) ((-716) . T) ((-718) . T) ((-720) . T) ((-723) . T) ((-758) . T) ((-761) . T) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1130) . T)) 
-((-2570 (((-85) $ $) 7 T ELT)) (-2533 (($ $ $) 23 T ELT)) (-2859 (($ $ $) 22 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1035) $) 12 T ELT)) (-3947 (((-774) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2568 (((-85) $ $) 21 T ELT)) (-2569 (((-85) $ $) 19 T ELT)) (-3058 (((-85) $ $) 8 T ELT)) (-2686 (((-85) $ $) 20 T ELT)) (-2687 (((-85) $ $) 18 T ELT))) 
-(((-758) (-113)) (T -758)) 
-NIL 
-(-13 (-1015) (-761)) 
-(((-72) . T) ((-554 (-774)) . T) ((-13) . T) ((-761) . T) ((-1015) . T) ((-1130) . T)) 
-((-2570 (((-85) $ $) NIL T ELT)) (-2533 (($ $ $) NIL T ELT)) (-2859 (($ $ $) NIL T ELT)) (-3947 (($ |#1|) 10 T ELT) ((|#1| $) 9 T ELT) (((-774) $) 15 (|has| |#1| (-554 (-774))) ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-2568 (((-85) $ $) NIL T ELT)) (-2569 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) NIL T ELT)) (-2686 (((-85) $ $) NIL T ELT)) (-2687 (((-85) $ $) 12 T ELT))) 
-(((-759 |#1| |#2|) (-13 (-761) (-428 |#1|) (-10 -7 (IF (|has| |#1| (-554 (-774))) (-6 (-554 (-774))) |%noBranch|))) (-1130) (-1 (-85) |#1| |#1|)) (T -759)) 
-NIL 
-((-2533 (($ $ $) 16 T ELT)) (-2859 (($ $ $) 15 T ELT)) (-1266 (((-85) $ $) 17 T ELT)) (-2568 (((-85) $ $) 12 T ELT)) (-2569 (((-85) $ $) 9 T ELT)) (-3058 (((-85) $ $) 14 T ELT)) (-2686 (((-85) $ $) 11 T ELT))) 
-(((-760 |#1|) (-10 -7 (-15 -2533 (|#1| |#1| |#1|)) (-15 -2859 (|#1| |#1| |#1|)) (-15 -2568 ((-85) |#1| |#1|)) (-15 -2686 ((-85) |#1| |#1|)) (-15 -2569 ((-85) |#1| |#1|)) (-15 -1266 ((-85) |#1| |#1|)) (-15 -3058 ((-85) |#1| |#1|))) (-761)) (T -760)) 
-NIL 
-((-2570 (((-85) $ $) 7 T ELT)) (-2533 (($ $ $) 10 T ELT)) (-2859 (($ $ $) 11 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2568 (((-85) $ $) 12 T ELT)) (-2569 (((-85) $ $) 14 T ELT)) (-3058 (((-85) $ $) 8 T ELT)) (-2686 (((-85) $ $) 13 T ELT)) (-2687 (((-85) $ $) 15 T ELT))) 
-(((-761) (-113)) (T -761)) 
-((-2687 (*1 *2 *1 *1) (-12 (-4 *1 (-761)) (-5 *2 (-85)))) (-2569 (*1 *2 *1 *1) (-12 (-4 *1 (-761)) (-5 *2 (-85)))) (-2686 (*1 *2 *1 *1) (-12 (-4 *1 (-761)) (-5 *2 (-85)))) (-2568 (*1 *2 *1 *1) (-12 (-4 *1 (-761)) (-5 *2 (-85)))) (-2859 (*1 *1 *1 *1) (-4 *1 (-761))) (-2533 (*1 *1 *1 *1) (-4 *1 (-761)))) 
-(-13 (-72) (-10 -8 (-15 -2687 ((-85) $ $)) (-15 -2569 ((-85) $ $)) (-15 -2686 ((-85) $ $)) (-15 -2568 ((-85) $ $)) (-15 -2859 ($ $ $)) (-15 -2533 ($ $ $)))) 
-(((-72) . T) ((-13) . T) ((-1130) . T)) 
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-NIL 
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-(((-763 |#1|) (-113) (-963)) (T -763)) 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) |has| |#1| (-146)) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-557 (-348 (-485))) |has| |#1| (-952 (-348 (-485)))) ((-557 (-485)) . T) ((-557 |#1|) . T) ((-554 (-774)) . T) ((-353 |#1|) . T) ((-13) . T) ((-590 (-485)) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-592 |#1|) . T) ((-592 $) . T) ((-584 |#1|) |has| |#1| (-146)) ((-656 |#1|) |has| |#1| (-146)) ((-665) . T) ((-952 (-348 (-485))) |has| |#1| (-952 (-348 (-485)))) ((-952 (-485)) |has| |#1| (-952 (-485))) ((-952 |#1|) . T) ((-965 |#1|) . T) ((-970 |#1|) . T) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1130) . T)) 
-((-2546 ((|#2| |#2| |#2| (-69 |#1|) (-1 |#1| |#1|)) 20 T ELT)) (-2551 (((-2 (|:| -1974 |#2|) (|:| -2904 |#2|)) |#2| |#2| (-69 |#1|)) 46 (|has| |#1| (-312)) ELT)) (-2549 (((-2 (|:| -1974 |#2|) (|:| -2904 |#2|)) |#2| |#2| (-69 |#1|)) 43 (|has| |#1| (-496)) ELT)) (-2548 (((-2 (|:| -1974 |#2|) (|:| -2904 |#2|)) |#2| |#2| (-69 |#1|)) 42 (|has| |#1| (-496)) ELT)) (-2550 (((-2 (|:| -1974 |#2|) (|:| -2904 |#2|)) |#2| |#2| (-69 |#1|)) 45 (|has| |#1| (-312)) ELT)) (-2547 ((|#1| |#2| |#1| |#1| (-69 |#1|) (-1 |#1| |#1|)) 33 T ELT))) 
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-((-3534 (*1 *2 *1 *2) (-12 (-5 *2 (-774)) (-5 *1 (-765 *3 *4 *5)) (-4 *3 (-963)) (-14 *4 (-69 *3)) (-14 *5 (-1 *3 *3))))) 
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-NIL 
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-((-2554 (*1 *2 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-38 (-348 (-485)))) (-4 *2 (-146)))) (-2553 (*1 *2 *3 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-146)))) (-2553 (*1 *2 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-146)))) (-2552 (*1 *2 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-146)))) (-2802 (*1 *2 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-146)))) (-2801 (*1 *2 *3 *2) (-12 (-5 *3 (-696)) (-5 *1 (-767 *2)) (-4 *2 (-146))))) 
-((-2570 (((-85) $ $) 7 T ELT)) (-2533 (($ $ $) 23 T ELT)) (-2859 (($ $ $) 22 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1035) $) 12 T ELT)) (-3947 (((-774) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2568 (((-85) $ $) 21 T ELT)) (-2569 (((-85) $ $) 19 T ELT)) (-3058 (((-85) $ $) 8 T ELT)) (-2686 (((-85) $ $) 20 T ELT)) (-2687 (((-85) $ $) 18 T ELT)) (** (($ $ (-832)) 26 T ELT)) (* (($ $ $) 25 T ELT))) 
-(((-768) (-113)) (T -768)) 
-NIL 
-(-13 (-758) (-1027)) 
-(((-72) . T) ((-554 (-774)) . T) ((-13) . T) ((-758) . T) ((-761) . T) ((-1027) . T) ((-1015) . T) ((-1130) . T)) 
-((-2570 (((-85) $ $) NIL T ELT)) (-3403 (((-485) $) 14 T ELT)) (-2533 (($ $ $) NIL T ELT)) (-2859 (($ $ $) NIL T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3245 (((-1035) $) NIL T ELT)) (-3947 (((-774) $) 20 T ELT) (($ (-485)) 13 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-2568 (((-85) $ $) NIL T ELT)) (-2569 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) 10 T ELT)) (-2686 (((-85) $ $) NIL T ELT)) (-2687 (((-85) $ $) 12 T ELT))) 
-(((-769) (-13 (-758) (-10 -8 (-15 -3947 ($ (-485))) (-15 -3403 ((-485) $))))) (T -769)) 
-((-3947 (*1 *1 *2) (-12 (-5 *2 (-485)) (-5 *1 (-769)))) (-3403 (*1 *2 *1) (-12 (-5 *2 (-485)) (-5 *1 (-769))))) 
-((-2555 (((-1186) (-585 (-51))) 23 T ELT)) (-3461 (((-1186) (-1074) (-774)) 13 T ELT) (((-1186) (-774)) 8 T ELT) (((-1186) (-1074)) 10 T ELT))) 
-(((-770) (-10 -7 (-15 -3461 ((-1186) (-1074))) (-15 -3461 ((-1186) (-774))) (-15 -3461 ((-1186) (-1074) (-774))) (-15 -2555 ((-1186) (-585 (-51)))))) (T -770)) 
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-((-2557 (((-634 (-1139)) $ (-1139)) 15 T ELT)) (-2558 (((-634 (-489)) $ (-489)) 12 T ELT)) (-2556 (((-696) $ (-102)) 30 T ELT))) 
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-NIL 
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-(((-772) (-113)) (T -772)) 
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+(-13 (-1014) (-760)) 
+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-760) . T) ((-1014) . T) ((-1129) . T)) 
+((-2569 (((-85) $ $) NIL T ELT)) (-2532 (($ $ $) NIL T ELT)) (-2858 (($ $ $) NIL T ELT)) (-3946 (($ |#1|) 10 T ELT) ((|#1| $) 9 T ELT) (((-773) $) 15 (|has| |#1| (-553 (-773))) ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-2567 (((-85) $ $) NIL T ELT)) (-2568 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) NIL T ELT)) (-2685 (((-85) $ $) NIL T ELT)) (-2686 (((-85) $ $) 12 T ELT))) 
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+NIL 
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+NIL 
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+(((-760) (-113)) (T -760)) 
+((-2686 (*1 *2 *1 *1) (-12 (-4 *1 (-760)) (-5 *2 (-85)))) (-2568 (*1 *2 *1 *1) (-12 (-4 *1 (-760)) (-5 *2 (-85)))) (-2685 (*1 *2 *1 *1) (-12 (-4 *1 (-760)) (-5 *2 (-85)))) (-2567 (*1 *2 *1 *1) (-12 (-4 *1 (-760)) (-5 *2 (-85)))) (-2858 (*1 *1 *1 *1) (-4 *1 (-760))) (-2532 (*1 *1 *1 *1) (-4 *1 (-760)))) 
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+(((-72) . T) ((-13) . T) ((-1129) . T)) 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) |has| |#1| (-146)) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-556 (-348 (-484))) |has| |#1| (-951 (-348 (-484)))) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-353 |#1|) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) |has| |#1| (-146)) ((-655 |#1|) |has| |#1| (-146)) ((-664) . T) ((-951 (-348 (-484))) |has| |#1| (-951 (-348 (-484)))) ((-951 (-484)) |has| |#1| (-951 (-484))) ((-951 |#1|) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1061) . T) ((-1014) . T) ((-1129) . T)) 
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+(((-764 |#1| |#2| |#3|) (-13 (-762 |#1|) (-10 -8 (-15 -3533 ((-773) $ (-773))))) (-962) (-69 |#1|) (-1 |#1| |#1|)) (T -764)) 
+((-3533 (*1 *2 *1 *2) (-12 (-5 *2 (-773)) (-5 *1 (-764 *3 *4 *5)) (-4 *3 (-962)) (-14 *4 (-69 *3)) (-14 *5 (-1 *3 *3))))) 
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+NIL 
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 (((-147) . T)) 
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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 
-(((-1130) (-113)) (T -1130)) 
+(((-64) . T) ((-72) . T) ((-556 (-1095)) . T) ((-553 (-773)) . T) ((-553 (-1095)) . T) ((-428 (-1095)) . T) ((-13) . T) ((-1014) . T) ((-1129) . T)) 
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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 T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) 58 T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) 60 T ELT)) (-3957 (((-695) $) NIL (|has| $ (-6 -3995)) ELT))) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-485)) . T) ((-25) . T) ((-38 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-348 (-485)))) ((-66) |has| |#1| (-38 (-348 (-485)))) ((-72) . T) ((-82 (-348 (-485)) (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-557 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-557 (-485)) . T) ((-557 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-952 (-1091)))) ((-557 |#1|) |has| |#1| (-146)) ((-557 |#2|) . 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T) ((-146) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-555 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-935))) ((-555 (-328)) -12 (|has| |#1| (-312)) (|has| |#2| (-935))) ((-555 (-474)) -12 (|has| |#1| (-312)) (|has| |#2| (-555 (-474)))) ((-555 (-802 (-328))) -12 (|has| |#1| (-312)) (|has| |#2| (-555 (-802 (-328))))) ((-555 (-802 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-555 (-802 (-485))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-312)) ((-190) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-312)) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-348 (-485)))) ((-241 (-485) |#1|) . T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-485) (-1027)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-327 |#2|) |has| |#1| (-312)) ((-341 |#2|) |has| |#1| (-312)) ((-390) |has| |#1| (-312)) ((-431) |has| |#1| (-38 (-348 (-485)))) ((-454 (-1091) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-454 (-1091) |#2|))) ((-454 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-13) . T) ((-590 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-590 (-485)) . T) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-592 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-592 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-582 (-485)))) ((-592 |#1|) . T) ((-592 |#2|) |has| |#1| (-312)) ((-592 $) . T) ((-584 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-584 |#1|) |has| |#1| (-146)) ((-584 |#2|) |has| |#1| (-312)) ((-584 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-582 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-582 (-485)))) ((-582 |#2|) |has| |#1| (-312)) ((-656 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-656 |#1|) |has| |#1| (-146)) ((-656 |#2|) |has| |#1| (-312)) ((-656 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-665) . T) ((-716) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-718) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-720) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-723) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-742) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-757) -12 (|has| |#1| (-312)) (|has| |#2| (-742))) ((-758) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-758))) (-12 (|has| |#1| (-312)) (|has| |#2| (-742)))) ((-761) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-758))) (-12 (|has| |#1| (-312)) (|has| |#2| (-742)))) ((-808 $ (-1091)) OR (-12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-813 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1091))))) ((-811 (-1091)) OR (-12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1091))))) ((-813 (-1091)) OR (-12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-813 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1091))))) ((-798 (-328)) -12 (|has| |#1| (-312)) (|has| |#2| (-798 (-328)))) ((-798 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-798 (-485)))) ((-796 |#2|) |has| |#1| (-312)) ((-823) -12 (|has| |#1| (-312)) (|has| |#2| (-823))) ((-888 |#1| (-485) (-996)) . T) ((-834) |has| |#1| (-312)) ((-906 |#2|) |has| |#1| (-312)) ((-917) |has| |#1| (-38 (-348 (-485)))) ((-935) -12 (|has| |#1| (-312)) (|has| |#2| (-935))) ((-952 (-348 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-952 (-485)))) ((-952 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-952 (-485)))) ((-952 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-952 (-1091)))) ((-952 |#2|) . T) ((-965 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-965 |#1|) . T) ((-965 |#2|) |has| |#1| (-312)) ((-965 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-970 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-970 |#1|) . T) ((-970 |#2|) |has| |#1| (-312)) ((-970 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1067) -12 (|has| |#1| (-312)) (|has| |#2| (-1067))) ((-1116) |has| |#1| (-38 (-348 (-485)))) ((-1119) |has| |#1| (-38 (-348 (-485)))) ((-1130) . T) ((-1135) |has| |#1| (-312)) ((-1142 |#1|) . T) ((-1159 |#1| (-485)) . T)) 
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-((-3959 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) 
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-NIL 
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-((-3819 (*1 *1 *2) (-12 (-5 *2 (-1070 (-2 (|:| |k| (-696)) (|:| |c| *3)))) (-4 *3 (-963)) (-4 *1 (-1173 *3)))) (-3818 (*1 *2 *1) (-12 (-4 *1 (-1173 *3)) (-4 *3 (-963)) (-5 *2 (-1070 *3)))) (-3819 (*1 *1 *2) (-12 (-5 *2 (-1070 *3)) (-4 *3 (-963)) (-4 *1 (-1173 *3)))) (-3817 (*1 *1 *1) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-963)))) (-3816 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-485))) (-4 *1 (-1173 *3)) (-4 *3 (-963)))) (-3815 (*1 *2 *1 *3) (-12 (-5 *3 (-696)) (-4 *1 (-1173 *4)) (-4 *4 (-963)) (-5 *2 (-859 *4)))) (-3815 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-696)) (-4 *1 (-1173 *4)) (-4 *4 (-963)) (-5 *2 (-859 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-963)) (-4 *2 (-312)))) (-3813 (*1 *1 *1) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-963)) (-4 *2 (-38 (-348 (-485)))))) (-3813 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-963)) (-12 (-4 *3 (-29 (-485))) (-4 *3 (-873)) (-4 *3 (-1116)) (-4 *3 (-38 (-348 (-485)))))) (-12 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-963)) (-12 (|has| *3 (-15 -3083 ((-585 *2) *3))) (|has| *3 (-15 -3813 (*3 *3 *2))) (-4 *3 (-38 (-348 (-485))))))))) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-696)) . T) ((-25) . T) ((-38 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-496)) ((-35) |has| |#1| (-38 (-348 (-485)))) ((-66) |has| |#1| (-38 (-348 (-485)))) ((-72) . T) ((-82 (-348 (-485)) (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-557 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-557 (-485)) . T) ((-557 |#1|) |has| |#1| (-146)) ((-557 $) |has| |#1| (-496)) ((-554 (-774)) . T) ((-146) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-696) |#1|))) ((-239) |has| |#1| (-38 (-348 (-485)))) ((-241 (-696) |#1|) . T) ((-241 $ $) |has| (-696) (-1027)) ((-246) |has| |#1| (-496)) ((-431) |has| |#1| (-38 (-348 (-485)))) ((-496) |has| |#1| (-496)) ((-13) . T) ((-590 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-590 (-485)) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-592 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-592 |#1|) . T) ((-592 $) . T) ((-584 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-584 |#1|) |has| |#1| (-146)) ((-584 $) |has| |#1| (-496)) ((-656 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-656 |#1|) |has| |#1| (-146)) ((-656 $) |has| |#1| (-496)) ((-665) . T) ((-808 $ (-1091)) -12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-811 (-1091)) -12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-813 (-1091)) -12 (|has| |#1| (-811 (-1091))) (|has| |#1| (-15 * (|#1| (-696) |#1|)))) ((-888 |#1| (-696) (-996)) . T) ((-917) |has| |#1| (-38 (-348 (-485)))) ((-965 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-965 |#1|) . T) ((-965 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-970 (-348 (-485))) |has| |#1| (-38 (-348 (-485)))) ((-970 |#1|) . T) ((-970 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-963) . T) ((-972) . T) ((-1027) . T) ((-1062) . T) ((-1015) . T) ((-1116) |has| |#1| (-38 (-348 (-485)))) ((-1119) |has| |#1| (-38 (-348 (-485)))) ((-1130) . T) ((-1159 |#1| (-696)) . T)) 
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-NIL 
-(((-1176) (-113)) (T -1176)) 
-NIL 
-(-13 (-10 -7 (-6 -2289))) 
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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 
-NIL 
-((-3 2820661 2820666 2820671 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2820646 2820651 2820656 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2820631 2820636 2820641 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2820616 2820621 2820626 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1210 2819595 2820534 2820611 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1209 2818810 2818989 2819208 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1208 2809969 2811838 2813772 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2809357 2809510 2809699 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2808819 2809122 2809235 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2806379 2808281 2808484 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2803143 2804796 2805367 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2800400 2802130 2802184 "XPOLYC" 2802469 XPOLYC (NIL T T) -9 NIL 2802582 NIL) (-1202 2797919 2799904 2800107 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2794167 2796778 2797166 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2789014 2790647 2790701 "XFALG" 2792846 XFALG (NIL T T) -9 NIL 2793630 NIL) (-1199 2784170 2786903 2786945 "XF" 2787563 XF (NIL T) -9 NIL 2787959 NIL) (-1198 2783888 2783998 2784165 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2783115 2783237 2783441 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2780857 2783015 2783110 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2779438 2780233 2780275 "XALG" 2780280 XALG (NIL T) -9 NIL 2780389 NIL) (-1194 2772995 2777848 2778326 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2771238 2772240 2772561 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2770837 2771109 2771178 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2770324 2770627 2770720 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2769401 2769611 2769906 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2767697 2768160 2768622 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2766586 2767171 2767213 "VSPACE" 2767349 VSPACE (NIL T) -9 NIL 2767423 NIL) (-1187 2766457 2766490 2766581 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2766300 2766354 2766422 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2763283 2764078 2764815 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2754381 2756982 2759155 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2747958 2749849 2751428 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2746442 2746837 2747243 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2745269 2745550 2745866 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2740383 2745096 2745188 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2733485 2738093 2738136 "VECTCAT" 2739124 VECTCAT (NIL T) -9 NIL 2739708 NIL) (-1178 2732764 2733090 2733480 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2732258 2732500 2732620 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2732191 2732196 2732226 "UTYPE" 2732231 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2731178 2731354 2731615 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2729029 2729537 2730061 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2718911 2724881 2724923 "UTSCAT" 2726021 UTSCAT (NIL T) -9 NIL 2726778 NIL) (-1172 2716976 2717919 2718906 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2716650 2716699 2716830 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2708361 2714846 2715325 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2702356 2705169 2705212 "URAGG" 2707282 URAGG (NIL T) -9 NIL 2708004 NIL) (-1168 2700371 2701333 2702351 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2696078 2699347 2699809 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2688507 2696002 2696073 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2677158 2684645 2684706 "UPXSCCA" 2685274 UPXSCCA (NIL T T) -9 NIL 2685506 NIL) (-1164 2676879 2676981 2677153 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2665431 2672643 2672685 "UPXSCAT" 2673325 UPXSCAT (NIL T) -9 NIL 2673933 NIL) (-1162 2664944 2665029 2665206 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2656630 2664535 2664797 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2655525 2655795 2656145 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2648228 2651713 2651767 "UPSCAT" 2652836 UPSCAT (NIL T T) -9 NIL 2653600 NIL) (-1158 2647648 2647900 2648223 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2647322 2647371 2647502 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2631452 2640406 2640448 "UPOLYC" 2642526 UPOLYC (NIL T) -9 NIL 2643746 NIL) (-1155 2625507 2628355 2631447 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2624943 2625068 2625231 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2624577 2624664 2624803 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2623390 2623657 2623961 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2622723 2622853 2623038 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2622315 2622390 2622537 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2613079 2622081 2622209 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2612441 2612578 2612783 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2611042 2611889 2612165 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2610271 2610468 2610693 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2597081 2610195 2610266 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2576933 2590168 2590229 "ULSCCAT" 2590860 ULSCCAT (NIL T T) -9 NIL 2591147 NIL) (-1143 2576268 2576554 2576928 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2564640 2571774 2571816 "ULSCAT" 2572669 ULSCAT (NIL T) -9 NIL 2573399 NIL) (-1141 2564153 2564238 2564415 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2546270 2563652 2563893 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2545304 2545997 2546111 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2546222) (-1138 2544337 2545030 2545144 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2545255) (-1137 2543370 2544063 2544177 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2544288) (-1136 2542403 2543096 2543210 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2543321) (-1135 2540410 2541631 2541661 "UFD" 2541872 UFD (NIL) -9 NIL 2541985 NIL) (-1134 2540254 2540311 2540405 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2539506 2539713 2539929 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2537726 2538179 2538644 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2537451 2537691 2537721 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2537389 2537394 2537424 "TYPE" 2537429 TYPE (NIL) -9 NIL 2537436 NIL) (-1129 2536548 2536768 2537008 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2535726 2536157 2536392 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2533880 2534453 2534992 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2532914 2533150 2533386 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2521268 2525736 2525832 "TSETCAT" 2531047 TSETCAT (NIL T T T T) -9 NIL 2532559 NIL) (-1124 2517605 2519421 2521263 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2511997 2516831 2517113 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2507334 2508347 2509276 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2506831 2506906 2507069 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2504907 2505197 2505552 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2504391 2504540 2504570 "TRIGCAT" 2504783 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2504142 2504245 2504386 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2501138 2503251 2503529 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2500244 2500940 2500970 "TRANFUN" 2501005 TRANFUN (NIL) -9 NIL 2501071 NIL) (-1115 2499708 2499959 2500239 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2499545 2499583 2499644 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2499002 2499133 2499284 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2497743 2498400 2498636 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2497555 2497592 2497664 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2495769 2496415 2496844 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2494149 2494486 2494808 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2485207 2491950 2492006 "TBAGG" 2492408 TBAGG (NIL T T) -9 NIL 2492621 NIL) (-1107 2481738 2483430 2485202 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2481215 2481340 2481485 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2480725 2481045 2481135 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2480222 2480339 2480477 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2473309 2480124 2480217 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2469062 2470357 2471602 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2468431 2468590 2468771 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2465585 2466338 2467121 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2465359 2465549 2465580 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2464313 2464998 2465124 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2465310) (-1097 2463577 2464125 2464204 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2464264) (-1096 2460400 2461559 2462259 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2458083 2458766 2459400 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2454161 2455207 2456184 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2451260 2453816 2454045 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2450856 2450943 2451065 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2447480 2448954 2449773 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2440440 2446677 2446970 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2432126 2440031 2440293 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2431405 2431544 2431761 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2431089 2431154 2431265 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2421812 2430801 2430926 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2420542 2420840 2421195 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2419947 2420025 2420216 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2402099 2419446 2419687 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2401698 2401970 2402039 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2401034 2401315 2401455 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2395636 2396895 2397848 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2395168 2395268 2395432 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2390279 2391561 2392708 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2384737 2386208 2387519 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2377652 2379716 2381507 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2370482 2377564 2377647 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2365176 2370196 2370311 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2364763 2364846 2364990 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2363914 2364115 2364350 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2363654 2363712 2363805 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2356392 2361859 2362465 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2355568 2355773 2356004 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2354813 2355184 2355331 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2354301 2354543 2354573 "STEP" 2354667 STEP (NIL) -9 NIL 2354738 NIL) (-1066 2347404 2354219 2354296 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2341619 2346202 2346245 "STAGG" 2346672 STAGG (NIL T) -9 NIL 2346846 NIL) (-1064 2339998 2340746 2341614 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2338155 2339825 2339917 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2337435 2337974 2338004 "SRING" 2338009 SRING (NIL) -9 NIL 2338029 NIL) (-1061 2330057 2335973 2336412 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2323831 2325270 2326774 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2316256 2321167 2321197 "SRAGG" 2322496 SRAGG (NIL) -9 NIL 2323100 NIL) (-1058 2315553 2315873 2316251 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2309608 2314875 2315298 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2303821 2306990 2307712 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2300250 2301069 2301706 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2299225 2299530 2299560 "SPFCAT" 2300004 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2298162 2298414 2298678 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2288920 2291194 2291224 "SPADXPT" 2295861 SPADXPT (NIL) -9 NIL 2297985 NIL) (-1051 2288722 2288768 2288837 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2286378 2288686 2288717 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2278052 2280141 2280183 "SPACEC" 2284498 SPACEC (NIL T) -9 NIL 2286303 NIL) (-1048 2275881 2277999 2278047 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2274814 2275003 2275292 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2273218 2273551 2273962 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2272483 2272717 2272978 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2268663 2269623 2270618 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2265021 2265720 2266449 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2258807 2264361 2264457 "SNTSCAT" 2264462 SNTSCAT (NIL T T T T) -9 NIL 2264532 NIL) (-1041 2252628 2257448 2257838 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2246400 2252547 2252623 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2244832 2245163 2245561 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2236437 2241416 2241518 "SMATCAT" 2242861 SMATCAT (NIL NIL T T T) -9 NIL 2243409 NIL) (-1037 2234278 2235262 2236432 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2231870 2233484 2233527 "SKAGG" 2233788 SKAGG (NIL T) -9 NIL 2233922 NIL) (-1035 2227916 2231690 2231801 "SINT" NIL SINT (NIL) -8 NIL NIL 2231842) (-1034 2227726 2227770 2227836 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1033 2226801 2227033 2227301 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1032 2225805 2225967 2226243 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1031 2225151 2225491 2225614 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1030 2224497 2224804 2224944 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1029 2222608 2223100 2223606 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1028 2216048 2222527 2222603 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1027 2215551 2215788 2215818 "SGROUP" 2215911 SGROUP (NIL) -9 NIL 2215973 NIL) (-1026 2215441 2215473 2215546 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1025 2215079 2215119 2215160 "SGPOPC" 2215165 SGPOPC (NIL T) -9 NIL 2215366 NIL) (-1024 2214613 2214890 2214996 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1023 2212036 2212805 2213527 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1022 2205921 2211475 2211571 "SFRTCAT" 2211576 SFRTCAT (NIL T T T T) -9 NIL 2211614 NIL) (-1021 2200313 2201426 2202553 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1020 2194489 2195650 2196814 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2193461 2194363 2194484 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1018 2189069 2189964 2190059 "SEXCAT" 2192672 SEXCAT (NIL T T T T T) -9 NIL 2193223 NIL) (-1017 2188042 2188996 2189064 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1016 2186433 2187018 2187320 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1015 2185956 2186141 2186171 "SETCAT" 2186288 SETCAT (NIL) -9 NIL 2186372 NIL) (-1014 2185788 2185852 2185951 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1013 2182011 2184242 2184285 "SETAGG" 2185153 SETAGG (NIL T) -9 NIL 2185491 NIL) (-1012 2181617 2181769 2182006 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1011 2178571 2181564 2181612 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1010 2178037 2178347 2178447 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1009 2177164 2177530 2177591 "SEGXCAT" 2177877 SEGXCAT (NIL T T) -9 NIL 2177997 NIL) (-1008 2176089 2176357 2176400 "SEGCAT" 2176922 SEGCAT (NIL T) -9 NIL 2177143 NIL) (-1007 2175769 2175834 2175947 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1006 2174835 2175305 2175513 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1005 2174413 2174692 2174768 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1004 2173778 2173914 2174118 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1003 2172844 2173591 2173773 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1002 2172097 2172792 2172839 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1001 2163582 2171964 2172092 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1000 2162436 2162726 2163045 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-999 2161742 2161954 2162142 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-998 2161092 2161249 2161425 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-997 2160665 2160896 2160924 "SASTCAT" 2160929 SASTCAT (NIL) -9 NIL 2160942 NIL) (-996 2160132 2160557 2160631 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-995 2159735 2159776 2159947 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-994 2159366 2159407 2159564 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-993 2152447 2159283 2159361 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-992 2151097 2151426 2151822 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-991 2149858 2150219 2150519 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-990 2149482 2149703 2149784 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-989 2146942 2147576 2148029 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-988 2146781 2146814 2146882 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-987 2146272 2146575 2146666 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-986 2141900 2142768 2143679 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-985 2130719 2136273 2136367 "RSETCAT" 2140423 RSETCAT (NIL T T T T) -9 NIL 2141511 NIL) (-984 2129257 2129899 2130714 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-983 2123031 2124476 2125983 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-982 2120913 2121470 2121542 "RRCC" 2122615 RRCC (NIL T T) -9 NIL 2122956 NIL) (-981 2120438 2120637 2120908 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-980 2119908 2120218 2120316 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-979 2092460 2103173 2103237 "RPOLCAT" 2113711 RPOLCAT (NIL T T T) -9 NIL 2116856 NIL) (-978 2086559 2089382 2092455 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-977 2082726 2086307 2086445 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-976 2081054 2081793 2082049 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-975 2076697 2079509 2079537 "RNS" 2079799 RNS (NIL) -9 NIL 2080051 NIL) (-974 2075600 2076087 2076624 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-973 2074718 2075119 2075319 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-972 2073856 2074418 2074446 "RNG" 2074506 RNG (NIL) -9 NIL 2074560 NIL) (-971 2073745 2073779 2073851 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-970 2073007 2073512 2073552 "RMODULE" 2073557 RMODULE (NIL T) -9 NIL 2073583 NIL) (-969 2071946 2072052 2072382 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-968 2068792 2071536 2071829 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-967 2061441 2063933 2064045 "RMATCAT" 2067350 RMATCAT (NIL NIL NIL T T T) -9 NIL 2068327 NIL) (-966 2060958 2061137 2061436 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-965 2060526 2060737 2060778 "RLINSET" 2060839 RLINSET (NIL T) -9 NIL 2060883 NIL) (-964 2060171 2060252 2060378 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-963 2059017 2059748 2059776 "RING" 2059831 RING (NIL) -9 NIL 2059923 NIL) (-962 2058862 2058918 2059012 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-961 2057916 2058183 2058439 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-960 2048903 2057544 2057745 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-959 2048128 2048639 2048678 "RGBCSPC" 2048735 RGBCSPC (NIL T) -9 NIL 2048786 NIL) (-958 2047162 2047648 2047687 "RGBCMDL" 2047915 RGBCMDL (NIL T) -9 NIL 2048029 NIL) (-957 2046874 2046943 2047044 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-956 2046637 2046678 2046773 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-955 2045061 2045491 2045871 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-954 2042648 2043316 2043984 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-953 2042198 2042296 2042456 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-952 2041820 2041918 2041959 "RETRACT" 2042090 RETRACT (NIL T) -9 NIL 2042177 NIL) (-951 2041700 2041731 2041815 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-950 2041302 2041574 2041641 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-949 2039782 2040673 2040870 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-948 2039473 2039534 2039630 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-947 2039216 2039257 2039362 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-946 2038951 2038992 2039101 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-945 2034022 2035473 2036688 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-944 2031121 2031879 2032687 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-943 2029090 2029712 2030312 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-942 2021725 2027641 2028077 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-941 2021037 2021317 2021466 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-940 2020522 2020637 2020802 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-939 2016115 2019925 2020146 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-938 2015347 2015546 2015759 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-937 2012637 2013475 2014357 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-936 2009219 2010255 2011314 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-935 2009055 2009108 2009136 "REAL" 2009141 REAL (NIL) -9 NIL 2009176 NIL) (-934 2008545 2008849 2008940 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-933 2008025 2008103 2008308 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-932 2007258 2007450 2007661 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-931 2006146 2006443 2006810 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-930 2004413 2004883 2005416 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-929 2003335 2003612 2003999 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-928 2002162 2002471 2002890 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-927 1995510 1999022 1999050 "RCFIELD" 2000327 RCFIELD (NIL) -9 NIL 2001057 NIL) (-926 1994128 1994740 1995437 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-925 1990328 1992220 1992261 "RCAGG" 1993328 RCAGG (NIL T) -9 NIL 1993789 NIL) (-924 1990055 1990165 1990323 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-923 1989500 1989629 1989790 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-922 1989117 1989196 1989315 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-921 1988532 1988682 1988832 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-920 1988314 1988364 1988435 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-919 1980756 1987432 1987740 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-918 1970458 1980623 1980751 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-917 1970092 1970185 1970213 "RADCAT" 1970370 RADCAT (NIL) -9 NIL NIL NIL) (-916 1969930 1969990 1970087 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-915 1968030 1969761 1969850 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-914 1967711 1967760 1967887 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-913 1959998 1964082 1964122 "QUATCAT" 1964900 QUATCAT (NIL T) -9 NIL 1965664 NIL) (-912 1957248 1958528 1959904 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-911 1953088 1957198 1957243 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-910 1950475 1952142 1952183 "QUAGG" 1952558 QUAGG (NIL T) -9 NIL 1952732 NIL) (-909 1950077 1950349 1950416 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-908 1949083 1949713 1949876 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-907 1948764 1948813 1948940 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-906 1938389 1944558 1944598 "QFCAT" 1945256 QFCAT (NIL T) -9 NIL 1946249 NIL) (-905 1935273 1936712 1938295 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-904 1934819 1934953 1935083 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-903 1929015 1930176 1931338 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-902 1928434 1928614 1928846 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-901 1926256 1926784 1927207 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-900 1925155 1925397 1925714 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-899 1923516 1923714 1924067 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-898 1919272 1920488 1920529 "PTRANFN" 1922413 PTRANFN (NIL T) -9 NIL NIL NIL) (-897 1917919 1918264 1918585 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-896 1917612 1917675 1917782 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-895 1911685 1916408 1916448 "PTCAT" 1916740 PTCAT (NIL T) -9 NIL 1916893 NIL) (-894 1911378 1911419 1911543 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-893 1910257 1910573 1910907 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-892 1899136 1901697 1904006 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-891 1892043 1894939 1895033 "PSETCAT" 1898007 PSETCAT (NIL T T T T) -9 NIL 1898814 NIL) (-890 1890493 1891227 1892038 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-889 1889812 1890007 1890035 "PSCURVE" 1890303 PSCURVE (NIL) -9 NIL 1890470 NIL) (-888 1885414 1887234 1887298 "PSCAT" 1888133 PSCAT (NIL T T T) -9 NIL 1888372 NIL) (-887 1884728 1885010 1885409 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-886 1883125 1884040 1884303 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-885 1882616 1882919 1883010 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-884 1873636 1876058 1878246 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-883 1871379 1872956 1872996 "PRQAGG" 1873179 PRQAGG (NIL T) -9 NIL 1873280 NIL) (-882 1870552 1870998 1871026 "PROPLOG" 1871165 PROPLOG (NIL) -9 NIL 1871279 NIL) (-881 1870227 1870290 1870413 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-880 1869663 1869802 1869974 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-879 1867911 1868674 1868971 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-878 1867463 1867595 1867723 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-877 1861904 1866403 1867223 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-876 1861733 1861771 1861830 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-875 1861172 1861312 1861463 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-874 1859640 1860059 1860525 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-873 1859357 1859418 1859446 "PRIMCAT" 1859570 PRIMCAT (NIL) -9 NIL NIL NIL) (-872 1858528 1858724 1858952 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-871 1854406 1858478 1858523 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-870 1854105 1854167 1854278 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-869 1851241 1853754 1853987 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-868 1850692 1850849 1850877 "PPCURVE" 1851082 PPCURVE (NIL) -9 NIL 1851218 NIL) (-867 1850305 1850550 1850633 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-866 1848061 1848482 1849074 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-865 1847504 1847568 1847801 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-864 1844224 1844710 1845321 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-863 1829815 1835944 1836008 "POLYCAT" 1839493 POLYCAT (NIL T T T) -9 NIL 1841370 NIL) (-862 1825325 1827472 1829810 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-861 1824982 1825056 1825175 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-860 1824675 1824738 1824845 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-859 1818038 1824408 1824567 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-858 1816925 1817188 1817464 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-857 1815529 1815842 1816172 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-856 1810691 1815479 1815524 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-855 1809179 1809590 1809965 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-854 1807936 1808245 1808641 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-853 1807607 1807691 1807808 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-852 1807186 1807261 1807435 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-851 1806672 1806768 1806928 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-850 1806144 1806264 1806418 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-849 1805039 1805257 1805634 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-848 1804650 1804735 1804887 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-847 1804201 1804283 1804464 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-846 1803893 1803974 1804087 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-845 1803406 1803481 1803689 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-844 1802754 1802882 1803084 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-843 1802116 1802250 1802413 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-842 1801420 1801602 1801783 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-841 1801143 1801217 1801311 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-840 1797711 1798900 1799816 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-839 1796795 1796996 1797231 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-838 1792360 1793744 1794886 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-837 1772281 1777168 1782015 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-836 1772021 1772074 1772177 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-835 1771462 1771596 1771776 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-834 1769471 1770692 1770720 "PID" 1770917 PID (NIL) -9 NIL 1771044 NIL) (-833 1769259 1769302 1769377 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-832 1768446 1769106 1769193 "PI" NIL PI (NIL) -8 NIL NIL 1769233) (-831 1767898 1768049 1768225 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-830 1764226 1765184 1766089 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-829 1762590 1762879 1763245 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-828 1762032 1762147 1762308 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-827 1758573 1760901 1761254 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-826 1757179 1757459 1757784 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-825 1755944 1756198 1756546 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-824 1754654 1754881 1755233 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-823 1751664 1753224 1753252 "PFECAT" 1753845 PFECAT (NIL) -9 NIL 1754222 NIL) (-822 1751287 1751452 1751659 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-821 1750111 1750393 1750694 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-820 1748293 1748680 1749110 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-819 1744263 1748219 1748288 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-818 1740166 1741313 1742180 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-817 1738098 1739187 1739228 "PERMCAT" 1739627 PERMCAT (NIL T) -9 NIL 1739924 NIL) (-816 1737794 1737841 1737964 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-815 1734243 1735924 1736569 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-814 1731708 1733998 1734119 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-813 1730577 1730840 1730881 "PDSPC" 1731414 PDSPC (NIL T) -9 NIL 1731659 NIL) (-812 1729944 1730210 1730572 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-811 1728579 1729572 1729613 "PDRING" 1729618 PDRING (NIL T) -9 NIL 1729645 NIL) (-810 1727289 1728078 1728131 "PDMOD" 1728136 PDMOD (NIL T T) -9 NIL 1728239 NIL) (-809 1726382 1726594 1726843 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-808 1725987 1726054 1726108 "PDDOM" 1726273 PDDOM (NIL T T) -9 NIL 1726353 NIL) (-807 1725839 1725875 1725982 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-806 1725625 1725664 1725753 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-805 1723942 1724696 1724995 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-804 1723631 1723694 1723803 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-803 1721769 1722199 1722650 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-802 1715389 1717218 1718510 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-801 1715020 1715093 1715225 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-800 1712722 1713402 1713883 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-799 1710926 1711354 1711757 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-798 1710372 1710620 1710661 "PATMAB" 1710768 PATMAB (NIL T) -9 NIL 1710851 NIL) (-797 1709019 1709423 1709680 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-796 1708557 1708688 1708729 "PATAB" 1708734 PATAB (NIL T) -9 NIL 1708906 NIL) (-795 1707100 1707537 1707960 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-794 1706778 1706853 1706955 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-793 1706467 1706530 1706639 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-792 1706272 1706318 1706385 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-791 1705950 1706025 1706127 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-790 1705639 1705702 1705811 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-789 1705330 1705400 1705497 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-788 1705019 1705082 1705191 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-787 1704180 1704559 1704738 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-786 1703787 1703885 1704004 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-785 1702755 1703180 1703399 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-784 1701420 1702074 1702434 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-783 1694510 1700824 1701018 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-782 1686931 1694008 1694192 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-781 1683656 1685571 1685611 "PADICCT" 1686192 PADICCT (NIL NIL) -9 NIL 1686474 NIL) (-780 1681646 1683606 1683651 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-779 1680808 1681018 1681284 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-778 1680150 1680293 1680497 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-777 1678531 1679558 1679836 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-776 1678055 1678314 1678411 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-775 1677114 1677792 1677964 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-774 1667536 1670405 1672604 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-773 1666928 1667242 1667368 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-772 1666205 1666400 1666428 "OUTBCON" 1666746 OUTBCON (NIL) -9 NIL 1666912 NIL) (-771 1665913 1666043 1666200 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-770 1665294 1665439 1665600 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-769 1664665 1665092 1665181 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-768 1664080 1664495 1664523 "OSGROUP" 1664528 OSGROUP (NIL) -9 NIL 1664550 NIL) (-767 1663044 1663305 1663590 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-766 1660313 1662919 1663039 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-765 1657454 1660064 1660190 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-764 1655472 1656000 1656560 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-763 1648814 1651354 1651394 "OREPCAT" 1653715 OREPCAT (NIL T) -9 NIL 1654817 NIL) (-762 1646840 1647774 1648809 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-761 1646037 1646308 1646336 "ORDTYPE" 1646641 ORDTYPE (NIL) -9 NIL 1646799 NIL) (-760 1645571 1645782 1646032 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-759 1645033 1645409 1645566 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-758 1644527 1644890 1644918 "ORDSET" 1644923 ORDSET (NIL) -9 NIL 1644945 NIL) (-757 1643105 1644127 1644155 "ORDRING" 1644160 ORDRING (NIL) -9 NIL 1644188 NIL) (-756 1642353 1642910 1642938 "ORDMON" 1642943 ORDMON (NIL) -9 NIL 1642964 NIL) (-755 1641657 1641819 1642011 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-754 1640868 1641376 1641404 "ORDFIN" 1641469 ORDFIN (NIL) -9 NIL 1641543 NIL) (-753 1640262 1640401 1640587 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-752 1636937 1639230 1639636 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-751 1636344 1636699 1636804 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-750 1636152 1636197 1636263 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-749 1635453 1635729 1635770 "OPERCAT" 1635981 OPERCAT (NIL T) -9 NIL 1636077 NIL) (-748 1635265 1635332 1635448 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-747 1632631 1634067 1634563 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-746 1632052 1632179 1632353 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-745 1628953 1631191 1631557 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-744 1625584 1628383 1628423 "OMSAGG" 1628484 OMSAGG (NIL T) -9 NIL 1628548 NIL) (-743 1623996 1625255 1625423 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-742 1622205 1623446 1623474 "OINTDOM" 1623479 OINTDOM (NIL) -9 NIL 1623500 NIL) (-741 1619635 1621207 1621536 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-740 1618889 1619585 1619630 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-739 1616091 1618730 1618884 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-738 1607628 1615962 1616086 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-737 1601039 1607519 1607623 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-736 1600011 1600248 1600521 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-735 1597645 1598315 1599019 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-734 1593422 1594382 1595405 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-733 1592930 1593018 1593212 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-732 1590379 1590961 1591634 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-731 1587774 1588282 1588878 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-730 1584771 1585310 1585956 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-729 1584126 1584234 1584492 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-728 1583284 1583409 1583630 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-727 1579568 1580364 1581277 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-726 1579008 1579103 1579325 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-725 1578689 1578738 1578865 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-724 1575292 1578488 1578607 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-723 1574452 1575074 1575102 "OCAMON" 1575107 OCAMON (NIL) -9 NIL 1575128 NIL) (-722 1568664 1571478 1571518 "OC" 1572613 OC (NIL T) -9 NIL 1573469 NIL) (-721 1566664 1567590 1568570 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-720 1566080 1566498 1566526 "OASGP" 1566531 OASGP (NIL) -9 NIL 1566551 NIL) (-719 1565143 1565792 1565820 "OAMONS" 1565860 OAMONS (NIL) -9 NIL 1565903 NIL) (-718 1564288 1564869 1564897 "OAMON" 1564954 OAMON (NIL) -9 NIL 1565005 NIL) (-717 1564184 1564216 1564283 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-716 1562935 1563709 1563737 "OAGROUP" 1563883 OAGROUP (NIL) -9 NIL 1563975 NIL) (-715 1562665 1562783 1562930 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-714 1562405 1562461 1562549 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-713 1557467 1559030 1560557 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-712 1554162 1555196 1556231 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-711 1553272 1553505 1553723 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-710 1542133 1545161 1547609 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-709 1536020 1541574 1541668 "NTSCAT" 1541673 NTSCAT (NIL T T T T) -9 NIL 1541711 NIL) (-708 1535361 1535540 1535733 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-707 1535054 1535117 1535224 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-706 1522721 1532674 1533484 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-705 1511730 1522586 1522716 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-704 1510450 1510775 1511132 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-703 1509286 1509550 1509908 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-702 1508453 1508586 1508802 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-701 1506771 1507090 1507496 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-700 1506484 1506518 1506642 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-699 1506303 1506338 1506407 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-698 1506079 1506269 1506298 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-697 1505643 1505710 1505887 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-696 1503929 1505006 1505261 "NNI" NIL NNI (NIL) -8 NIL NIL 1505608) (-695 1502657 1502994 1503358 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-694 1501634 1501886 1502188 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-693 1500721 1501286 1501327 "NETCLT" 1501498 NETCLT (NIL T) -9 NIL 1501579 NIL) (-692 1499625 1499892 1500173 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-691 1499424 1499467 1499542 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-690 1497955 1498343 1498763 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-689 1496588 1497554 1497582 "NASRING" 1497692 NASRING (NIL) -9 NIL 1497772 NIL) (-688 1496433 1496489 1496583 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-687 1495362 1496040 1496068 "NARNG" 1496185 NARNG (NIL) -9 NIL 1496276 NIL) (-686 1495138 1495223 1495357 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-685 1493904 1494658 1494698 "NAALG" 1494777 NAALG (NIL T) -9 NIL 1494838 NIL) (-684 1493774 1493809 1493899 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-683 1488753 1489938 1491124 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-682 1488148 1488235 1488419 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-681 1480158 1484652 1484704 "MTSCAT" 1485764 MTSCAT (NIL T T) -9 NIL 1486278 NIL) (-680 1479924 1479984 1480076 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-679 1479750 1479789 1479849 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-678 1476612 1479301 1479342 "MSETAGG" 1479347 MSETAGG (NIL T) -9 NIL 1479381 NIL) (-677 1472749 1475658 1475976 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-676 1469023 1470846 1471586 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-675 1468660 1468733 1468862 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-674 1468313 1468354 1468498 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-673 1466178 1466515 1466946 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-672 1459576 1466077 1466173 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-671 1459101 1459142 1459350 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-670 1458660 1458709 1458892 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-669 1457934 1458027 1458246 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1456551 1456912 1457302 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-667 1456072 1456139 1456178 "MONOPC" 1456238 MONOPC (NIL T) -9 NIL 1456457 NIL) (-666 1455523 1455859 1455987 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-665 1454665 1455044 1455072 "MONOID" 1455290 MONOID (NIL) -9 NIL 1455434 NIL) (-664 1454324 1454474 1454660 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-663 1443262 1450132 1450191 "MONOGEN" 1450865 MONOGEN (NIL T T) -9 NIL 1451321 NIL) (-662 1441274 1442160 1443143 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-661 1439988 1440532 1440560 "MONADWU" 1440951 MONADWU (NIL) -9 NIL 1441186 NIL) (-660 1439536 1439736 1439983 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-659 1438813 1439114 1439142 "MONAD" 1439349 MONAD (NIL) -9 NIL 1439461 NIL) (-658 1438580 1438676 1438808 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-657 1436970 1437740 1438019 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-656 1436104 1436631 1436671 "MODULE" 1436676 MODULE (NIL T) -9 NIL 1436714 NIL) (-655 1435783 1435909 1436099 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-654 1433494 1434380 1434694 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-653 1430673 1432090 1432603 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-652 1429307 1429881 1430157 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-651 1418526 1427972 1428385 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-650 1415482 1417526 1417795 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-649 1414566 1414933 1415123 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-648 1414135 1414184 1414363 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-647 1411960 1412956 1412996 "MLO" 1413413 MLO (NIL T) -9 NIL 1413653 NIL) (-646 1409841 1410368 1410963 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-645 1409309 1409405 1409559 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-644 1408979 1409055 1409178 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-643 1408191 1408377 1408605 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-642 1407684 1407800 1407956 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-641 1407056 1407170 1407355 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-640 1406083 1406356 1406633 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-639 1405516 1405604 1405775 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-638 1402674 1403553 1404432 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-637 1401341 1401689 1402042 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-636 1397998 1400465 1400506 "MDAGG" 1400763 MDAGG (NIL T) -9 NIL 1400908 NIL) (-635 1397272 1397436 1397636 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-634 1396350 1396636 1396866 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-633 1394447 1395024 1395585 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-632 1390218 1394037 1394284 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-631 1386567 1387336 1388070 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-630 1385320 1385489 1385818 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-629 1374833 1378422 1378498 "MATCAT" 1383486 MATCAT (NIL T T T) -9 NIL 1384954 NIL) (-628 1372114 1373420 1374828 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-627 1370515 1370875 1371259 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-626 1369648 1369845 1370067 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-625 1368399 1368725 1369052 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-624 1367561 1367963 1368139 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-623 1367230 1367294 1367417 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-622 1366878 1366951 1367065 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-621 1366413 1366528 1366670 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-620 1364622 1365390 1365691 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-619 1364116 1364418 1364508 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-618 1357625 1362431 1362472 "LZSTAGG" 1363249 LZSTAGG (NIL T) -9 NIL 1363539 NIL) (-617 1354744 1356178 1357620 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-616 1352131 1353097 1353580 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-615 1351712 1351991 1352065 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-614 1343876 1351573 1351707 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-613 1343239 1343384 1343612 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-612 1340723 1341421 1342133 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-611 1338835 1339158 1339606 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-610 1332004 1337922 1337963 "LSAGG" 1338025 LSAGG (NIL T) -9 NIL 1338103 NIL) (-609 1329698 1330797 1331999 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-608 1327178 1329047 1329296 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-607 1326845 1326936 1327059 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-606 1326516 1326595 1326623 "LOGIC" 1326734 LOGIC (NIL) -9 NIL 1326816 NIL) (-605 1326411 1326440 1326511 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-604 1325730 1325888 1326081 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-603 1324515 1324764 1325115 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-602 1320337 1323136 1323176 "LODOCAT" 1323608 LODOCAT (NIL T) -9 NIL 1323819 NIL) (-601 1320130 1320206 1320332 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-600 1317130 1320007 1320125 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-599 1314228 1317080 1317125 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-598 1311315 1314158 1314223 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-597 1310368 1310543 1310845 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-596 1308500 1309630 1309883 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-595 1303595 1306659 1306700 "LNAGG" 1307562 LNAGG (NIL T) -9 NIL 1307997 NIL) (-594 1302982 1303249 1303590 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-593 1299554 1300495 1301132 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-592 1298816 1299321 1299361 "LMODULE" 1299366 LMODULE (NIL T) -9 NIL 1299392 NIL) (-591 1295995 1298553 1298675 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-590 1295563 1295774 1295815 "LLINSET" 1295876 LLINSET (NIL T) -9 NIL 1295920 NIL) (-589 1295239 1295499 1295558 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-588 1294838 1294918 1295057 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-587 1293289 1293637 1294036 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-586 1292460 1292656 1292884 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-585 1285506 1291716 1291970 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-584 1285083 1285316 1285357 "LINSET" 1285362 LINSET (NIL T) -9 NIL 1285395 NIL) (-583 1283984 1284706 1284873 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-582 1282250 1283005 1283045 "LINEXP" 1283531 LINEXP (NIL T) -9 NIL 1283804 NIL) (-581 1280872 1281859 1282040 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-580 1279699 1279971 1280273 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-579 1278912 1279501 1279611 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-578 1276462 1277184 1277934 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-577 1275092 1275389 1275780 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-576 1273885 1274487 1274527 "LIECAT" 1274667 LIECAT (NIL T) -9 NIL 1274818 NIL) (-575 1273759 1273792 1273880 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-574 1268015 1273449 1273677 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-573 1260364 1267691 1267847 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-572 1256816 1257765 1258700 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-571 1255440 1256348 1256376 "LFCAT" 1256583 LFCAT (NIL) -9 NIL 1256722 NIL) (-570 1253679 1254009 1254354 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-569 1251196 1251861 1252542 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-568 1248208 1249186 1249689 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-567 1247699 1248002 1248093 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-566 1246406 1246730 1247130 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-565 1245672 1245757 1245983 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-564 1240675 1244240 1244776 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-563 1240300 1240350 1240510 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-562 1239071 1239844 1239884 "LALG" 1239945 LALG (NIL T) -9 NIL 1240003 NIL) (-561 1238854 1238931 1239066 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-560 1236707 1238122 1238373 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-559 1236536 1236566 1236607 "KVTFROM" 1236669 KVTFROM (NIL T) -9 NIL NIL NIL) (-558 1235352 1236067 1236256 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-557 1235181 1235211 1235252 "KRCFROM" 1235314 KRCFROM (NIL T) -9 NIL NIL NIL) (-556 1234283 1234480 1234775 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-555 1234112 1234142 1234183 "KONVERT" 1234245 KONVERT (NIL T) -9 NIL NIL NIL) (-554 1233941 1233971 1234012 "KOERCE" 1234074 KOERCE (NIL T) -9 NIL NIL NIL) (-553 1233511 1233604 1233736 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-552 1231564 1232458 1232830 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-551 1224741 1229756 1229810 "KDAGG" 1230186 KDAGG (NIL T T) -9 NIL 1230393 NIL) (-550 1224389 1224531 1224736 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-549 1217219 1224170 1224327 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-548 1216869 1217151 1217214 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-547 1215839 1216338 1216587 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-546 1214965 1215414 1215619 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-545 1213829 1214321 1214621 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-544 1213111 1213510 1213671 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-543 1212821 1213057 1213106 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-542 1207076 1212511 1212739 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-541 1206494 1206827 1206947 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-540 1202656 1204671 1204725 "IXAGG" 1205652 IXAGG (NIL T T) -9 NIL 1206109 NIL) (-539 1201862 1202233 1202651 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-538 1197116 1201798 1201857 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-537 1196083 1196358 1196621 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1194745 1194952 1195245 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1193696 1193918 1194201 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1193371 1193434 1193557 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1192633 1193005 1193179 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1190609 1191909 1192183 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1180157 1185926 1187083 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1179402 1179554 1179790 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1178893 1179196 1179287 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1178186 1178277 1178490 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1177318 1177543 1177783 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1175731 1176112 1176540 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1175516 1175560 1175636 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1174366 1174663 1174958 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1173639 1173990 1174141 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1172842 1172973 1173186 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1170997 1171494 1172038 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1168078 1169346 1170035 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1167903 1167943 1168003 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1163901 1167829 1167898 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1161904 1163840 1163896 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1161275 1161574 1161704 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1160728 1161016 1161148 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1159809 1160434 1160560 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1159219 1159713 1159741 "IOBCON" 1159746 IOBCON (NIL) -9 NIL 1159767 NIL) (-512 1158790 1158854 1159036 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1150834 1153205 1155530 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1147945 1148728 1149592 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1147622 1147719 1147836 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1145064 1147558 1147617 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1143176 1143705 1144272 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1142678 1142792 1142932 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1141062 1141468 1141930 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1138841 1139435 1140046 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1136214 1136824 1137544 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1135618 1135776 1135984 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1135137 1135223 1135411 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1133342 1133863 1134320 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1126424 1128077 1129806 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1125790 1125952 1126125 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1123663 1124127 1124671 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1121789 1122739 1122767 "INTDOM" 1123066 INTDOM (NIL) -9 NIL 1123271 NIL) (-495 1121342 1121544 1121784 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1117149 1119621 1119675 "INTCAT" 1120471 INTCAT (NIL T) -9 NIL 1120787 NIL) (-493 1116714 1116834 1116961 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1115554 1115726 1116032 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1115127 1115223 1115380 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1108167 1114982 1115122 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1107465 1108020 1108085 "INT8" NIL INT8 (NIL) -8 NIL NIL 1108119) (-488 1106762 1107317 1107382 "INT64" NIL INT64 (NIL) -8 NIL NIL 1107416) (-487 1106059 1106614 1106679 "INT32" NIL INT32 (NIL) -8 NIL NIL 1106713) (-486 1105356 1105911 1105976 "INT16" NIL INT16 (NIL) -8 NIL NIL 1106010) (-485 1101819 1105275 1105351 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1095876 1099359 1099387 "INS" 1100317 INS (NIL) -9 NIL 1100976 NIL) (-483 1093938 1094856 1095803 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1092997 1093220 1093495 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1092211 1092352 1092549 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1091201 1091342 1091579 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1090353 1090517 1090777 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1089633 1089748 1089936 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1088372 1088641 1088965 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1087652 1087793 1087976 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1087315 1087387 1087485 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1084393 1085879 1086402 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1083992 1084099 1084213 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1083148 1083793 1083894 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1081998 1082266 1082587 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1080988 1081928 1081993 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1080613 1080693 1080810 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1079527 1080072 1080276 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1075622 1076677 1077620 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1074476 1074799 1074827 "INBCON" 1075340 INBCON (NIL) -9 NIL 1075606 NIL) (-465 1073930 1074195 1074471 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1073424 1073726 1073816 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1072881 1073190 1073295 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1068981 1072773 1072876 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-461 1067821 1067960 1068275 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1066245 1066512 1066849 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1064061 1066127 1066240 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-458 1058904 1063992 1064056 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1058284 1058618 1058733 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1053091 1057722 1057908 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1052121 1053013 1053086 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1051693 1051770 1051824 "IEVALAB" 1052031 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1051448 1051528 1051688 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050833 1051060 1051217 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049826 1050753 1050828 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048889 1049746 1049821 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047971 1048618 1048755 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1046334 1046905 1046956 "IDPC" 1047462 IDPC (NIL T T) -9 NIL 1047775 NIL) (-447 1045621 1046256 1046329 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044791 1045543 1045616 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1044484 1044697 1044757 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1044188 1044228 1044267 "IDEMOPC" 1044272 IDEMOPC (NIL T) -9 NIL 1044409 NIL) (-443 1041259 1042140 1043032 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034885 1036162 1037201 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1034147 1034277 1034476 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1033320 1033819 1033957 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031709 1032040 1032431 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1027478 1031665 1031704 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024736 1025360 1026055 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022962 1023442 1023975 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020726 1022854 1022957 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-434 1016595 1020664 1020721 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1010174 1015559 1016027 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009742 1009805 1009978 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1009234 1009383 1009411 "HYPCAT" 1009618 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008890 1009043 1009229 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1008503 1008748 1008831 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1008336 1008385 1008426 "HOMOTOP" 1008431 HOMOTOP (NIL T) -9 NIL 1008464 NIL) (-427 1004904 1006278 1006319 "HOAGG" 1007294 HOAGG (NIL T) -9 NIL 1008015 NIL) (-426 1003910 1004380 1004899 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 997110 1003635 1003783 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 996045 996303 996566 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 994980 995910 996040 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 993174 994813 994901 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 992489 992841 992974 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 985943 992422 992484 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 979082 985679 985830 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 978535 978692 978855 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 971618 978426 978530 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 971109 971412 971503 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968659 970896 971075 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 964052 968542 968654 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 957138 963949 964047 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 949075 956507 956762 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 948099 948608 948636 "GROUP" 948839 GROUP (NIL) -9 NIL 948973 NIL) (-410 947642 947843 948094 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 946314 946653 947040 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 945136 945493 945544 "GRMOD" 946073 GRMOD (NIL T T) -9 NIL 946239 NIL) (-407 944955 945003 945131 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 941078 942289 943289 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939800 940124 940439 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 939353 939481 939622 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 938426 938925 938976 "GRALG" 939129 GRALG (NIL T T) -9 NIL 939219 NIL) (-402 938145 938246 938421 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934862 937827 938003 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 934275 934338 934595 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 930129 931025 931550 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 929304 929506 929744 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 924307 925234 926253 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 924055 924112 924201 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 923537 923626 923791 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 923046 923087 923300 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921847 922130 922434 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 915122 921537 921698 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904905 909912 911016 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 902957 904060 904088 "GCDDOM" 904343 GCDDOM (NIL) -9 NIL 904500 NIL) (-389 902580 902737 902952 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 893373 895843 898231 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 891508 891833 892251 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 890449 890638 890905 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 889320 889527 889831 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888783 888925 889073 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 887395 887743 888056 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 885940 886261 886583 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 883566 883922 884327 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876818 878479 880057 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 876470 876691 876759 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 876094 876315 876396 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 874191 874874 875334 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872784 873091 873483 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 871439 871798 872122 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870742 870866 871053 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869716 869982 870329 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 867374 867904 868386 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 866957 867017 867186 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 865257 866171 866474 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 864405 864539 864762 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 863576 863737 863964 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 859559 862510 862551 "FSAGG" 862921 FSAGG (NIL T) -9 NIL 863180 NIL) (-366 857913 858672 859464 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855869 856165 856709 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854916 855098 855398 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 854597 854646 854773 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834753 844254 844295 "FS" 848165 FS (NIL T) -9 NIL 850443 NIL) (-361 826984 830477 834456 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 826518 826645 826797 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 821041 824199 824239 "FRNAALG" 825559 FRNAALG (NIL T) -9 NIL 826157 NIL) (-358 817782 819033 820291 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 817463 817512 817639 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 815950 816507 816801 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 815236 815329 815616 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 813070 813836 814152 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 812179 812622 812663 "FRETRCT" 812668 FRETRCT (NIL T) -9 NIL 812839 NIL) (-352 811552 811830 812174 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 808296 809816 809875 "FRAMALG" 810757 FRAMALG (NIL T T) -9 NIL 811049 NIL) (-350 806892 807443 808073 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 806585 806648 806755 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 800226 806390 806580 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799919 799982 800089 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 792227 796798 798126 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 786005 789508 789536 "FPS" 790655 FPS (NIL) -9 NIL 791211 NIL) (-344 785562 785695 785859 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 782372 784415 784443 "FPC" 784668 FPC (NIL) -9 NIL 784810 NIL) (-342 782218 782270 782367 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 780995 781704 781745 "FPATMAB" 781750 FPATMAB (NIL T) -9 NIL 781902 NIL) (-340 779425 780021 780368 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 779000 779058 779231 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 777503 778398 778572 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 776118 776623 776651 "FNCAT" 777108 FNCAT (NIL) -9 NIL 777365 NIL) (-336 775575 776085 776113 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 774162 775524 775570 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770750 772108 772149 "FMONCAT" 773366 FMONCAT (NIL T) -9 NIL 773970 NIL) (-333 767608 768686 768739 "FMCAT" 769920 FMCAT (NIL T T) -9 NIL 770412 NIL) (-332 766308 767431 767530 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 765356 766156 766303 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 763543 763995 764489 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 761478 762014 762592 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754864 759815 760429 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 753345 754446 754486 "FLINEXP" 754491 FLINEXP (NIL T) -9 NIL 754584 NIL) (-326 752754 753013 753340 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 751969 752128 752349 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748852 749931 749983 "FLALG" 751210 FLALG (NIL T T) -9 NIL 751677 NIL) (-323 748023 748184 748411 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 741432 745442 745483 "FLAGG" 746738 FLAGG (NIL T) -9 NIL 747383 NIL) (-321 740540 740944 741427 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 737101 738365 738424 "FINRALG" 739552 FINRALG (NIL T T) -9 NIL 740060 NIL) (-319 736492 736757 737096 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735790 736086 736114 "FINITE" 736310 FINITE (NIL) -9 NIL 736417 NIL) (-317 735698 735724 735785 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727659 730250 730290 "FINAALG" 733942 FINAALG (NIL T) -9 NIL 735380 NIL) (-315 723926 725171 726294 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 722478 722897 722951 "FILECAT" 723635 FILECAT (NIL T T) -9 NIL 723851 NIL) (-313 721829 722303 722406 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 719077 720955 720983 "FIELD" 721023 FIELD (NIL) -9 NIL 721103 NIL) (-311 718102 718563 719072 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 716106 717052 717398 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 715349 715530 715749 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 710619 715287 715344 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 710281 710348 710483 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709821 709863 710072 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 706501 707378 708155 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701785 706433 706496 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 696464 701274 701464 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 690945 695745 696003 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 685152 690396 690607 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 684175 684385 684700 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 679615 682320 682348 "FFIELDC" 682967 FFIELDC (NIL) -9 NIL 683342 NIL) (-298 678684 679124 679610 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 678299 678357 678481 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 676443 676966 677483 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 671537 676242 676343 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 666637 671326 671433 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 661303 666428 666536 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660757 660806 661041 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 639332 650366 650452 "FFCAT" 655602 FFCAT (NIL T T T) -9 NIL 657038 NIL) (-290 635572 636798 638104 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 630415 635503 635567 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 629307 629776 629817 "FEVALAB" 629901 FEVALAB (NIL T) -9 NIL 630162 NIL) (-287 628712 628964 629302 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 625539 626450 626565 "FDIVCAT" 628132 FDIVCAT (NIL T T T T) -9 NIL 628568 NIL) (-285 625333 625365 625534 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624640 624733 625010 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 623126 624124 624327 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 622219 622603 622805 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 621341 621830 621970 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612928 617571 617611 "FAXF" 619412 FAXF (NIL T) -9 NIL 620102 NIL) (-279 610844 611648 612463 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605708 610366 610540 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 600166 602589 602641 "FAMR" 603652 FAMR (NIL T T) -9 NIL 604111 NIL) (-276 599365 599730 600161 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 598386 599307 599360 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 595980 596859 596912 "FAMONC" 597853 FAMONC (NIL T T) -9 NIL 598238 NIL) (-273 594536 595838 595975 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 592616 592977 593379 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591893 592090 592312 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583753 591340 591539 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581772 582342 582928 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578674 579316 580036 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573831 574538 575343 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 573520 573583 573692 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 558313 572569 572995 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548840 557633 557921 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 548334 548636 548726 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 548110 548300 548329 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547799 547867 547980 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 547316 547458 547499 "EVALAB" 547669 EVALAB (NIL T) -9 NIL 547773 NIL) (-259 546944 547090 547311 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 543987 545582 545610 "EUCDOM" 546164 EUCDOM (NIL) -9 NIL 546513 NIL) (-257 542914 543407 543982 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542639 542695 542795 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 542327 542391 542500 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 536098 537998 538026 "ES" 540768 ES (NIL) -9 NIL 542152 NIL) (-253 532613 534145 535937 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 531961 532114 532290 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 525050 531865 531956 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524739 524802 524911 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518366 521491 522924 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514669 515765 516858 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513498 513848 514153 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512383 513114 513142 "ENTIRER" 513147 ENTIRER (NIL) -9 NIL 513191 NIL) (-245 512272 512306 512378 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508905 510702 511051 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507997 508208 508262 "ELTAGG" 508642 ELTAGG (NIL T T) -9 NIL 508853 NIL) (-242 507777 507851 507992 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507523 507558 507612 "ELTAB" 507696 ELTAB (NIL T T) -9 NIL 507748 NIL) (-240 506774 506944 507143 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506498 506572 506600 "ELEMFUN" 506705 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506398 506425 506493 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500944 504439 504480 "ELAGG" 505417 ELAGG (NIL T) -9 NIL 505877 NIL) (-236 499742 500280 500939 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 499160 499327 499483 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 498073 498392 498671 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491466 493464 494291 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485445 487441 488251 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 483259 483665 484136 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 474259 476172 477713 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473372 473873 474022 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 472070 472744 472784 "DVARCAT" 473067 DVARCAT (NIL T) -9 NIL 473207 NIL) (-227 471489 471753 472065 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463556 471357 471484 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461894 462685 462726 "DSEXT" 463089 DSEXT (NIL T) -9 NIL 463383 NIL) (-224 460699 461223 461889 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460423 460488 460586 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456574 457790 458921 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 452220 453575 454639 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450895 451256 451642 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450581 450640 450758 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449556 449854 450144 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 449141 449216 449366 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441554 443666 445781 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 437071 438090 439169 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433666 435735 435776 "DQAGG" 436405 DQAGG (NIL T) -9 NIL 436678 NIL) (-213 420209 427849 427931 "DPOLCAT" 429768 DPOLCAT (NIL T T T T) -9 NIL 430311 NIL) (-212 416617 418265 420204 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409622 416515 416612 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402536 409451 409617 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402129 402389 402478 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401543 401991 402071 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400829 401154 401305 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393968 400565 400716 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391717 393034 393074 "DMEXT" 393079 DMEXT (NIL T) -9 NIL 393254 NIL) (-204 391373 391435 391579 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384698 390858 391048 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381364 383521 383562 "DLAGG" 384112 DLAGG (NIL T) -9 NIL 384341 NIL) (-201 379715 380586 380614 "DIVRING" 380706 DIVRING (NIL) -9 NIL 380789 NIL) (-200 379166 379410 379710 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377594 378011 378417 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376631 376852 377117 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370105 376563 376626 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358425 364885 364938 "DIRPCAT" 365194 DIRPCAT (NIL NIL T) -9 NIL 366067 NIL) (-195 356431 357201 358088 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355878 356044 356230 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352424 354764 354805 "DIOPS" 355237 DIOPS (NIL T) -9 NIL 355463 NIL) (-192 352084 352228 352419 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351091 351837 351865 "DIOID" 351870 DIOID (NIL) -9 NIL 351892 NIL) (-190 349919 350748 350776 "DIFRING" 350781 DIFRING (NIL) -9 NIL 350802 NIL) (-189 349555 349653 349681 "DIFFSPC" 349800 DIFFSPC (NIL) -9 NIL 349875 NIL) (-188 349296 349398 349550 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348199 348824 348864 "DIFFMOD" 348869 DIFFMOD (NIL T) -9 NIL 348966 NIL) (-186 347883 347940 347981 "DIFFDOM" 348102 DIFFDOM (NIL T) -9 NIL 348170 NIL) (-185 347764 347794 347878 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345437 346958 346998 "DIFEXT" 347003 DIFEXT (NIL T) -9 NIL 347155 NIL) (-183 342598 344938 344979 "DIAGG" 344984 DIAGG (NIL T) -9 NIL 345004 NIL) (-182 342154 342344 342593 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337366 341344 341621 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333824 334877 335887 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328374 332978 333305 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326940 327232 327607 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324060 325312 325708 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321780 323891 323980 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321163 321308 321490 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 318481 319205 320005 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 316590 317048 317610 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 315973 316306 316420 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309173 315698 315846 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307093 307603 308107 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306732 306781 306932 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 305991 306553 306644 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304015 304457 304817 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303307 303596 303742 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302758 302904 303056 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300120 300913 301640 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 299559 299705 299876 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 297631 297942 298309 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297188 297443 297544 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 296389 296772 296800 "CTORCAT" 296981 CTORCAT (NIL) -9 NIL 297093 NIL) (-159 296092 296226 296384 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 295585 295842 295950 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295001 295432 295505 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 294460 294577 294730 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290854 291610 292365 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290345 290648 290739 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 289564 289773 290001 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289068 289173 289377 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288821 288855 288961 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285760 286522 287240 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285279 285421 285560 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281172 283742 284234 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281046 281073 281101 "CONDUIT" 281138 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279925 280656 280684 "COMRING" 280689 COMRING (NIL) -9 NIL 280739 NIL) (-145 279090 279457 279635 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278786 278827 278955 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278479 278542 278649 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267321 278429 278474 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266782 266921 267081 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266535 266576 266674 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 247966 260216 260256 "COMPCAT" 261257 COMPCAT (NIL T) -9 NIL 262599 NIL) (-138 240504 244017 247610 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240263 240297 240399 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240093 240132 240190 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239674 239953 240027 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239251 239492 239579 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238446 238694 238722 "COMBOPC" 239060 COMBOPC (NIL) -9 NIL 239235 NIL) (-132 237510 237762 238004 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234442 235126 235749 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233322 233773 234008 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232813 233116 233207 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232500 232553 232678 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 231970 232280 232378 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228490 229560 230640 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226785 227770 228008 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222897 224905 224946 "CLAGG" 225872 CLAGG (NIL T) -9 NIL 226405 NIL) (-123 221790 222317 222892 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221419 221510 221650 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219356 219863 220411 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218317 219048 219076 "CHARZ" 219081 CHARZ (NIL) -9 NIL 219095 NIL) (-119 218111 218157 218235 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 216950 217713 217741 "CHARNZ" 217802 CHARNZ (NIL) -9 NIL 217850 NIL) (-117 214428 215525 216048 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214136 214215 214243 "CFCAT" 214354 CFCAT (NIL) -9 NIL NIL NIL) (-115 213479 213608 213790 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209468 212892 213172 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208846 209033 209210 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208374 208793 208841 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207847 208156 208253 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207338 207641 207732 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 206587 206747 206968 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202687 203944 204652 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201053 202084 202335 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 200634 200913 200987 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200068 200321 200349 "CACHSET" 200481 CACHSET (NIL) -9 NIL 200559 NIL) (-104 199420 199835 199863 "CABMON" 199913 CABMON (NIL) -9 NIL 199969 NIL) (-103 198950 199214 199324 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 194173 198607 198779 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 193143 193847 193982 "BYTE" NIL BYTE (NIL) -8 NIL NIL 194145) (-100 190614 192910 193016 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 188045 190357 190476 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 185285 187489 187528 "BTCAT" 187595 BTCAT (NIL T) -9 NIL 187671 NIL) (-97 185036 185134 185280 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 180146 184267 184293 "BTAGG" 184404 BTAGG (NIL) -9 NIL 184512 NIL) (-95 179777 179938 180141 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176839 179247 179459 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 176109 176261 176439 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172642 174815 174854 "BRAGG" 175495 BRAGG (NIL T) -9 NIL 175752 NIL) (-91 171597 172092 172637 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164131 171102 171283 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162123 164083 164126 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161856 161892 162003 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160095 160528 160976 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156061 157477 158367 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154937 155828 155950 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154523 154680 154706 "BOOLE" 154814 BOOLE (NIL) -9 NIL 154895 NIL) (-83 154316 154397 154518 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153454 153981 154031 "BMODULE" 154036 BMODULE (NIL T T) -9 NIL 154100 NIL) (-81 149071 153311 153380 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148884 148924 148963 "BINOPC" 148968 BINOPC (NIL T) -9 NIL 149013 NIL) (-79 148426 148699 148801 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147947 148091 148229 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141153 147677 147822 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138887 140382 140421 "BGAGG" 140677 BGAGG (NIL T) -9 NIL 140814 NIL) (-75 138756 138794 138882 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 137607 137808 138093 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 134245 136765 137092 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133830 133923 133949 "BASTYPE" 134120 BASTYPE (NIL) -9 NIL 134216 NIL) (-71 133600 133696 133825 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 133115 133203 133353 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 132014 132689 132874 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131740 131745 131771 "ATTREG" 131776 ATTREG (NIL) -9 NIL NIL NIL) (-67 131345 131617 131682 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130845 130994 131020 "ATRIG" 131221 ATRIG (NIL) -9 NIL NIL NIL) (-65 130700 130753 130840 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 130270 130501 130527 "ASTCAT" 130532 ASTCAT (NIL) -9 NIL 130562 NIL) (-63 130069 130146 130265 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 128228 129902 129990 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 127035 127348 127713 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124835 126939 127030 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 124026 124217 124438 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 119613 123757 123871 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113779 115811 115886 "ARR2CAT" 118516 ARR2CAT (NIL T T T) -9 NIL 119274 NIL) (-56 112156 112926 113774 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111524 111895 112017 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110456 110624 110920 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110157 110211 110329 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109540 109686 109842 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 108945 109235 109355 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106513 107674 107997 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106038 106298 106394 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99733 105100 105542 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95267 96930 96980 "AMR" 97718 AMR (NIL T T) -9 NIL 98315 NIL) (-46 94621 94901 95262 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77801 94555 94616 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74204 77477 77646 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71214 71874 72481 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70593 70706 70890 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67005 67630 68222 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56494 66698 66848 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55811 55965 56143 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54524 55319 55357 "ALGEBRA" 55362 ALGEBRA (NIL T) -9 NIL 55402 NIL) (-37 54310 54387 54519 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34307 51516 51568 "ALAGG" 51706 ALAGG (NIL T T) -9 NIL 51871 NIL) (-35 33807 33956 33982 "AHYP" 34183 AHYP (NIL) -9 NIL NIL NIL) (-34 33103 33284 33310 "AGG" 33591 AGG (NIL) -9 NIL 33778 NIL) (-33 32892 32979 33098 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31031 31491 31891 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30526 30829 30918 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29896 30191 30347 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17454 26733 26771 "ACFS" 27378 ACFS (NIL T) -9 NIL 27617 NIL) (-28 16077 16687 17449 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11629 14008 14034 "ACF" 14913 ACF (NIL) -9 NIL 15325 NIL) (-26 10725 11131 11624 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10227 10467 10493 "ABELSG" 10585 ABELSG (NIL) -9 NIL 10650 NIL) (-24 10125 10156 10222 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9280 9654 9680 "ABELMON" 9905 ABELMON (NIL) -9 NIL 10038 NIL) (-22 8962 9102 9275 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8174 8657 8683 "ABELGRP" 8755 ABELGRP (NIL) -9 NIL 8830 NIL) (-20 7788 7953 8169 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 7046 7085 "A1AGG" 7090 A1AGG (NIL T) -9 NIL 7130 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
+((-2569 (((-85) $ $) NIL T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3244 (((-1034) $) NIL T ELT)) (-3946 (((-773) $) 9 T ELT) (($ (-1095)) NIL T ELT) (((-1095) $) NIL T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) NIL T ELT))) 
+(((-1130) (-996)) (T -1130)) 
+NIL 
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T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-484) (-1026)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-327 |#2|) |has| |#1| (-312)) ((-341 |#2|) |has| |#1| (-312)) ((-390) |has| |#1| (-312)) ((-431) |has| |#1| (-38 (-348 (-484)))) ((-454 (-1090) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-454 (-1090) |#2|))) ((-454 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-589 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-591 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-591 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-484)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-312)) ((-591 $) . T) ((-583 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-312)) ((-583 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-581 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-484)))) ((-581 |#2|) |has| |#1| (-312)) ((-655 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-312)) ((-655 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-664) . T) ((-715) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-717) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-719) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-722) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-741) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-756) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-757) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-760) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-807 $ (-1090)) OR (-12 (|has| |#1| (-810 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1090))))) ((-810 (-1090)) OR (-12 (|has| |#1| (-810 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1090))))) ((-812 (-1090)) OR (-12 (|has| |#1| (-810 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1090))))) ((-797 (-328)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-328)))) ((-797 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-484)))) ((-795 |#2|) |has| |#1| (-312)) ((-822) -12 (|has| |#1| (-312)) (|has| |#2| (-822))) ((-887 |#1| (-484) (-995)) . T) ((-833) |has| |#1| (-312)) ((-905 |#2|) |has| |#1| (-312)) ((-916) |has| |#1| (-38 (-348 (-484)))) ((-934) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-951 (-348 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-484)))) ((-951 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-484)))) ((-951 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-1090)))) ((-951 |#2|) . T) ((-964 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-312)) ((-964 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-969 (-348 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-484))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-312)) ((-969 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1061) . T) ((-1014) . 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+NIL 
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+NIL 
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+NIL 
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(-258) (-120) (-934))) (-5 *2 (-584 (-2 (|:| -1747 (-1085 *5)) (|:| -3225 (-584 (-858 *5)))))) (-5 *1 (-1207 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1090))) (-14 *7 (-584 (-1090))))) (-3968 (*1 *2 *3) (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *5 (-584 (-1090))) (-5 *2 (-584 (-2 (|:| -1747 (-1085 *4)) (|:| -3225 (-584 (-858 *4)))))) (-5 *1 (-1207 *4 *5 *6)) (-14 *6 (-584 (-1090))))) (-3967 (*1 *2 *3) (-12 (-5 *3 (-584 (-858 *4))) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *4 *5))) (-5 *1 (-1207 *4 *5 *6)) (-14 *5 (-584 (-1090))) (-14 *6 (-584 (-1090))))) (-3967 (*1 *2 *3 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1207 *5 *6 *7)) (-14 *6 (-584 (-1090))) (-14 *7 (-584 (-1090))))) (-3967 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1207 *5 *6 *7)) (-14 *6 (-584 (-1090))) (-14 *7 (-584 (-1090)))))) 
+((-3975 (((-3 (-1179 (-348 (-484))) #1="failed") (-1179 |#1|) |#1|) 21 T ELT)) (-3973 (((-85) (-1179 |#1|)) 12 T ELT)) (-3974 (((-3 (-1179 (-484)) #1#) (-1179 |#1|)) 16 T ELT))) 
+(((-1208 |#1|) (-10 -7 (-15 -3973 ((-85) (-1179 |#1|))) (-15 -3974 ((-3 (-1179 (-484)) #1="failed") (-1179 |#1|))) (-15 -3975 ((-3 (-1179 (-348 (-484))) #1#) (-1179 |#1|) |#1|))) (-13 (-962) (-581 (-484)))) (T -1208)) 
+((-3975 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-1179 (-348 (-484)))) (-5 *1 (-1208 *4)))) (-3974 (*1 *2 *3) (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4)))) (-3973 (*1 *2 *3) (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-85)) (-5 *1 (-1208 *4))))) 
+((-2569 (((-85) $ $) NIL T ELT)) (-3189 (((-85) $) 12 T ELT)) (-1312 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3137 (((-695)) 9 T ELT)) (-3724 (($) NIL T CONST)) (-3467 (((-3 $ #1#) $) 57 T ELT)) (-2995 (($) 46 T ELT)) (-1214 (((-85) $ $) NIL T ELT)) (-2411 (((-85) $) 38 T ELT)) (-3445 (((-633 $) $) 36 T ELT)) (-2011 (((-831) $) 14 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3446 (($) 26 T CONST)) (-2401 (($ (-831)) 47 T ELT)) (-3244 (((-1034) $) NIL T ELT)) (-3972 (((-484) $) 16 T ELT)) (-3946 (((-773) $) 21 T ELT) (($ (-484)) 18 T ELT)) (-3127 (((-695)) 10 T CONST)) (-1265 (((-85) $ $) 59 T ELT)) (-3126 (((-85) $ $) NIL T ELT)) (-2661 (($) 23 T CONST)) (-2667 (($) 25 T CONST)) (-3057 (((-85) $ $) 31 T ELT)) (-3837 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3839 (($ $ $) 29 T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) 52 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) 41 T ELT) (($ $ $) 40 T ELT))) 
+(((-1209 |#1|) (-13 (-146) (-318) (-554 (-484)) (-1066)) (-831)) (T -1209)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2816755 2816760 2816765 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2816740 2816745 2816750 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2816725 2816730 2816735 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2816710 2816715 2816720 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1209 2815689 2816628 2816705 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1208 2814904 2815083 2815302 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1207 2806063 2807932 2809866 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1206 2805451 2805604 2805793 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1205 2804913 2805216 2805329 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1204 2802473 2804375 2804578 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1203 2799237 2800890 2801461 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1202 2796494 2798224 2798278 "XPOLYC" 2798563 XPOLYC (NIL T T) -9 NIL 2798676 NIL) (-1201 2794013 2795998 2796201 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1200 2790261 2792872 2793260 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1199 2785108 2786741 2786795 "XFALG" 2788940 XFALG (NIL T T) -9 NIL 2789724 NIL) (-1198 2780264 2782997 2783039 "XF" 2783657 XF (NIL T) -9 NIL 2784053 NIL) (-1197 2779982 2780092 2780259 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1196 2779209 2779331 2779535 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1195 2776951 2779109 2779204 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1194 2775532 2776327 2776369 "XALG" 2776374 XALG (NIL T) -9 NIL 2776483 NIL) (-1193 2769089 2773942 2774420 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1192 2767332 2768334 2768655 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1191 2766931 2767203 2767272 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1190 2766418 2766721 2766814 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1189 2765495 2765705 2766000 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1188 2763791 2764254 2764716 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1187 2762680 2763265 2763307 "VSPACE" 2763443 VSPACE (NIL T) -9 NIL 2763517 NIL) (-1186 2762551 2762584 2762675 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1185 2762394 2762448 2762516 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1184 2759377 2760172 2760909 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1183 2750475 2753076 2755249 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1182 2744052 2745943 2747522 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1181 2742536 2742931 2743337 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1180 2741363 2741644 2741960 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1179 2736477 2741190 2741282 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1178 2729579 2734187 2734230 "VECTCAT" 2735218 VECTCAT (NIL T) -9 NIL 2735802 NIL) (-1177 2728858 2729184 2729574 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1176 2728352 2728594 2728714 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1175 2728285 2728290 2728320 "UTYPE" 2728325 UTYPE (NIL) -9 NIL NIL NIL) (-1174 2727272 2727448 2727709 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1173 2725123 2725631 2726155 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1172 2715005 2720975 2721017 "UTSCAT" 2722115 UTSCAT (NIL T) -9 NIL 2722872 NIL) (-1171 2713070 2714013 2715000 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1170 2712744 2712793 2712924 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1169 2704455 2710940 2711419 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1168 2698450 2701263 2701306 "URAGG" 2703376 URAGG (NIL T) -9 NIL 2704098 NIL) (-1167 2696465 2697427 2698445 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1166 2692172 2695441 2695903 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1165 2684601 2692096 2692167 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1164 2673252 2680739 2680800 "UPXSCCA" 2681368 UPXSCCA (NIL T T) -9 NIL 2681600 NIL) (-1163 2672973 2673075 2673247 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1162 2661525 2668737 2668779 "UPXSCAT" 2669419 UPXSCAT (NIL T) -9 NIL 2670027 NIL) (-1161 2661038 2661123 2661300 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1160 2652724 2660629 2660891 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2651619 2651889 2652239 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1158 2644322 2647807 2647861 "UPSCAT" 2648930 UPSCAT (NIL T T) -9 NIL 2649694 NIL) (-1157 2643742 2643994 2644317 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1156 2643416 2643465 2643596 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1155 2627546 2636500 2636542 "UPOLYC" 2638620 UPOLYC (NIL T) -9 NIL 2639840 NIL) (-1154 2621601 2624449 2627541 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1153 2621037 2621162 2621325 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1152 2620671 2620758 2620897 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1151 2619484 2619751 2620055 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1150 2618817 2618947 2619132 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1149 2618409 2618484 2618631 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1148 2609173 2618175 2618303 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1147 2608535 2608672 2608877 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1146 2607136 2607983 2608259 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1145 2606365 2606562 2606787 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1144 2593175 2606289 2606360 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1143 2573027 2586262 2586323 "ULSCCAT" 2586954 ULSCCAT (NIL T T) -9 NIL 2587241 NIL) (-1142 2572362 2572648 2573022 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1141 2560734 2567868 2567910 "ULSCAT" 2568763 ULSCAT (NIL T) -9 NIL 2569493 NIL) (-1140 2560247 2560332 2560509 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1139 2542364 2559746 2559987 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1138 2541398 2542091 2542205 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2542316) (-1137 2540431 2541124 2541238 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2541349) (-1136 2539464 2540157 2540271 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2540382) (-1135 2538497 2539190 2539304 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2539415) (-1134 2536504 2537725 2537755 "UFD" 2537966 UFD (NIL) -9 NIL 2538079 NIL) (-1133 2536348 2536405 2536499 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1132 2535600 2535807 2536023 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1131 2533820 2534273 2534738 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1130 2533545 2533785 2533815 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1129 2533483 2533488 2533518 "TYPE" 2533523 TYPE (NIL) -9 NIL 2533530 NIL) (-1128 2532642 2532862 2533102 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1127 2531820 2532251 2532486 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1126 2529974 2530547 2531086 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1125 2529008 2529244 2529480 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1124 2517362 2521830 2521926 "TSETCAT" 2527141 TSETCAT (NIL T T T T) -9 NIL 2528653 NIL) (-1123 2513699 2515515 2517357 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1122 2508091 2512925 2513207 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1121 2503428 2504441 2505370 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1120 2502925 2503000 2503163 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1119 2501001 2501291 2501646 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1118 2500485 2500634 2500664 "TRIGCAT" 2500877 TRIGCAT (NIL) -9 NIL NIL NIL) (-1117 2500236 2500339 2500480 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1116 2497232 2499345 2499623 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1115 2496338 2497034 2497064 "TRANFUN" 2497099 TRANFUN (NIL) -9 NIL 2497165 NIL) (-1114 2495802 2496053 2496333 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1113 2495639 2495677 2495738 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1112 2495096 2495227 2495378 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1111 2493837 2494494 2494730 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1110 2493649 2493686 2493758 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1109 2491863 2492509 2492938 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1108 2490243 2490580 2490902 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1107 2481301 2488044 2488100 "TBAGG" 2488502 TBAGG (NIL T T) -9 NIL 2488715 NIL) (-1106 2477832 2479524 2481296 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1105 2477309 2477434 2477579 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1104 2476819 2477139 2477229 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1103 2476316 2476433 2476571 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1102 2469403 2476218 2476311 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1101 2465156 2466451 2467696 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1100 2464525 2464684 2464865 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1099 2461679 2462432 2463215 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1098 2461453 2461643 2461674 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1097 2460407 2461092 2461218 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2461404) (-1096 2459671 2460219 2460298 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2460358) (-1095 2456494 2457653 2458353 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1094 2454177 2454860 2455494 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1093 2450255 2451301 2452278 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1092 2447354 2449910 2450139 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1091 2446950 2447037 2447159 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1090 2443574 2445048 2445867 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1089 2436534 2442771 2443064 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2428220 2436125 2436387 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2427499 2427638 2427855 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1086 2427183 2427248 2427359 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1085 2417906 2426895 2427020 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1084 2416636 2416934 2417289 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1083 2416041 2416119 2416310 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1082 2398193 2415540 2415781 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1081 2397792 2398064 2398133 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1080 2397128 2397409 2397549 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1079 2391730 2392989 2393942 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1078 2391262 2391362 2391526 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1077 2386373 2387655 2388802 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1076 2380831 2382302 2383613 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1075 2373746 2375810 2377601 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1074 2366576 2373658 2373741 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1073 2361270 2366290 2366405 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1072 2360857 2360940 2361084 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1071 2360008 2360209 2360444 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1070 2359748 2359806 2359899 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1069 2352486 2357953 2358559 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1068 2351662 2351867 2352098 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1067 2350907 2351278 2351425 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1066 2350395 2350637 2350667 "STEP" 2350761 STEP (NIL) -9 NIL 2350832 NIL) (-1065 2343498 2350313 2350390 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1064 2337713 2342296 2342339 "STAGG" 2342766 STAGG (NIL T) -9 NIL 2342940 NIL) (-1063 2336092 2336840 2337708 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1062 2334249 2335919 2336011 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1061 2333529 2334068 2334098 "SRING" 2334103 SRING (NIL) -9 NIL 2334123 NIL) (-1060 2326151 2332067 2332506 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1059 2319925 2321364 2322868 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1058 2312350 2317261 2317291 "SRAGG" 2318590 SRAGG (NIL) -9 NIL 2319194 NIL) (-1057 2311647 2311967 2312345 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1056 2305702 2310969 2311392 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1055 2299915 2303084 2303806 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1054 2296344 2297163 2297800 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1053 2295319 2295624 2295654 "SPFCAT" 2296098 SPFCAT (NIL) -9 NIL NIL NIL) (-1052 2294256 2294508 2294772 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1051 2285014 2287288 2287318 "SPADXPT" 2291955 SPADXPT (NIL) -9 NIL 2294079 NIL) (-1050 2284816 2284862 2284931 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1049 2282472 2284780 2284811 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1048 2274146 2276235 2276277 "SPACEC" 2280592 SPACEC (NIL T) -9 NIL 2282397 NIL) (-1047 2271975 2274093 2274141 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1046 2270908 2271097 2271386 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1045 2269312 2269645 2270056 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1044 2268577 2268811 2269072 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1043 2264757 2265717 2266712 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1042 2261115 2261814 2262543 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1041 2254901 2260455 2260551 "SNTSCAT" 2260556 SNTSCAT (NIL T T T T) -9 NIL 2260626 NIL) (-1040 2248722 2253542 2253932 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1039 2242494 2248641 2248717 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1038 2240926 2241257 2241655 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1037 2232531 2237510 2237612 "SMATCAT" 2238955 SMATCAT (NIL NIL T T T) -9 NIL 2239503 NIL) (-1036 2230372 2231356 2232526 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1035 2227964 2229578 2229621 "SKAGG" 2229882 SKAGG (NIL T) -9 NIL 2230016 NIL) (-1034 2224010 2227784 2227895 "SINT" NIL SINT (NIL) -8 NIL NIL 2227936) (-1033 2223820 2223864 2223930 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2222895 2223127 2223395 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2221899 2222061 2222337 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2221245 2221585 2221708 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2220591 2220898 2221038 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2218702 2219194 2219700 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2212142 2218621 2218697 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2211645 2211882 2211912 "SGROUP" 2212005 SGROUP (NIL) -9 NIL 2212067 NIL) (-1025 2211535 2211567 2211640 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2211173 2211213 2211254 "SGPOPC" 2211259 SGPOPC (NIL T) -9 NIL 2211460 NIL) (-1023 2210707 2210984 2211090 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2208130 2208899 2209621 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2202015 2207569 2207665 "SFRTCAT" 2207670 SFRTCAT (NIL T T T T) -9 NIL 2207708 NIL) (-1020 2196407 2197520 2198647 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2190583 2191744 2192908 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2189555 2190457 2190578 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2185163 2186058 2186153 "SEXCAT" 2188766 SEXCAT (NIL T T T T T) -9 NIL 2189317 NIL) (-1016 2184136 2185090 2185158 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2182527 2183112 2183414 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2182050 2182235 2182265 "SETCAT" 2182382 SETCAT (NIL) -9 NIL 2182466 NIL) (-1013 2181882 2181946 2182045 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2178105 2180336 2180379 "SETAGG" 2181247 SETAGG (NIL T) -9 NIL 2181585 NIL) (-1011 2177711 2177863 2178100 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2174665 2177658 2177706 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2174131 2174441 2174541 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2173258 2173624 2173685 "SEGXCAT" 2173971 SEGXCAT (NIL T T) -9 NIL 2174091 NIL) (-1007 2172183 2172451 2172494 "SEGCAT" 2173016 SEGCAT (NIL T) -9 NIL 2173237 NIL) (-1006 2171863 2171928 2172041 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2170929 2171399 2171607 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2170507 2170786 2170862 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2169872 2170008 2170212 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2168938 2169685 2169867 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2168191 2168886 2168933 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2159676 2168058 2168186 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2158536 2158826 2159143 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2157842 2158054 2158242 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2157192 2157349 2157525 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2156765 2156996 2157024 "SASTCAT" 2157029 SASTCAT (NIL) -9 NIL 2157042 NIL) (-995 2156232 2156657 2156731 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2155835 2155876 2156047 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2155466 2155507 2155664 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2148547 2155383 2155461 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2147197 2147526 2147922 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2145958 2146319 2146619 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2145582 2145803 2145884 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2143042 2143676 2144129 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2142881 2142914 2142982 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2142372 2142675 2142766 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2138000 2138868 2139779 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2126819 2132373 2132467 "RSETCAT" 2136523 RSETCAT (NIL T T T T) -9 NIL 2137611 NIL) (-983 2125357 2125999 2126814 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2119131 2120576 2122083 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2117013 2117570 2117642 "RRCC" 2118715 RRCC (NIL T T) -9 NIL 2119056 NIL) (-980 2116538 2116737 2117008 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2116008 2116318 2116416 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2088560 2099273 2099337 "RPOLCAT" 2109811 RPOLCAT (NIL T T T) -9 NIL 2112956 NIL) (-977 2082659 2085482 2088555 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2078826 2082407 2082545 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2077154 2077893 2078149 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2072797 2075609 2075637 "RNS" 2075899 RNS (NIL) -9 NIL 2076151 NIL) (-973 2071700 2072187 2072724 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2070818 2071219 2071419 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2069956 2070518 2070546 "RNG" 2070606 RNG (NIL) -9 NIL 2070660 NIL) (-970 2069845 2069879 2069951 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2069107 2069612 2069652 "RMODULE" 2069657 RMODULE (NIL T) -9 NIL 2069683 NIL) (-968 2068046 2068152 2068482 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2064892 2067636 2067929 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2057541 2060033 2060145 "RMATCAT" 2063450 RMATCAT (NIL NIL NIL T T T) -9 NIL 2064427 NIL) (-965 2057058 2057237 2057536 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2056626 2056837 2056878 "RLINSET" 2056939 RLINSET (NIL T) -9 NIL 2056983 NIL) (-963 2056271 2056352 2056478 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2055117 2055848 2055876 "RING" 2055931 RING (NIL) -9 NIL 2056023 NIL) (-961 2054962 2055018 2055112 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2054016 2054283 2054539 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2045003 2053644 2053845 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2044228 2044739 2044778 "RGBCSPC" 2044835 RGBCSPC (NIL T) -9 NIL 2044886 NIL) (-957 2043262 2043748 2043787 "RGBCMDL" 2044015 RGBCMDL (NIL T) -9 NIL 2044129 NIL) (-956 2042974 2043043 2043144 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2042737 2042778 2042873 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2041161 2041591 2041971 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2038748 2039416 2040084 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2038298 2038396 2038556 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2037920 2038018 2038059 "RETRACT" 2038190 RETRACT (NIL T) -9 NIL 2038277 NIL) (-950 2037800 2037831 2037915 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2037402 2037674 2037741 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2035882 2036773 2036970 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2035573 2035634 2035730 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2035316 2035357 2035462 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2035051 2035092 2035201 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2030122 2031573 2032788 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2027221 2027979 2028787 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2025190 2025812 2026412 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2017825 2023741 2024177 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2017137 2017417 2017566 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2016622 2016737 2016902 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2012215 2016025 2016246 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2011447 2011646 2011859 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2008737 2009575 2010457 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 2005319 2006355 2007414 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 2005155 2005208 2005236 "REAL" 2005241 REAL (NIL) -9 NIL 2005276 NIL) (-933 2004645 2004949 2005040 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 2004125 2004203 2004408 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 2003358 2003550 2003761 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 2002246 2002543 2002910 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 2000513 2000983 2001516 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1999435 1999712 2000099 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1998262 1998571 1998990 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1991610 1995122 1995150 "RCFIELD" 1996427 RCFIELD (NIL) -9 NIL 1997157 NIL) (-925 1990228 1990840 1991537 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1986428 1988320 1988361 "RCAGG" 1989428 RCAGG (NIL T) -9 NIL 1989889 NIL) (-923 1986155 1986265 1986423 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1985600 1985729 1985890 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1985217 1985296 1985415 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1984632 1984782 1984932 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1984414 1984464 1984535 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1976856 1983532 1983840 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1966558 1976723 1976851 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1966192 1966285 1966313 "RADCAT" 1966470 RADCAT (NIL) -9 NIL NIL NIL) (-915 1966030 1966090 1966187 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1964130 1965861 1965950 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1963811 1963860 1963987 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1956098 1960182 1960222 "QUATCAT" 1961000 QUATCAT (NIL T) -9 NIL 1961764 NIL) (-911 1953348 1954628 1956004 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1949188 1953298 1953343 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1946575 1948242 1948283 "QUAGG" 1948658 QUAGG (NIL T) -9 NIL 1948832 NIL) (-908 1946177 1946449 1946516 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1945183 1945813 1945976 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1944864 1944913 1945040 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1934489 1940658 1940698 "QFCAT" 1941356 QFCAT (NIL T) -9 NIL 1942349 NIL) (-904 1931373 1932812 1934395 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1930919 1931053 1931183 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1925115 1926276 1927438 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1924534 1924714 1924946 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1922356 1922884 1923307 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1921255 1921497 1921814 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1919616 1919814 1920167 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1915372 1916588 1916629 "PTRANFN" 1918513 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1914019 1914364 1914685 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1913712 1913775 1913882 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1907785 1912508 1912548 "PTCAT" 1912840 PTCAT (NIL T) -9 NIL 1912993 NIL) (-893 1907478 1907519 1907643 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1906357 1906673 1907007 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1895236 1897797 1900106 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1888143 1891039 1891133 "PSETCAT" 1894107 PSETCAT (NIL T T T T) -9 NIL 1894914 NIL) (-889 1886593 1887327 1888138 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1885912 1886107 1886135 "PSCURVE" 1886403 PSCURVE (NIL) -9 NIL 1886570 NIL) (-887 1881514 1883334 1883398 "PSCAT" 1884233 PSCAT (NIL T T T) -9 NIL 1884472 NIL) (-886 1880828 1881110 1881509 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1879225 1880140 1880403 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1878716 1879019 1879110 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1869736 1872158 1874346 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1867479 1869056 1869096 "PRQAGG" 1869279 PRQAGG (NIL T) -9 NIL 1869380 NIL) (-881 1866652 1867098 1867126 "PROPLOG" 1867265 PROPLOG (NIL) -9 NIL 1867379 NIL) (-880 1866327 1866390 1866513 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1865763 1865902 1866074 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1864011 1864774 1865071 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1863563 1863695 1863823 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1858004 1862503 1863323 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1857833 1857871 1857930 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1857272 1857412 1857563 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1855740 1856159 1856625 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1855457 1855518 1855546 "PRIMCAT" 1855670 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1854628 1854824 1855052 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1850506 1854578 1854623 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1850205 1850267 1850378 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1847341 1849854 1850087 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1846792 1846949 1846977 "PPCURVE" 1847182 PPCURVE (NIL) -9 NIL 1847318 NIL) (-866 1846405 1846650 1846733 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1844161 1844582 1845174 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1843604 1843668 1843901 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1840324 1840810 1841421 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1825915 1832044 1832108 "POLYCAT" 1835593 POLYCAT (NIL T T T) -9 NIL 1837470 NIL) (-861 1821425 1823572 1825910 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1821082 1821156 1821275 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1820775 1820838 1820945 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1814138 1820508 1820667 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1813025 1813288 1813564 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1811629 1811942 1812272 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1806791 1811579 1811624 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1805279 1805690 1806065 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1804036 1804345 1804741 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1803707 1803791 1803908 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1803286 1803361 1803535 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1802772 1802868 1803028 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1802244 1802364 1802518 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1801139 1801357 1801734 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1800750 1800835 1800987 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1800301 1800383 1800564 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1799993 1800074 1800187 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1799506 1799581 1799789 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1798854 1798982 1799184 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1798216 1798350 1798513 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1797520 1797702 1797883 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1797243 1797317 1797411 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1793811 1795000 1795916 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1792895 1793096 1793331 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1788460 1789844 1790986 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1768381 1773268 1778115 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1768121 1768174 1768277 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1767562 1767696 1767876 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1765571 1766792 1766820 "PID" 1767017 PID (NIL) -9 NIL 1767144 NIL) (-832 1765359 1765402 1765477 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1764546 1765206 1765293 "PI" NIL PI (NIL) -8 NIL NIL 1765333) (-830 1763998 1764149 1764325 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1760326 1761284 1762189 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1758690 1758979 1759345 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1758132 1758247 1758408 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1754673 1757001 1757354 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1753279 1753559 1753884 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1752044 1752298 1752646 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1750754 1750981 1751333 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1747764 1749324 1749352 "PFECAT" 1749945 PFECAT (NIL) -9 NIL 1750322 NIL) (-821 1747387 1747552 1747759 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1746211 1746493 1746794 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1744393 1744780 1745210 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1740363 1744319 1744388 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1736266 1737413 1738280 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1734198 1735287 1735328 "PERMCAT" 1735727 PERMCAT (NIL T) -9 NIL 1736024 NIL) (-815 1733894 1733941 1734064 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1730343 1732024 1732669 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1727808 1730098 1730219 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1726677 1726940 1726981 "PDSPC" 1727514 PDSPC (NIL T) -9 NIL 1727759 NIL) (-811 1726044 1726310 1726672 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1724679 1725672 1725713 "PDRING" 1725718 PDRING (NIL T) -9 NIL 1725745 NIL) (-809 1723389 1724178 1724231 "PDMOD" 1724236 PDMOD (NIL T T) -9 NIL 1724339 NIL) (-808 1722482 1722694 1722943 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1722087 1722154 1722208 "PDDOM" 1722373 PDDOM (NIL T T) -9 NIL 1722453 NIL) (-806 1721939 1721975 1722082 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1721725 1721764 1721853 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1720042 1720796 1721095 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1719731 1719794 1719903 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1717869 1718299 1718750 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1711489 1713318 1714610 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1711120 1711193 1711325 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1708822 1709502 1709983 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1707026 1707454 1707857 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1706472 1706720 1706761 "PATMAB" 1706868 PATMAB (NIL T) -9 NIL 1706951 NIL) (-796 1705119 1705523 1705780 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1704657 1704788 1704829 "PATAB" 1704834 PATAB (NIL T) -9 NIL 1705006 NIL) (-794 1703200 1703637 1704060 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1702878 1702953 1703055 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1702567 1702630 1702739 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1702372 1702418 1702485 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1702050 1702125 1702227 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1701739 1701802 1701911 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1701430 1701500 1701597 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1701119 1701182 1701291 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1700280 1700659 1700838 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1699887 1699985 1700104 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1698855 1699280 1699499 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1697520 1698174 1698534 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1690610 1696924 1697118 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1683031 1690108 1690292 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1679756 1681671 1681711 "PADICCT" 1682292 PADICCT (NIL NIL) -9 NIL 1682574 NIL) (-779 1677746 1679706 1679751 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1676908 1677118 1677384 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1676250 1676393 1676597 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1674631 1675658 1675936 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1674155 1674414 1674511 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1673214 1673892 1674064 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1663636 1666505 1668704 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1663028 1663342 1663468 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1662305 1662500 1662528 "OUTBCON" 1662846 OUTBCON (NIL) -9 NIL 1663012 NIL) (-770 1662013 1662143 1662300 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1661394 1661539 1661700 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1660765 1661192 1661281 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1660180 1660595 1660623 "OSGROUP" 1660628 OSGROUP (NIL) -9 NIL 1660650 NIL) (-766 1659144 1659405 1659690 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1656413 1659019 1659139 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1653554 1656164 1656290 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1651572 1652100 1652660 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1644914 1647454 1647494 "OREPCAT" 1649815 OREPCAT (NIL T) -9 NIL 1650917 NIL) (-761 1642940 1643874 1644909 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1642137 1642408 1642436 "ORDTYPE" 1642741 ORDTYPE (NIL) -9 NIL 1642899 NIL) (-759 1641671 1641882 1642132 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1641133 1641509 1641666 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1640627 1640990 1641018 "ORDSET" 1641023 ORDSET (NIL) -9 NIL 1641045 NIL) (-756 1639205 1640227 1640255 "ORDRING" 1640260 ORDRING (NIL) -9 NIL 1640288 NIL) (-755 1638453 1639010 1639038 "ORDMON" 1639043 ORDMON (NIL) -9 NIL 1639064 NIL) (-754 1637757 1637919 1638111 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1636968 1637476 1637504 "ORDFIN" 1637569 ORDFIN (NIL) -9 NIL 1637643 NIL) (-752 1636362 1636501 1636687 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1633037 1635330 1635736 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1632444 1632799 1632904 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1632252 1632297 1632363 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1631553 1631829 1631870 "OPERCAT" 1632081 OPERCAT (NIL T) -9 NIL 1632177 NIL) (-747 1631365 1631432 1631548 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1628731 1630167 1630663 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1628152 1628279 1628453 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1625053 1627291 1627657 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1621684 1624483 1624523 "OMSAGG" 1624584 OMSAGG (NIL T) -9 NIL 1624648 NIL) (-742 1620096 1621355 1621523 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1618305 1619546 1619574 "OINTDOM" 1619579 OINTDOM (NIL) -9 NIL 1619600 NIL) (-740 1615735 1617307 1617636 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1614989 1615685 1615730 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1612191 1614830 1614984 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1603728 1612062 1612186 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1597139 1603619 1603723 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1596111 1596348 1596621 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1593745 1594415 1595119 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1589522 1590482 1591505 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1589030 1589118 1589312 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1586479 1587061 1587734 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1583874 1584382 1584978 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1580871 1581410 1582056 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1580226 1580334 1580592 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1579384 1579509 1579730 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1575668 1576464 1577377 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1575108 1575203 1575425 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1574789 1574838 1574965 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1571392 1574588 1574707 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1570552 1571174 1571202 "OCAMON" 1571207 OCAMON (NIL) -9 NIL 1571228 NIL) (-721 1564764 1567578 1567618 "OC" 1568713 OC (NIL T) -9 NIL 1569569 NIL) (-720 1562764 1563690 1564670 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1562180 1562598 1562626 "OASGP" 1562631 OASGP (NIL) -9 NIL 1562651 NIL) (-718 1561243 1561892 1561920 "OAMONS" 1561960 OAMONS (NIL) -9 NIL 1562003 NIL) (-717 1560388 1560969 1560997 "OAMON" 1561054 OAMON (NIL) -9 NIL 1561105 NIL) (-716 1560284 1560316 1560383 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1559035 1559809 1559837 "OAGROUP" 1559983 OAGROUP (NIL) -9 NIL 1560075 NIL) (-714 1558765 1558883 1559030 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1558505 1558561 1558649 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1553567 1555130 1556657 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1550262 1551296 1552331 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1549372 1549605 1549823 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1538233 1541261 1543709 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1532120 1537674 1537768 "NTSCAT" 1537773 NTSCAT (NIL T T T T) -9 NIL 1537811 NIL) (-707 1531461 1531640 1531833 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1531154 1531217 1531324 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1518821 1528774 1529584 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1507830 1518686 1518816 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1506550 1506875 1507232 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1505386 1505650 1506008 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1504553 1504686 1504902 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1502871 1503190 1503596 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1502584 1502618 1502742 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1502403 1502438 1502507 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1502179 1502369 1502398 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1501743 1501810 1501987 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1500029 1501106 1501361 "NNI" NIL NNI (NIL) -8 NIL NIL 1501708) (-694 1498757 1499094 1499458 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1497734 1497986 1498288 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1496821 1497386 1497427 "NETCLT" 1497598 NETCLT (NIL T) -9 NIL 1497679 NIL) (-691 1495725 1495992 1496273 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1495524 1495567 1495642 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1494055 1494443 1494863 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1492688 1493654 1493682 "NASRING" 1493792 NASRING (NIL) -9 NIL 1493872 NIL) (-687 1492533 1492589 1492683 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1491462 1492140 1492168 "NARNG" 1492285 NARNG (NIL) -9 NIL 1492376 NIL) (-685 1491238 1491323 1491457 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1490004 1490758 1490798 "NAALG" 1490877 NAALG (NIL T) -9 NIL 1490938 NIL) (-683 1489874 1489909 1489999 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1484853 1486038 1487224 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1484248 1484335 1484519 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1476258 1480752 1480804 "MTSCAT" 1481864 MTSCAT (NIL T T) -9 NIL 1482378 NIL) (-679 1476024 1476084 1476176 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1475850 1475889 1475949 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1472712 1475401 1475442 "MSETAGG" 1475447 MSETAGG (NIL T) -9 NIL 1475481 NIL) (-676 1468849 1471758 1472076 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1465123 1466946 1467686 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1464760 1464833 1464962 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1464413 1464454 1464598 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1462278 1462615 1463046 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1455676 1462177 1462273 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1455201 1455242 1455450 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1454760 1454809 1454992 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1454034 1454127 1454346 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1452651 1453012 1453402 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1452172 1452239 1452278 "MONOPC" 1452338 MONOPC (NIL T) -9 NIL 1452557 NIL) (-665 1451623 1451959 1452087 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1450765 1451144 1451172 "MONOID" 1451390 MONOID (NIL) -9 NIL 1451534 NIL) (-663 1450424 1450574 1450760 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1439362 1446232 1446291 "MONOGEN" 1446965 MONOGEN (NIL T T) -9 NIL 1447421 NIL) (-661 1437374 1438260 1439243 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1436088 1436632 1436660 "MONADWU" 1437051 MONADWU (NIL) -9 NIL 1437286 NIL) (-659 1435636 1435836 1436083 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1434913 1435214 1435242 "MONAD" 1435449 MONAD (NIL) -9 NIL 1435561 NIL) (-657 1434680 1434776 1434908 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1433070 1433840 1434119 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1432204 1432731 1432771 "MODULE" 1432776 MODULE (NIL T) -9 NIL 1432814 NIL) (-654 1431883 1432009 1432199 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1429594 1430480 1430794 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1426773 1428190 1428703 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1425407 1425981 1426257 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1414626 1424072 1424485 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1411582 1413626 1413895 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1410666 1411033 1411223 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1410235 1410284 1410463 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1408060 1409056 1409096 "MLO" 1409513 MLO (NIL T) -9 NIL 1409753 NIL) (-645 1405941 1406468 1407063 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1405409 1405505 1405659 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1405079 1405155 1405278 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1404291 1404477 1404705 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1403784 1403900 1404056 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1403156 1403270 1403455 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1402183 1402456 1402733 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1401616 1401704 1401875 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1398774 1399653 1400532 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1397441 1397789 1398142 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1394098 1396565 1396606 "MDAGG" 1396863 MDAGG (NIL T) -9 NIL 1397008 NIL) (-634 1393372 1393536 1393736 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1392450 1392736 1392966 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1390547 1391124 1391685 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1386318 1390137 1390384 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1382667 1383436 1384170 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1381420 1381589 1381918 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1370933 1374522 1374598 "MATCAT" 1379586 MATCAT (NIL T T T) -9 NIL 1381054 NIL) (-627 1368214 1369520 1370928 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1366615 1366975 1367359 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1365748 1365945 1366167 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1364499 1364825 1365152 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1363661 1364063 1364239 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1363330 1363394 1363517 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1362978 1363051 1363165 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1362513 1362628 1362770 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1360722 1361490 1361791 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1360216 1360518 1360608 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1353725 1358531 1358572 "LZSTAGG" 1359349 LZSTAGG (NIL T) -9 NIL 1359639 NIL) (-616 1350844 1352278 1353720 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1348231 1349197 1349680 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1347812 1348091 1348165 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1339976 1347673 1347807 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1339339 1339484 1339712 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1336823 1337521 1338233 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1334935 1335258 1335706 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1328104 1334022 1334063 "LSAGG" 1334125 LSAGG (NIL T) -9 NIL 1334203 NIL) (-608 1325798 1326897 1328099 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1323278 1325147 1325396 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1322945 1323036 1323159 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1322616 1322695 1322723 "LOGIC" 1322834 LOGIC (NIL) -9 NIL 1322916 NIL) (-604 1322511 1322540 1322611 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1321830 1321988 1322181 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1320615 1320864 1321215 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1316437 1319236 1319276 "LODOCAT" 1319708 LODOCAT (NIL T) -9 NIL 1319919 NIL) (-600 1316230 1316306 1316432 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1313230 1316107 1316225 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1310328 1313180 1313225 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1307415 1310258 1310323 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1306468 1306643 1306945 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1304600 1305730 1305983 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1299695 1302759 1302800 "LNAGG" 1303662 LNAGG (NIL T) -9 NIL 1304097 NIL) (-593 1299082 1299349 1299690 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1295654 1296595 1297232 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1294916 1295421 1295461 "LMODULE" 1295466 LMODULE (NIL T) -9 NIL 1295492 NIL) (-590 1292095 1294653 1294775 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1291663 1291874 1291915 "LLINSET" 1291976 LLINSET (NIL T) -9 NIL 1292020 NIL) (-588 1291339 1291599 1291658 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1290938 1291018 1291157 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1289389 1289737 1290136 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1288560 1288756 1288984 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1281606 1287816 1288070 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1281183 1281416 1281457 "LINSET" 1281462 LINSET (NIL T) -9 NIL 1281495 NIL) (-582 1280084 1280806 1280973 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1278350 1279105 1279145 "LINEXP" 1279631 LINEXP (NIL T) -9 NIL 1279904 NIL) (-580 1276972 1277959 1278140 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1275799 1276071 1276373 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1275012 1275601 1275711 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1272562 1273284 1274034 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1271192 1271489 1271880 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1269985 1270587 1270627 "LIECAT" 1270767 LIECAT (NIL T) -9 NIL 1270918 NIL) (-574 1269859 1269892 1269980 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1264115 1269549 1269777 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1256464 1263791 1263947 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1252916 1253865 1254800 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1251540 1252448 1252476 "LFCAT" 1252683 LFCAT (NIL) -9 NIL 1252822 NIL) (-569 1249779 1250109 1250454 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1247296 1247961 1248642 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1244308 1245286 1245789 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1243799 1244102 1244193 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1242506 1242830 1243230 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1241772 1241857 1242083 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1236775 1240340 1240876 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1236400 1236450 1236610 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1235171 1235944 1235984 "LALG" 1236045 LALG (NIL T) -9 NIL 1236103 NIL) (-560 1234954 1235031 1235166 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1232807 1234222 1234473 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1232636 1232666 1232707 "KVTFROM" 1232769 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1231452 1232167 1232356 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1231281 1231311 1231352 "KRCFROM" 1231414 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1230383 1230580 1230875 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1230212 1230242 1230283 "KONVERT" 1230345 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1230041 1230071 1230112 "KOERCE" 1230174 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1229611 1229704 1229836 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1227664 1228558 1228930 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1220841 1225856 1225910 "KDAGG" 1226286 KDAGG (NIL T T) -9 NIL 1226493 NIL) (-549 1220489 1220631 1220836 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1213319 1220270 1220427 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1212969 1213251 1213314 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1211939 1212438 1212687 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1211065 1211514 1211719 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1209929 1210421 1210721 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1209211 1209610 1209771 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1208921 1209157 1209206 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1203176 1208611 1208839 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1202594 1202927 1203047 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1198756 1200771 1200825 "IXAGG" 1201752 IXAGG (NIL T T) -9 NIL 1202209 NIL) (-538 1197962 1198333 1198751 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1193216 1197898 1197957 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-536 1192183 1192458 1192721 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1190845 1191052 1191345 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1189796 1190018 1190301 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1189471 1189534 1189657 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1188733 1189105 1189279 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1186709 1188009 1188283 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1176257 1182026 1183183 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1175502 1175654 1175890 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1174993 1175296 1175387 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1174286 1174377 1174590 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1173418 1173643 1173883 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1171831 1172212 1172640 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1171616 1171660 1171736 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1170466 1170763 1171058 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1169739 1170090 1170241 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1168942 1169073 1169286 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1167097 1167594 1168138 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1164178 1165446 1166135 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1164003 1164043 1164103 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1160001 1163929 1163998 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1158004 1159940 1159996 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1157375 1157674 1157804 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1156828 1157116 1157248 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1155909 1156534 1156660 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1155319 1155813 1155841 "IOBCON" 1155846 IOBCON (NIL) -9 NIL 1155867 NIL) (-511 1154890 1154954 1155136 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1146934 1149305 1151630 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1144045 1144828 1145692 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1143722 1143819 1143936 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1141164 1143658 1143717 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1139276 1139805 1140372 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1138778 1138892 1139032 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1137162 1137568 1138030 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1134941 1135535 1136146 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1132314 1132924 1133644 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1131718 1131876 1132084 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1131237 1131323 1131511 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1129442 1129963 1130420 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1122524 1124177 1125906 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1121890 1122052 1122225 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1119763 1120227 1120771 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1117889 1118839 1118867 "INTDOM" 1119166 INTDOM (NIL) -9 NIL 1119371 NIL) (-494 1117442 1117644 1117884 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1113249 1115721 1115775 "INTCAT" 1116571 INTCAT (NIL T) -9 NIL 1116887 NIL) (-492 1112814 1112934 1113061 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1111654 1111826 1112132 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1111227 1111323 1111480 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1104267 1111082 1111222 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1103565 1104120 1104185 "INT8" NIL INT8 (NIL) -8 NIL NIL 1104219) (-487 1102862 1103417 1103482 "INT64" NIL INT64 (NIL) -8 NIL NIL 1103516) (-486 1102159 1102714 1102779 "INT32" NIL INT32 (NIL) -8 NIL NIL 1102813) (-485 1101456 1102011 1102076 "INT16" NIL INT16 (NIL) -8 NIL NIL 1102110) (-484 1097919 1101375 1101451 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1091976 1095459 1095487 "INS" 1096417 INS (NIL) -9 NIL 1097076 NIL) (-482 1090038 1090956 1091903 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1089097 1089320 1089595 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1088311 1088452 1088649 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1087301 1087442 1087679 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1086453 1086617 1086877 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1085733 1085848 1086036 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1084472 1084741 1085065 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1083752 1083893 1084076 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1083415 1083487 1083585 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1080493 1081979 1082502 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1080092 1080199 1080313 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1079248 1079893 1079994 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1078098 1078366 1078687 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1077088 1078028 1078093 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1076713 1076793 1076910 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1075627 1076172 1076376 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1071722 1072777 1073720 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1070576 1070899 1070927 "INBCON" 1071440 INBCON (NIL) -9 NIL 1071706 NIL) (-464 1070030 1070295 1070571 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1069524 1069826 1069916 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1068981 1069290 1069395 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1067821 1067960 1068275 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1066245 1066512 1066849 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1064061 1066127 1066240 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-458 1058904 1063992 1064056 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1058284 1058618 1058733 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1053091 1057722 1057908 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1052121 1053013 1053086 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1051693 1051770 1051824 "IEVALAB" 1052031 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1051448 1051528 1051688 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050833 1051060 1051217 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049826 1050753 1050828 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048889 1049746 1049821 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047971 1048618 1048755 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1046334 1046905 1046956 "IDPC" 1047462 IDPC (NIL T T) -9 NIL 1047775 NIL) (-447 1045621 1046256 1046329 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044791 1045543 1045616 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1044484 1044697 1044757 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1044188 1044228 1044267 "IDEMOPC" 1044272 IDEMOPC (NIL T) -9 NIL 1044409 NIL) (-443 1041259 1042140 1043032 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034885 1036162 1037201 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1034147 1034277 1034476 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1033320 1033819 1033957 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031709 1032040 1032431 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1027478 1031665 1031704 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024736 1025360 1026055 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022962 1023442 1023975 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020726 1022854 1022957 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-434 1016595 1020664 1020721 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1010174 1015559 1016027 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009742 1009805 1009978 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1009234 1009383 1009411 "HYPCAT" 1009618 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008890 1009043 1009229 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1008503 1008748 1008831 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1008336 1008385 1008426 "HOMOTOP" 1008431 HOMOTOP (NIL T) -9 NIL 1008464 NIL) (-427 1004904 1006278 1006319 "HOAGG" 1007294 HOAGG (NIL T) -9 NIL 1008015 NIL) (-426 1003910 1004380 1004899 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 997110 1003635 1003783 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 996045 996303 996566 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 994980 995910 996040 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 993174 994813 994901 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 992489 992841 992974 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 985943 992422 992484 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 979082 985679 985830 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 978535 978692 978855 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 971618 978426 978530 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 971109 971412 971503 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968659 970896 971075 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 964052 968542 968654 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 957138 963949 964047 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 949075 956507 956762 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 948099 948608 948636 "GROUP" 948839 GROUP (NIL) -9 NIL 948973 NIL) (-410 947642 947843 948094 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 946314 946653 947040 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 945136 945493 945544 "GRMOD" 946073 GRMOD (NIL T T) -9 NIL 946239 NIL) (-407 944955 945003 945131 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 941078 942289 943289 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939800 940124 940439 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 939353 939481 939622 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 938426 938925 938976 "GRALG" 939129 GRALG (NIL T T) -9 NIL 939219 NIL) (-402 938145 938246 938421 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934862 937827 938003 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 934275 934338 934595 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 930129 931025 931550 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 929304 929506 929744 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 924307 925234 926253 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 924055 924112 924201 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 923537 923626 923791 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 923046 923087 923300 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921847 922130 922434 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 915122 921537 921698 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904905 909912 911016 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 902957 904060 904088 "GCDDOM" 904343 GCDDOM (NIL) -9 NIL 904500 NIL) (-389 902580 902737 902952 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 893373 895843 898231 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 891508 891833 892251 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 890449 890638 890905 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 889320 889527 889831 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888783 888925 889073 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 887395 887743 888056 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 885940 886261 886583 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 883566 883922 884327 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876818 878479 880057 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 876470 876691 876759 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 876094 876315 876396 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 874191 874874 875334 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872784 873091 873483 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 871439 871798 872122 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870742 870866 871053 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869716 869982 870329 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 867374 867904 868386 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 866957 867017 867186 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 865257 866171 866474 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 864405 864539 864762 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 863576 863737 863964 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 859559 862510 862551 "FSAGG" 862921 FSAGG (NIL T) -9 NIL 863180 NIL) (-366 857913 858672 859464 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855869 856165 856709 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854916 855098 855398 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 854597 854646 854773 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834753 844254 844295 "FS" 848165 FS (NIL T) -9 NIL 850443 NIL) (-361 826984 830477 834456 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 826518 826645 826797 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 821041 824199 824239 "FRNAALG" 825559 FRNAALG (NIL T) -9 NIL 826157 NIL) (-358 817782 819033 820291 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 817463 817512 817639 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 815950 816507 816801 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 815236 815329 815616 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 813070 813836 814152 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 812179 812622 812663 "FRETRCT" 812668 FRETRCT (NIL T) -9 NIL 812839 NIL) (-352 811552 811830 812174 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 808296 809816 809875 "FRAMALG" 810757 FRAMALG (NIL T T) -9 NIL 811049 NIL) (-350 806892 807443 808073 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 806585 806648 806755 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 800226 806390 806580 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799919 799982 800089 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 792227 796798 798126 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 786005 789508 789536 "FPS" 790655 FPS (NIL) -9 NIL 791211 NIL) (-344 785562 785695 785859 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 782372 784415 784443 "FPC" 784668 FPC (NIL) -9 NIL 784810 NIL) (-342 782218 782270 782367 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 780995 781704 781745 "FPATMAB" 781750 FPATMAB (NIL T) -9 NIL 781902 NIL) (-340 779425 780021 780368 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 779000 779058 779231 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 777503 778398 778572 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 776118 776623 776651 "FNCAT" 777108 FNCAT (NIL) -9 NIL 777365 NIL) (-336 775575 776085 776113 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 774162 775524 775570 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770750 772108 772149 "FMONCAT" 773366 FMONCAT (NIL T) -9 NIL 773970 NIL) (-333 767608 768686 768739 "FMCAT" 769920 FMCAT (NIL T T) -9 NIL 770412 NIL) (-332 766308 767431 767530 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 765356 766156 766303 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 763543 763995 764489 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 761478 762014 762592 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754864 759815 760429 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 753345 754446 754486 "FLINEXP" 754491 FLINEXP (NIL T) -9 NIL 754584 NIL) (-326 752754 753013 753340 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 751969 752128 752349 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748852 749931 749983 "FLALG" 751210 FLALG (NIL T T) -9 NIL 751677 NIL) (-323 748023 748184 748411 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 741432 745442 745483 "FLAGG" 746738 FLAGG (NIL T) -9 NIL 747383 NIL) (-321 740540 740944 741427 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 737101 738365 738424 "FINRALG" 739552 FINRALG (NIL T T) -9 NIL 740060 NIL) (-319 736492 736757 737096 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735790 736086 736114 "FINITE" 736310 FINITE (NIL) -9 NIL 736417 NIL) (-317 735698 735724 735785 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727659 730250 730290 "FINAALG" 733942 FINAALG (NIL T) -9 NIL 735380 NIL) (-315 723926 725171 726294 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 722478 722897 722951 "FILECAT" 723635 FILECAT (NIL T T) -9 NIL 723851 NIL) (-313 721829 722303 722406 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 719077 720955 720983 "FIELD" 721023 FIELD (NIL) -9 NIL 721103 NIL) (-311 718102 718563 719072 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 716106 717052 717398 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 715349 715530 715749 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 710619 715287 715344 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 710281 710348 710483 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709821 709863 710072 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 706501 707378 708155 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701785 706433 706496 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 696464 701274 701464 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 690945 695745 696003 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 685152 690396 690607 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 684175 684385 684700 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 679615 682320 682348 "FFIELDC" 682967 FFIELDC (NIL) -9 NIL 683342 NIL) (-298 678684 679124 679610 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 678299 678357 678481 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 676443 676966 677483 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 671537 676242 676343 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 666637 671326 671433 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 661303 666428 666536 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660757 660806 661041 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 639332 650366 650452 "FFCAT" 655602 FFCAT (NIL T T T) -9 NIL 657038 NIL) (-290 635572 636798 638104 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 630415 635503 635567 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 629307 629776 629817 "FEVALAB" 629901 FEVALAB (NIL T) -9 NIL 630162 NIL) (-287 628712 628964 629302 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 625539 626450 626565 "FDIVCAT" 628132 FDIVCAT (NIL T T T T) -9 NIL 628568 NIL) (-285 625333 625365 625534 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624640 624733 625010 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 623126 624124 624327 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 622219 622603 622805 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 621341 621830 621970 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612928 617571 617611 "FAXF" 619412 FAXF (NIL T) -9 NIL 620102 NIL) (-279 610844 611648 612463 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605708 610366 610540 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 600166 602589 602641 "FAMR" 603652 FAMR (NIL T T) -9 NIL 604111 NIL) (-276 599365 599730 600161 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 598386 599307 599360 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 595980 596859 596912 "FAMONC" 597853 FAMONC (NIL T T) -9 NIL 598238 NIL) (-273 594536 595838 595975 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 592616 592977 593379 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591893 592090 592312 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583753 591340 591539 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581772 582342 582928 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578674 579316 580036 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573831 574538 575343 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 573520 573583 573692 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 558313 572569 572995 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548840 557633 557921 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 548334 548636 548726 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 548110 548300 548329 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547799 547867 547980 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 547316 547458 547499 "EVALAB" 547669 EVALAB (NIL T) -9 NIL 547773 NIL) (-259 546944 547090 547311 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 543987 545582 545610 "EUCDOM" 546164 EUCDOM (NIL) -9 NIL 546513 NIL) (-257 542914 543407 543982 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542639 542695 542795 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 542327 542391 542500 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 536098 537998 538026 "ES" 540768 ES (NIL) -9 NIL 542152 NIL) (-253 532613 534145 535937 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 531961 532114 532290 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 525050 531865 531956 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524739 524802 524911 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518366 521491 522924 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514669 515765 516858 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513498 513848 514153 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512383 513114 513142 "ENTIRER" 513147 ENTIRER (NIL) -9 NIL 513191 NIL) (-245 512272 512306 512378 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508905 510702 511051 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507997 508208 508262 "ELTAGG" 508642 ELTAGG (NIL T T) -9 NIL 508853 NIL) (-242 507777 507851 507992 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507523 507558 507612 "ELTAB" 507696 ELTAB (NIL T T) -9 NIL 507748 NIL) (-240 506774 506944 507143 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506498 506572 506600 "ELEMFUN" 506705 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506398 506425 506493 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500944 504439 504480 "ELAGG" 505417 ELAGG (NIL T) -9 NIL 505877 NIL) (-236 499742 500280 500939 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 499160 499327 499483 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 498073 498392 498671 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491466 493464 494291 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485445 487441 488251 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 483259 483665 484136 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 474259 476172 477713 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473372 473873 474022 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 472070 472744 472784 "DVARCAT" 473067 DVARCAT (NIL T) -9 NIL 473207 NIL) (-227 471489 471753 472065 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463556 471357 471484 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461894 462685 462726 "DSEXT" 463089 DSEXT (NIL T) -9 NIL 463383 NIL) (-224 460699 461223 461889 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460423 460488 460586 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456574 457790 458921 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 452220 453575 454639 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450895 451256 451642 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450581 450640 450758 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449556 449854 450144 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 449141 449216 449366 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441554 443666 445781 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 437071 438090 439169 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433666 435735 435776 "DQAGG" 436405 DQAGG (NIL T) -9 NIL 436678 NIL) (-213 420209 427849 427931 "DPOLCAT" 429768 DPOLCAT (NIL T T T T) -9 NIL 430311 NIL) (-212 416617 418265 420204 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409622 416515 416612 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402536 409451 409617 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402129 402389 402478 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401543 401991 402071 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400829 401154 401305 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393968 400565 400716 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391717 393034 393074 "DMEXT" 393079 DMEXT (NIL T) -9 NIL 393254 NIL) (-204 391373 391435 391579 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384698 390858 391048 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381364 383521 383562 "DLAGG" 384112 DLAGG (NIL T) -9 NIL 384341 NIL) (-201 379715 380586 380614 "DIVRING" 380706 DIVRING (NIL) -9 NIL 380789 NIL) (-200 379166 379410 379710 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377594 378011 378417 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376631 376852 377117 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370105 376563 376626 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358425 364885 364938 "DIRPCAT" 365194 DIRPCAT (NIL NIL T) -9 NIL 366067 NIL) (-195 356431 357201 358088 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355878 356044 356230 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352424 354764 354805 "DIOPS" 355237 DIOPS (NIL T) -9 NIL 355463 NIL) (-192 352084 352228 352419 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351091 351837 351865 "DIOID" 351870 DIOID (NIL) -9 NIL 351892 NIL) (-190 349919 350748 350776 "DIFRING" 350781 DIFRING (NIL) -9 NIL 350802 NIL) (-189 349555 349653 349681 "DIFFSPC" 349800 DIFFSPC (NIL) -9 NIL 349875 NIL) (-188 349296 349398 349550 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348199 348824 348864 "DIFFMOD" 348869 DIFFMOD (NIL T) -9 NIL 348966 NIL) (-186 347883 347940 347981 "DIFFDOM" 348102 DIFFDOM (NIL T) -9 NIL 348170 NIL) (-185 347764 347794 347878 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345437 346958 346998 "DIFEXT" 347003 DIFEXT (NIL T) -9 NIL 347155 NIL) (-183 342598 344938 344979 "DIAGG" 344984 DIAGG (NIL T) -9 NIL 345004 NIL) (-182 342154 342344 342593 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337366 341344 341621 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333824 334877 335887 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328374 332978 333305 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326940 327232 327607 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324060 325312 325708 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321780 323891 323980 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321163 321308 321490 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 318481 319205 320005 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 316590 317048 317610 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 315973 316306 316420 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309173 315698 315846 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307093 307603 308107 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306732 306781 306932 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 305991 306553 306644 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304015 304457 304817 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303307 303596 303742 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302758 302904 303056 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300120 300913 301640 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 299559 299705 299876 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 297631 297942 298309 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297188 297443 297544 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 296389 296772 296800 "CTORCAT" 296981 CTORCAT (NIL) -9 NIL 297093 NIL) (-159 296092 296226 296384 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 295585 295842 295950 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295001 295432 295505 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 294460 294577 294730 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290854 291610 292365 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290345 290648 290739 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 289564 289773 290001 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289068 289173 289377 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288821 288855 288961 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285760 286522 287240 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285279 285421 285560 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281172 283742 284234 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281046 281073 281101 "CONDUIT" 281138 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279925 280656 280684 "COMRING" 280689 COMRING (NIL) -9 NIL 280739 NIL) (-145 279090 279457 279635 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278786 278827 278955 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278479 278542 278649 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267321 278429 278474 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266782 266921 267081 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266535 266576 266674 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 247966 260216 260256 "COMPCAT" 261257 COMPCAT (NIL T) -9 NIL 262599 NIL) (-138 240504 244017 247610 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240263 240297 240399 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240093 240132 240190 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239674 239953 240027 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239251 239492 239579 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238446 238694 238722 "COMBOPC" 239060 COMBOPC (NIL) -9 NIL 239235 NIL) (-132 237510 237762 238004 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234442 235126 235749 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233322 233773 234008 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232813 233116 233207 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232500 232553 232678 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 231970 232280 232378 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228490 229560 230640 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226785 227770 228008 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222897 224905 224946 "CLAGG" 225872 CLAGG (NIL T) -9 NIL 226405 NIL) (-123 221790 222317 222892 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221419 221510 221650 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219356 219863 220411 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218317 219048 219076 "CHARZ" 219081 CHARZ (NIL) -9 NIL 219095 NIL) (-119 218111 218157 218235 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 216950 217713 217741 "CHARNZ" 217802 CHARNZ (NIL) -9 NIL 217850 NIL) (-117 214428 215525 216048 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214136 214215 214243 "CFCAT" 214354 CFCAT (NIL) -9 NIL NIL NIL) (-115 213479 213608 213790 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209468 212892 213172 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208846 209033 209210 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208374 208793 208841 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207847 208156 208253 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207338 207641 207732 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 206587 206747 206968 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202687 203944 204652 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201053 202084 202335 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 200634 200913 200987 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200068 200321 200349 "CACHSET" 200481 CACHSET (NIL) -9 NIL 200559 NIL) (-104 199420 199835 199863 "CABMON" 199913 CABMON (NIL) -9 NIL 199969 NIL) (-103 198950 199214 199324 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 194173 198607 198779 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 193143 193847 193982 "BYTE" NIL BYTE (NIL) -8 NIL NIL 194145) (-100 190614 192910 193016 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 188045 190357 190476 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 185285 187489 187528 "BTCAT" 187595 BTCAT (NIL T) -9 NIL 187671 NIL) (-97 185036 185134 185280 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 180146 184267 184293 "BTAGG" 184404 BTAGG (NIL) -9 NIL 184512 NIL) (-95 179777 179938 180141 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176839 179247 179459 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 176109 176261 176439 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172642 174815 174854 "BRAGG" 175495 BRAGG (NIL T) -9 NIL 175752 NIL) (-91 171597 172092 172637 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164131 171102 171283 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162123 164083 164126 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161856 161892 162003 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160095 160528 160976 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156061 157477 158367 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154937 155828 155950 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154523 154680 154706 "BOOLE" 154814 BOOLE (NIL) -9 NIL 154895 NIL) (-83 154316 154397 154518 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153454 153981 154031 "BMODULE" 154036 BMODULE (NIL T T) -9 NIL 154100 NIL) (-81 149071 153311 153380 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148884 148924 148963 "BINOPC" 148968 BINOPC (NIL T) -9 NIL 149013 NIL) (-79 148426 148699 148801 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147947 148091 148229 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141153 147677 147822 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138887 140382 140421 "BGAGG" 140677 BGAGG (NIL T) -9 NIL 140814 NIL) (-75 138756 138794 138882 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 137607 137808 138093 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 134245 136765 137092 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133830 133923 133949 "BASTYPE" 134120 BASTYPE (NIL) -9 NIL 134216 NIL) (-71 133600 133696 133825 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 133115 133203 133353 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 132014 132689 132874 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131740 131745 131771 "ATTREG" 131776 ATTREG (NIL) -9 NIL NIL NIL) (-67 131345 131617 131682 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130845 130994 131020 "ATRIG" 131221 ATRIG (NIL) -9 NIL NIL NIL) (-65 130700 130753 130840 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 130270 130501 130527 "ASTCAT" 130532 ASTCAT (NIL) -9 NIL 130562 NIL) (-63 130069 130146 130265 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 128228 129902 129990 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 127035 127348 127713 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124835 126939 127030 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 124026 124217 124438 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 119613 123757 123871 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113779 115811 115886 "ARR2CAT" 118516 ARR2CAT (NIL T T T) -9 NIL 119274 NIL) (-56 112156 112926 113774 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111524 111895 112017 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110456 110624 110920 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110157 110211 110329 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109540 109686 109842 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 108945 109235 109355 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106513 107674 107997 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106038 106298 106394 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99733 105100 105542 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95267 96930 96980 "AMR" 97718 AMR (NIL T T) -9 NIL 98315 NIL) (-46 94621 94901 95262 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77801 94555 94616 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74204 77477 77646 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71214 71874 72481 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70593 70706 70890 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67005 67630 68222 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56494 66698 66848 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55811 55965 56143 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54524 55319 55357 "ALGEBRA" 55362 ALGEBRA (NIL T) -9 NIL 55402 NIL) (-37 54310 54387 54519 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34307 51516 51568 "ALAGG" 51706 ALAGG (NIL T T) -9 NIL 51871 NIL) (-35 33807 33956 33982 "AHYP" 34183 AHYP (NIL) -9 NIL NIL NIL) (-34 33103 33284 33310 "AGG" 33591 AGG (NIL) -9 NIL 33778 NIL) (-33 32892 32979 33098 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31031 31491 31891 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30526 30829 30918 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29896 30191 30347 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17454 26733 26771 "ACFS" 27378 ACFS (NIL T) -9 NIL 27617 NIL) (-28 16077 16687 17449 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11629 14008 14034 "ACF" 14913 ACF (NIL) -9 NIL 15325 NIL) (-26 10725 11131 11624 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10227 10467 10493 "ABELSG" 10585 ABELSG (NIL) -9 NIL 10650 NIL) (-24 10125 10156 10222 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9280 9654 9680 "ABELMON" 9905 ABELMON (NIL) -9 NIL 10038 NIL) (-22 8962 9102 9275 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8174 8657 8683 "ABELGRP" 8755 ABELGRP (NIL) -9 NIL 8830 NIL) (-20 7788 7953 8169 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 7046 7085 "A1AGG" 7090 A1AGG (NIL T) -9 NIL 7130 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index b1131e15..1abc242b 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,793 +1,793 @@
 
-(631062 . 3577223101)        
+(631058 . 3577234983)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-963) (-582 (-485))))
-   (-5 *2 (-1180 (-348 (-485)))) (-5 *1 (-1209 *4))))) 
+  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484))))
+   (-5 *2 (-1179 (-348 (-484)))) (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-963) (-582 (-485))))
-   (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4))))) 
+  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484))))
+   (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-963) (-582 (-485)))) (-5 *2 (-85))
-   (-5 *1 (-1209 *4))))) 
+  (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-85))
+   (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-555 *2) (-146))) (-5 *2 (-802 *4)) (-5 *1 (-144 *4 *5 *3))
-   (-4 *4 (-1015)) (-4 *3 (-139 *5))))
+  (-12 (-4 *5 (-13 (-554 *2) (-146))) (-5 *2 (-801 *4)) (-5 *1 (-144 *4 *5 *3))
+   (-4 *4 (-1014)) (-4 *3 (-139 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-351 *3 *4))
-   (-4 *4 (-1156 *3))))
+  (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-351 *3 *4))
+   (-4 *4 (-1155 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-351 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1156 *3))
-   (-5 *2 (-1180 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-359 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-359 *3)) (-4 *3 (-146)) (-5 *2 (-1180 *3))))
+  (-12 (-4 *1 (-351 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1155 *3))
+   (-5 *2 (-1179 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-359 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-359 *3)) (-4 *3 (-146)) (-5 *2 (-1179 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-346 *1)) (-4 *1 (-362 *3)) (-4 *3 (-496)) (-4 *3 (-1015))))
+  (-12 (-5 *2 (-346 *1)) (-4 *1 (-362 *3)) (-4 *3 (-495)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-585 *6)) (-4 *6 (-979 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-719))
-   (-4 *5 (-758)) (-5 *1 (-401 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1017)) (-5 *1 (-474))))
- ((*1 *2 *1) (-12 (-4 *1 (-555 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2) (-12 (-4 *1 (-559 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-663 *3 *2)) (-4 *2 (-1156 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-585 (-802 *3))) (-5 *1 (-802 *3)) (-4 *3 (-1015))))
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-401 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1016)) (-5 *1 (-473))))
+ ((*1 *2 *1) (-12 (-4 *1 (-554 *2)) (-4 *2 (-1129))))
+ ((*1 *1 *2) (-12 (-4 *1 (-558 *2)) (-4 *2 (-1129))))
+ ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-662 *3 *2)) (-4 *2 (-1155 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-859 *3)) (-4 *3 (-963)) (-4 *1 (-979 *3 *4 *5))
-   (-4 *5 (-555 (-1091))) (-4 *4 (-719)) (-4 *5 (-758))))
+  (-12 (-5 *2 (-858 *3)) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5))
+   (-4 *5 (-554 (-1090))) (-4 *4 (-718)) (-4 *5 (-757))))
  ((*1 *1 *2)
   (OR
-   (-12 (-5 *2 (-859 (-485))) (-4 *1 (-979 *3 *4 *5))
-    (-12 (-2562 (-4 *3 (-38 (-348 (-485))))) (-4 *3 (-38 (-485)))
-     (-4 *5 (-555 (-1091))))
-    (-4 *3 (-963)) (-4 *4 (-719)) (-4 *5 (-758)))
-   (-12 (-5 *2 (-859 (-485))) (-4 *1 (-979 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-348 (-485)))) (-4 *5 (-555 (-1091)))) (-4 *3 (-963))
-    (-4 *4 (-719)) (-4 *5 (-758)))))
+   (-12 (-5 *2 (-858 (-484))) (-4 *1 (-978 *3 *4 *5))
+    (-12 (-2561 (-4 *3 (-38 (-348 (-484))))) (-4 *3 (-38 (-484)))
+     (-4 *5 (-554 (-1090))))
+    (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
+   (-12 (-5 *2 (-858 (-484))) (-4 *1 (-978 *3 *4 *5))
+    (-12 (-4 *3 (-38 (-348 (-484)))) (-4 *5 (-554 (-1090)))) (-4 *3 (-962))
+    (-4 *4 (-718)) (-4 *5 (-757)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-859 (-348 (-485)))) (-4 *1 (-979 *3 *4 *5))
-   (-4 *3 (-38 (-348 (-485)))) (-4 *5 (-555 (-1091))) (-4 *3 (-963))
-   (-4 *4 (-719)) (-4 *5 (-758))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-585 *7)) (|:| -1601 *8)))
-   (-4 *7 (-979 *4 *5 *6)) (-4 *8 (-985 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-719)) (-4 *6 (-758)) (-5 *2 (-1074))
-   (-5 *1 (-983 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-585 *7)) (|:| -1601 *8)))
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-   (-4 *5 (-719)) (-4 *6 (-758)) (-5 *2 (-1074))
-   (-5 *1 (-1060 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1017)) (-5 *1 (-1096))))
- ((*1 *2 *1) (-12 (-5 *2 (-1017)) (-5 *1 (-1096))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-774)) (-5 *3 (-485)) (-5 *1 (-1110))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-774)) (-5 *3 (-485)) (-5 *1 (-1110))))
- ((*1 *2 *3)
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-   (-14 *5 (-585 (-1091))) (-5 *2 (-705 *4 (-775 *6))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *6 (-585 (-1091)))))
- ((*1 *2 *3)
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-   (-5 *2 (-859 (-939 (-348 *4)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-585 (-1091))) (-14 *6 (-585 (-1091)))))
- ((*1 *2 *3)
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-   (-14 *6 (-585 (-1091))) (-5 *2 (-859 (-939 (-348 *4))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *5 (-585 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1086 *4)) (-4 *4 (-13 (-757) (-258) (-120) (-935)))
-   (-5 *2 (-1086 (-939 (-348 *4)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-585 (-1091))) (-14 *6 (-585 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1061 *4 (-470 (-775 *6)) (-775 *6) (-705 *4 (-775 *6))))
-   (-4 *4 (-13 (-757) (-258) (-120) (-935))) (-14 *6 (-585 (-1091)))
-   (-5 *2 (-585 (-705 *4 (-775 *6)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-585 (-1091)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-346 *3)) (-5 *1 (-498 *3)) (-4 *3 (-484))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-258)) (-5 *2 (-346 *3))
-   (-5 *1 (-683 *4 *5 *6 *3)) (-4 *3 (-863 *6 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-258)) (-4 *7 (-863 *6 *4 *5))
-   (-5 *2 (-346 (-1086 *7))) (-5 *1 (-683 *4 *5 *6 *7)) (-5 *3 (-1086 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-390)) (-4 *3 (-963)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-5 *2 (-346 *1)) (-4 *1 (-863 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-758)) (-4 *5 (-719)) (-4 *6 (-390)) (-5 *2 (-346 *3))
-   (-5 *1 (-894 *4 *5 *6 *3)) (-4 *3 (-863 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-390)) (-4 *7 (-863 *6 *4 *5))
-   (-5 *2 (-346 (-1086 (-348 *7)))) (-5 *1 (-1088 *4 *5 *6 *7))
-   (-5 *3 (-1086 (-348 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-346 *1)) (-4 *1 (-1135))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-496)) (-5 *2 (-346 *3)) (-5 *1 (-1160 *4 *3))
-   (-4 *3 (-13 (-1156 *4) (-496) (-10 -8 (-15 -3146 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-960 *4 *5)) (-4 *4 (-13 (-757) (-258) (-120) (-935)))
-   (-14 *5 (-585 (-1091)))
-   (-5 *2 (-585 (-1061 *4 (-470 (-775 *6)) (-775 *6) (-705 *4 (-775 *6)))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-585 (-1091)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-960 *4 *5)) (-4 *4 (-13 (-757) (-258) (-120) (-935)))
-   (-14 *5 (-585 (-1091))) (-5 *2 (-585 (-585 (-939 (-348 *4)))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-585 (-1091)))))
+  (-12 (-5 *2 (-858 (-348 (-484)))) (-4 *1 (-978 *3 *4 *5))
+   (-4 *3 (-38 (-348 (-484)))) (-4 *5 (-554 (-1090))) (-4 *3 (-962))
+   (-4 *4 (-718)) (-4 *5 (-757))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1600 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-390))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1073))
+   (-5 *1 (-982 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1600 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-1021 *4 *5 *6 *7)) (-4 *4 (-390))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1073))
+   (-5 *1 (-1059 *4 *5 *6 *7 *8))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1016)) (-5 *1 (-1095))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1016)) (-5 *1 (-1095))))
+ ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-773)) (-5 *3 (-484)) (-5 *1 (-1109))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-773)) (-5 *3 (-484)) (-5 *1 (-1109))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *5))) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-14 *5 (-584 (-1090))) (-5 *2 (-704 *4 (-774 *6))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *6 (-584 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-858 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-5 *2 (-858 (-938 (-348 *4)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-584 (-1090))) (-14 *6 (-584 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *6))) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-14 *6 (-584 (-1090))) (-5 *2 (-858 (-938 (-348 *4))))
+   (-5 *1 (-1207 *4 *5 *6)) (-14 *5 (-584 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-5 *2 (-1085 (-938 (-348 *4)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-584 (-1090))) (-14 *6 (-584 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1060 *4 (-469 (-774 *6)) (-774 *6) (-704 *4 (-774 *6))))
+   (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *6 (-584 (-1090)))
+   (-5 *2 (-584 (-704 *4 (-774 *6)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-584 (-1090)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-346 *3)) (-5 *1 (-497 *3)) (-4 *3 (-483))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-258)) (-5 *2 (-346 *3))
+   (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-862 *6 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-258)) (-4 *7 (-862 *6 *4 *5))
+   (-5 *2 (-346 (-1085 *7))) (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1085 *7))))
+ ((*1 *2 *1)
+  (-12 (-4 *3 (-390)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-5 *2 (-346 *1)) (-4 *1 (-862 *3 *4 *5))))
+ ((*1 *2 *3)
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@@ -796,10390 +796,10390 @@
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+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1182))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1183))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1183))))) 
+(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
+(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1073)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *3 *4 *4)
-  (-12 (-5 *3 (-696)) (-5 *4 (-832)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-696)) (-5 *4 (-832)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
+  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
 (((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3847 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
    (-5 *1 (-221))))
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3847 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
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- ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1186)) (-5 *1 (-1184))))
+   (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1185)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1185)) (-5 *1 (-1183))))
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-  (-12 (-5 *3 (-485)) (-5 *4 (-328)) (-5 *2 (-1186)) (-5 *1 (-1184))))
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   (-12
    (-5 *3
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3847 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *2 (-1186)) (-5 *1 (-1184))))
+   (-5 *2 (-1185)) (-5 *1 (-1183))))
  ((*1 *2 *1)
   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3847 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *1 (-1184))))
+   (-5 *1 (-1183))))
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-  (-12 (-5 *3 (-328)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
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+(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-785)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-485)) (-5 *2 (-1186)) (-5 *1 (-1184))))
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1002 (-179))) (-5 *1 (-837))))
+ ((*1 *1 *1 *2 *2 *2) (-12 (-5 *2 (-1002 (-179))) (-5 *1 (-839))))
+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1185)) (-5 *1 (-1183))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-328)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1183))))
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-130)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-328)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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 (((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-585 (-1074))) (-5 *2 (-1074)) (-5 *1 (-1183))))
- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1183))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1183))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1182))))
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- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1184))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-145))))
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-(((*1 *1 *2 *3) (-12 (-5 *2 (-406)) (-5 *3 (-585 (-221))) (-5 *1 (-1183))))
- ((*1 *1 *1) (-5 *1 (-1183)))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-1185)) (-5 *1 (-1182))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1185)) (-5 *1 (-1183))))) 
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+ ((*1 *1 *1) (-5 *1 (-1182)))) 
 (((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5)
-  (-12 (-5 *3 (-832)) (-5 *4 (-179)) (-5 *5 (-485)) (-5 *6 (-785))
-   (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-179)) (-5 *5 (-484)) (-5 *6 (-784))
+   (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-1180
+    (-1179
      (-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179))
-      (|:| |deltaY| (-179)) (|:| -3851 (-485)) (|:| -3849 (-485))
-      (|:| |spline| (-485)) (|:| -3880 (-485)) (|:| |axesColor| (-785))
-      (|:| -3852 (-485)) (|:| |unitsColor| (-785)) (|:| |showing| (-485)))))
-   (-5 *1 (-1183))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1093 (-348 (-485)))) (-5 *1 (-164))))
- ((*1 *2 *1) (-12 (-5 *2 (-1180 (-3 (-406) "undefined"))) (-5 *1 (-1183))))) 
+      (|:| |deltaY| (-179)) (|:| -3850 (-484)) (|:| -3848 (-484))
+      (|:| |spline| (-484)) (|:| -3879 (-484)) (|:| |axesColor| (-784))
+      (|:| -3851 (-484)) (|:| |unitsColor| (-784)) (|:| |showing| (-484)))))
+   (-5 *1 (-1182))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1092 (-348 (-484)))) (-5 *1 (-164))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1179 (-3 (-406) "undefined"))) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-406)) (-5 *4 (-832)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-832)) (-5 *2 (-406)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-406)) (-5 *4 (-831)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-831)) (-5 *2 (-406)) (-5 *1 (-1182))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-585 (-328))) (-5 *3 (-585 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-585 (-328))) (-5 *1 (-406))))
- ((*1 *2 *1) (-12 (-5 *2 (-585 (-328))) (-5 *1 (-406))))
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+ ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-328))) (-5 *1 (-406))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-328))) (-5 *1 (-406))))
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-  (-12 (-5 *3 (-832)) (-5 *4 (-785)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1185)) (-5 *1 (-1182))))
  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
-(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-181 *2)) (-4 *2 (-13 (-312) (-1116)))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-657 *2)) (-4 *2 (-312))))
- ((*1 *1 *2) (-12 (-5 *1 (-657 *2)) (-4 *2 (-312))))
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+ ((*1 *1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
+ ((*1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
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-  (-12 (-5 *3 (-832)) (-5 *4 (-328)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-328)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-832)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-406)) (-5 *4 (-832)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-406)) (-5 *4 (-831)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
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-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *4 (-785)) (-5 *5 (-832))
-   (-5 *6 (-585 (-221))) (-5 *2 (-1183)) (-5 *1 (-1182))))
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+   (-5 *6 (-584 (-221))) (-5 *2 (-1182)) (-5 *1 (-1181))))
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-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *4 (-585 (-221)))
-   (-5 *2 (-1183)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221)))
+   (-5 *2 (-1182)) (-5 *1 (-1181))))) 
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-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *4 (-785)) (-5 *5 (-832))
-   (-5 *6 (-585 (-221))) (-5 *2 (-406)) (-5 *1 (-1182))))
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+   (-5 *6 (-584 (-221))) (-5 *2 (-406)) (-5 *1 (-1181))))
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-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *2 (-406)) (-5 *1 (-1182))))
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-406)) (-5 *1 (-1181))))
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-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *4 (-585 (-221))) (-5 *2 (-406))
-   (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221))) (-5 *2 (-406))
+   (-5 *1 (-1181))))) 
 (((*1 *1 *1) (-5 *1 (-48)))
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-  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1130)) (-4 *2 (-1130))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1129)) (-4 *2 (-1129))
    (-5 *1 (-59 *5 *2))))
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-   (-4 *1 (-124 *2)) (-4 *2 (-1130))))
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+   (-4 *1 (-124 *2)) (-4 *2 (-1129))))
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-  (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *2))
-   (-4 *2 (-1130))))
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+   (-4 *2 (-1129))))
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-  (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *2))
-   (-4 *2 (-1130))))
+  (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3995)) (-4 *1 (-124 *2))
+   (-4 *2 (-1129))))
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+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))
+ ((*1 *1 *1 *1) (-5 *1 (-1137))) ((*1 *1 *1 *1) (-5 *1 (-1138)))) 
 (((*1 *1 *1 *1) (-5 *1 (-101)))
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- ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))
- ((*1 *1 *1 *1) (-5 *1 (-1138))) ((*1 *1 *1 *1) (-5 *1 (-1139)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))
+ ((*1 *1 *1 *1) (-5 *1 (-1137))) ((*1 *1 *1 *1) (-5 *1 (-1138)))) 
 (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-101)))
  ((*1 *1)
-  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-485)) (-14 *3 (-696)) (-4 *4 (-146))))
- ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487))) ((*1 *1) (-5 *1 (-488)))
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- ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-832))))
- ((*1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-832)))) ((*1 *1) (-5 *1 (-1136)))
- ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138))) ((*1 *1) (-5 *1 (-1139)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-142 (-485))) (-5 *2 (-85)) (-5 *1 (-384))))
+  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-484)) (-14 *3 (-695)) (-4 *4 (-146))))
+ ((*1 *1) (-5 *1 (-485))) ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487)))
+ ((*1 *1) (-5 *1 (-488))) ((*1 *1) (-4 *1 (-664))) ((*1 *1) (-5 *1 (-1090)))
+ ((*1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-831))))
+ ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-831)))) ((*1 *1) (-5 *1 (-1135)))
+ ((*1 *1) (-5 *1 (-1136))) ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138)))) 
+(((*1 *2 *3) (-12 (-5 *3 (-142 (-484))) (-5 *2 (-85)) (-5 *1 (-384))))
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   (-12
    (-5 *3
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- ((*1 *2 *1) (-12 (-4 *1 (-1135)) (-5 *2 (-85))))) 
-(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1133))))) 
+    (-442 (-348 (-484)) (-197 *5 (-695)) (-774 *4) (-206 *4 (-348 (-484)))))
+   (-14 *4 (-584 (-1090))) (-14 *5 (-695)) (-5 *2 (-85)) (-5 *1 (-443 *4 *5))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-874 *3)) (-4 *3 (-483))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1134)) (-5 *2 (-85))))) 
+(((*1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-1132))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3230 (-585 (-1091))) (|:| -3231 (-585 (-1091)))))
-   (-5 *1 (-1133))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-585 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-585 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))) 
+  (-12 (-5 *2 (-2 (|:| -3229 (-584 (-1090))) (|:| -3230 (-584 (-1090)))))
+   (-5 *1 (-1132))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-584 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-696)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-758)) (-4 *3 (-1015))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-757)) (-4 *3 (-1014))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-585 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1132 *2))
-   (-4 *2 (-1015))))
+  (-12 (-5 *3 (-584 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1131 *2))
+   (-4 *2 (-1014))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-585 *2)) (-4 *2 (-1015)) (-4 *2 (-758)) (-5 *1 (-1132 *2))))) 
-(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1015))))) 
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+(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1014))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-696)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1015))))
+  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1014))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1015)) (-5 *2 (-85))
-   (-5 *1 (-1132 *3))))) 
+  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1014)) (-5 *2 (-85))
+   (-5 *1 (-1131 *3))))) 
 (((*1 *2)
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+   (-5 *1 (-1131 *3)) (-4 *3 (-1014))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-585 *4)) (-4 *4 (-1015)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))
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  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *4)) (-4 *4 (-1015)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))) 
+  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1185)) (-5 *1 (-1131 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-485)) (-4 *5 (-299)) (-5 *2 (-346 (-1086 (-1086 *5))))
-   (-5 *1 (-1129 *5)) (-5 *3 (-1086 (-1086 *5)))))) 
+  (-12 (-5 *4 (-484)) (-4 *5 (-299)) (-5 *2 (-346 (-1085 (-1085 *5))))
+   (-5 *1 (-1128 *5)) (-5 *3 (-1085 (-1085 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-346 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
-   (-5 *3 (-1086 (-1086 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-346 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
+   (-5 *3 (-1085 (-1085 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-346 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
-   (-5 *3 (-1086 (-1086 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-346 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
+   (-5 *3 (-1085 (-1085 *4)))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *3))
-   (-4 *3 (-1130))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1130)) (-5 *1 (-537 *3))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-618 *3)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3995)) (-4 *1 (-124 *3))
+   (-4 *3 (-1129))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1129)) (-5 *1 (-536 *3))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1129))))
  ((*1 *2 *1 *3)
-  (|partial| -12 (-4 *1 (-1125 *4 *5 *3 *2)) (-4 *4 (-496)) (-4 *5 (-719))
-   (-4 *3 (-758)) (-4 *2 (-979 *4 *5 *3))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-696)) (-5 *1 (-1128 *2)) (-4 *2 (-1130))))) 
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+   (-4 *3 (-757)) (-4 *2 (-978 *4 *5 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-5 *1 (-1127 *2)) (-4 *2 (-1129))))) 
 (((*1 *2 *3 *3 *3 *4 *5)
-  (-12 (-5 *5 (-585 (-585 (-179)))) (-5 *4 (-179)) (-5 *2 (-585 (-856 *4)))
-   (-5 *1 (-1127)) (-5 *3 (-856 *4))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-485)) (-5 *2 (-585 (-585 (-179)))) (-5 *1 (-1127))))) 
+  (-12 (-5 *5 (-584 (-584 (-179)))) (-5 *4 (-179)) (-5 *2 (-584 (-855 *4)))
+   (-5 *1 (-1126)) (-5 *3 (-855 *4))))) 
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 (((*1 *1 *2)
-  (-12 (-5 *2 (-832)) (-4 *1 (-196 *3 *4)) (-4 *4 (-963)) (-4 *4 (-1130))))
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  ((*1 *1 *2)
-  (-12 (-14 *3 (-585 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-696)))
+  (-12 (-14 *3 (-584 (-1090))) (-4 *4 (-146)) (-4 *5 (-196 (-3957 *3) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2402 *2) (|:| -2403 *5))
-     (-2 (|:| -2402 *2) (|:| -2403 *5))))
-   (-5 *1 (-399 *3 *4 *2 *5 *6 *7)) (-4 *2 (-758))
-   (-4 *7 (-863 *4 *5 (-775 *3)))))
- ((*1 *2 *2) (-12 (-5 *2 (-856 (-179))) (-5 *1 (-1127))))) 
+    (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5))
+     (-2 (|:| -2401 *2) (|:| -2402 *5))))
+   (-5 *1 (-399 *3 *4 *2 *5 *6 *7)) (-4 *2 (-757))
+   (-4 *7 (-862 *4 *5 (-774 *3)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1126))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-856 (-179))) (-5 *4 (-785)) (-5 *2 (-1186)) (-5 *1 (-406))))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-585 *3)) (-4 *1 (-1049 *3)) (-4 *3 (-963))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-856 *3)) (-4 *1 (-1049 *3)) (-4 *3 (-963))))
+  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *2 (-1185)) (-5 *1 (-406))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-962)) (-4 *1 (-894 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1048 *3)) (-4 *3 (-962)) (-5 *2 (-855 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *3 (-962)) (-4 *1 (-1048 *3))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1048 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-962))))
  ((*1 *2 *3 *3 *3 *3)
-  (-12 (-5 *2 (-856 (-179))) (-5 *1 (-1127)) (-5 *3 (-179))))) 
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 (((*1 *2 *3 *4 *5)
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-   (-4 *3 (-889))))
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+   (-4 *3 (-888))))
  ((*1 *1 *2 *3 *4)
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-889))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-85)) (-5 *1 (-1125 *2))
+   (-4 *2 (-888))))) 
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+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-145))))
- ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-889))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *1 (-1126 *3)) (-4 *3 (-889))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-1126 *2)) (-4 *2 (-889))))) 
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 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
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+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
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+  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
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-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
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+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
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-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-4 *6 (-979 *3 *4 *5)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *4 *5)
   (|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9))
-   (-4 *9 (-979 *6 *7 *8)) (-4 *6 (-496)) (-4 *7 (-719)) (-4 *8 (-758))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-585 *9)))) (-5 *3 (-585 *9))
-   (-4 *1 (-1125 *6 *7 *8 *9))))
+   (-4 *9 (-978 *6 *7 *8)) (-4 *6 (-495)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-584 *9)))) (-5 *3 (-584 *9))
+   (-4 *1 (-1124 *6 *7 *8 *9))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-979 *5 *6 *7))
-   (-4 *5 (-496)) (-4 *6 (-719)) (-4 *7 (-758))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-585 *8)))) (-5 *3 (-585 *8))
-   (-4 *1 (-1125 *5 *6 *7 *8))))) 
+  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-978 *5 *6 *7))
+   (-4 *5 (-495)) (-4 *6 (-718)) (-4 *7 (-757))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-584 *8)))) (-5 *3 (-584 *8))
+   (-4 *1 (-1124 *5 *6 *7 *8))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-4 *6 (-979 *3 *4 *5)) (-5 *2 (-585 *6))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-584 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-2 (|:| -3862 (-585 *6)) (|:| -1703 (-585 *6))))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-2 (|:| -3861 (-584 *6)) (|:| -1702 (-584 *6))))))) 
 (((*1 *2 *1 *3)
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-   (-4 *6 (-758)) (-5 *2 (-85))))
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+   (-4 *6 (-757)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-979 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-719)) (-4 *5 (-758))
+  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-4 *6 (-979 *3 *4 *5)) (-5 *2 (-85))))
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
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-  (-12 (-4 *1 (-1125 *4 *5 *6 *3)) (-4 *4 (-496)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *3 (-979 *4 *5 *6)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1124 *4 *5 *6 *3)) (-4 *4 (-495)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-585 *1)) (-4 *1 (-979 *4 *5 *6)) (-4 *4 (-963)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85))))
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+   (-4 *6 (-757)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-979 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-719)) (-4 *5 (-758))
+  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *3 *1 *4)
-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *1 (-1125 *5 *6 *7 *3)) (-4 *5 (-496))
-   (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7)) (-5 *2 (-85))))) 
+  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *1 (-1124 *5 *6 *7 *3)) (-4 *5 (-495))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
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-   (-4 *6 (-979 *3 *4 *5)) (-5 *2 (-85))))
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    (-5 *2 (-85))))) 
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-   (-4 *2 (-979 *3 *4 *5))))) 
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+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-1022)) (-5 *3 (-484))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-1022)) (-5 *3 (-484))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-1022))))) 
+(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1179 (-484))) (-5 *3 (-484)) (-5 *1 (-1022))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-1180 (-485))) (-5 *3 (-585 (-485))) (-5 *4 (-485))
-   (-5 *1 (-1023))))) 
+  (-12 (-5 *2 (-1179 (-484))) (-5 *3 (-584 (-484))) (-5 *4 (-484))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-585 (-485))) (-5 *3 (-585 (-832))) (-5 *4 (-85))
-   (-5 *1 (-1023))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *3 (-584 (-831))) (-5 *4 (-85))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-632 (-485))) (-5 *3 (-585 (-485))) (-5 *1 (-1023))))) 
+  (-12 (-5 *2 (-631 (-484))) (-5 *3 (-584 (-484))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-585 (-832))) (-5 *4 (-585 (-485))) (-5 *2 (-632 (-485)))
-   (-5 *1 (-1023))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *4 (-584 (-484))) (-5 *2 (-631 (-484)))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-585 (-832))) (-5 *2 (-585 (-632 (-485)))) (-5 *1 (-1023))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *2 (-584 (-631 (-484)))) (-5 *1 (-1022))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-585 (-485))) (-5 *3 (-632 (-485))) (-5 *1 (-1023))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *3 (-631 (-484))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-585 (-485))) (-5 *2 (-632 (-485))) (-5 *1 (-1023))))) 
+  (-12 (-5 *3 (-584 (-484))) (-5 *2 (-631 (-484))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 *4)) (-5 *1 (-1021 *5 *6 *7 *3 *4))
-   (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-85)) (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-85)) (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 *4)) (-5 *1 (-1021 *5 *6 *7 *3 *4))
-   (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 *4)) (-5 *1 (-1021 *5 *6 *7 *3 *4))
-   (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4 *5 *5)
-  (-12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-719)) (-4 *8 (-758))
-   (-4 *3 (-979 *6 *7 *8)) (-5 *2 (-585 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1021 *6 *7 *8 *3 *4)) (-4 *4 (-985 *6 *7 *8 *3))))
+  (-12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *3 (-978 *6 *7 *8)) (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1020 *6 *7 *8 *3 *4)) (-4 *4 (-984 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-585 (-2 (|:| |val| (-585 *8)) (|:| -1601 *9)))) (-5 *5 (-85))
-   (-4 *8 (-979 *6 *7 *4)) (-4 *9 (-985 *6 *7 *4 *8)) (-4 *6 (-390))
-   (-4 *7 (-719)) (-4 *4 (-758))
-   (-5 *2 (-585 (-2 (|:| |val| *8) (|:| -1601 *9))))
-   (-5 *1 (-1021 *6 *7 *4 *8 *9))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| |val| (-584 *8)) (|:| -1600 *9)))) (-5 *5 (-85))
+   (-4 *8 (-978 *6 *7 *4)) (-4 *9 (-984 *6 *7 *4 *8)) (-4 *6 (-390))
+   (-4 *7 (-718)) (-4 *4 (-757))
+   (-5 *2 (-584 (-2 (|:| |val| *8) (|:| -1600 *9))))
+   (-5 *1 (-1020 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-719)) (-4 *7 (-758)) (-4 *3 (-979 *5 *6 *7))
-   (-5 *2 (-585 (-2 (|:| |val| (-585 *3)) (|:| -1601 *4))))
-   (-5 *1 (-1021 *5 *6 *7 *3 *4)) (-4 *4 (-985 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-390)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-584 *3)) (|:| -1600 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-986 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1021 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-986 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1021 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-986 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1021 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-986 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1021 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-719)) (-4 *8 (-758))
-   (-4 *9 (-979 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3268 (-585 *9)) (|:| -1601 *4) (|:| |ineq| (-585 *9))))
-   (-5 *1 (-903 *6 *7 *8 *9 *4)) (-5 *3 (-585 *9)) (-4 *4 (-985 *6 *7 *8 *9))))
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3267 (-584 *9)) (|:| -1600 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9))))
  ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-719)) (-4 *8 (-758))
-   (-4 *9 (-979 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3268 (-585 *9)) (|:| -1601 *4) (|:| |ineq| (-585 *9))))
-   (-5 *1 (-1020 *6 *7 *8 *9 *4)) (-5 *3 (-585 *9))
-   (-4 *4 (-985 *6 *7 *8 *9))))) 
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3267 (-584 *9)) (|:| -1600 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-1019 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9))
+   (-4 *4 (-984 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-585 *10)) (-5 *5 (-85)) (-4 *10 (-985 *6 *7 *8 *9))
-   (-4 *6 (-390)) (-4 *7 (-719)) (-4 *8 (-758)) (-4 *9 (-979 *6 *7 *8))
+  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-390)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-585 (-2 (|:| -3268 (-585 *9)) (|:| -1601 *10) (|:| |ineq| (-585 *9)))))
-   (-5 *1 (-903 *6 *7 *8 *9 *10)) (-5 *3 (-585 *9))))
+    (-584 (-2 (|:| -3267 (-584 *9)) (|:| -1600 *10) (|:| |ineq| (-584 *9)))))
+   (-5 *1 (-902 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))
  ((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-585 *10)) (-5 *5 (-85)) (-4 *10 (-985 *6 *7 *8 *9))
-   (-4 *6 (-390)) (-4 *7 (-719)) (-4 *8 (-758)) (-4 *9 (-979 *6 *7 *8))
+  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-390)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-585 (-2 (|:| -3268 (-585 *9)) (|:| -1601 *10) (|:| |ineq| (-585 *9)))))
-   (-5 *1 (-1020 *6 *7 *8 *9 *10)) (-5 *3 (-585 *9))))) 
+    (-584 (-2 (|:| -3267 (-584 *9)) (|:| -1600 *10) (|:| |ineq| (-584 *9)))))
+   (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-585 (-2 (|:| |val| (-585 *6)) (|:| -1601 *7))))
-   (-4 *6 (-979 *3 *4 *5)) (-4 *7 (-985 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-719)) (-4 *5 (-758)) (-5 *1 (-903 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1600 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-585 (-2 (|:| |val| (-585 *6)) (|:| -1601 *7))))
-   (-4 *6 (-979 *3 *4 *5)) (-4 *7 (-985 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-719)) (-4 *5 (-758)) (-5 *1 (-1020 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1600 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-585 *7)) (|:| -1601 *8)))
-   (-4 *7 (-979 *4 *5 *6)) (-4 *8 (-985 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-719)) (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1600 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-390))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-585 *7)) (|:| -1601 *8)))
-   (-4 *7 (-979 *4 *5 *6)) (-4 *8 (-985 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-719)) (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1600 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-390))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-585 *7)) (-4 *7 (-985 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *1 (-903 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-585 *7)) (-4 *7 (-985 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *1 (-1020 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-585 *3)) (-4 *3 (-985 *5 *6 *7 *8)) (-4 *5 (-390))
-   (-4 *6 (-719)) (-4 *7 (-758)) (-4 *8 (-979 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-903 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-390))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-902 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-585 *3)) (-4 *3 (-985 *5 *6 *7 *8)) (-4 *5 (-390))
-   (-4 *6 (-719)) (-4 *7 (-758)) (-4 *8 (-979 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1020 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-390))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-1019 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *3))
-   (-4 *3 (-985 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *3))
-   (-4 *3 (-985 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-585 *7)) (-4 *7 (-979 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-719))
-   (-4 *6 (-758)) (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
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-   (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *1 (-903 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-585 *7)) (-4 *7 (-985 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *1 (-1020 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-390))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-903 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758)) (-4 *7 (-979 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1020 *4 *5 *6 *7 *3)) (-4 *3 (-985 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-903 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-902 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *6 (-979 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-985 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-390)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-903 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-390)) (-4 *5 (-719)) (-4 *6 (-758))
-   (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-985 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-988))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-390)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
+(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-987))))
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-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
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+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-802 *3)) (-4 *3 (-1015))))
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-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-375))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-506 *3)) (-4 *3 (-952 (-485)))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-505 *3)) (-4 *3 (-951 (-484)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *7 (-1015)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-585 (-2 (|:| -3861 (-1091)) (|:| |entry| *4))))
-   (-5 *1 (-800 *3 *4)) (-4 *3 (-1015)) (-4 *4 (-1015))))
+  (-12 (-5 *2 (-584 (-2 (|:| -3860 (-1090)) (|:| |entry| *4))))
+   (-5 *1 (-799 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))
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-  (-12 (-4 *3 (-1015)) (-4 *4 (-1015)) (-4 *5 (-1015)) (-4 *6 (-1015))
-   (-4 *7 (-1015)) (-5 *2 (-585 *1)) (-4 *1 (-1018 *3 *4 *5 *6 *7))))) 
+  (-12 (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-4 *7 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-1017 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *2 *4 *5 *6)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *2 (-1015))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-485)) (-5 *1 (-506 *3)) (-4 *3 (-952 *2))))
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+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-484)) (-5 *1 (-505 *3)) (-4 *3 (-951 *2))))
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-  (-12 (-4 *1 (-1018 *3 *4 *2 *5 *6)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *2 (-1015))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-485)) (-5 *3 (-832)) (-4 *1 (-345))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-485)) (-4 *1 (-345))))
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+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
+(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-484)) (-5 *3 (-831)) (-4 *1 (-345))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-484)) (-4 *1 (-345))))
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-  (-12 (-4 *1 (-1018 *3 *4 *5 *2 *6)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *2 (-1015))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *2 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1018 *3 *4 *5 *6 *2)) (-4 *3 (-1015)) (-4 *4 (-1015))
-   (-4 *5 (-1015)) (-4 *6 (-1015)) (-4 *2 (-1015))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *2)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1018 *2 *3 *4 *5 *6)) (-4 *2 (-1015)) (-4 *3 (-1015))
-   (-4 *4 (-1015)) (-4 *5 (-1015)) (-4 *6 (-1015))))) 
+  (-12 (-4 *1 (-1017 *2 *3 *4 *5 *6)) (-4 *2 (-1014)) (-4 *3 (-1014))
+   (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1018 *2 *3 *4 *5 *6)) (-4 *2 (-1015)) (-4 *3 (-1015))
-   (-4 *4 (-1015)) (-4 *5 (-1015)) (-4 *6 (-1015))))) 
+  (-12 (-4 *1 (-1017 *2 *3 *4 *5 *6)) (-4 *2 (-1014)) (-4 *3 (-1014))
+   (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))))) 
 (((*1 *1 *1 *2)
-  (|partial| -12 (-5 *2 (-832)) (-5 *1 (-1016 *3 *4)) (-14 *3 *2) (-14 *4 *2)))) 
+  (|partial| -12 (-5 *2 (-831)) (-5 *1 (-1015 *3 *4)) (-14 *3 *2) (-14 *4 *2)))) 
 (((*1 *1 *1 *2 *2)
-  (|partial| -12 (-5 *2 (-832)) (-5 *1 (-1016 *3 *4)) (-14 *3 *2) (-14 *4 *2)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-1050))) (-5 *1 (-615))))
+  (|partial| -12 (-5 *2 (-831)) (-5 *1 (-1015 *3 *4)) (-14 *3 *2) (-14 *4 *2)))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-1049))) (-5 *1 (-614))))
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    (-14 *5 *3)))) 
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 (((*1 *2 *3)
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   (|partial| OR
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-     (-4 *5 (-555 (-1091))))
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-     (-4 *5 (-555 (-1091))))
-    (-4 *3 (-963)) (-4 *1 (-979 *3 *4 *5)) (-4 *4 (-719)) (-4 *5 (-758)))))
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   (|partial| OR
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   (OR
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+   (-12 (-5 *2 (-858 (-484))) (-4 *1 (-978 *3 *4 *5))
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-   (-4 *4 (-719)) (-4 *5 (-758))))) 
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 (((*1 *1 *1)
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-   (-4 *2 (-496))))) 
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+   (-4 *2 (-495))))) 
 (((*1 *1 *1)
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-   (-4 *2 (-496))))) 
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 (((*1 *1 *1 *1)
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-   (-4 *2 (-496))))
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 (((*1 *1 *1 *1)
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-   (-4 *2 (-496))))
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-   (-4 *2 (-496))))) 
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+   (-4 *2 (-495))))) 
 (((*1 *2 *1 *1)
   (-12
    (-5 *2
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-   (-5 *1 (-706 *3)) (-4 *3 (-496)) (-4 *3 (-963))))
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-   (-4 *1 (-979 *3 *4 *5))))) 
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 (((*1 *2 *1 *1)
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 (((*1 *2 *1 *1)
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 (((*1 *2 *1 *1)
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 (((*1 *1 *1 *1 *2)
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 (((*1 *1 *1 *1 *1 *2)
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 (((*1 *1 *1 *1 *1 *1)
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- ((*1 *1 *1 *1) (-5 *1 (-696)))
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    (-4 *2 (-390))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-979 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-719)) (-4 *4 (-758))
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    (-4 *2 (-390))))) 
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    (-4 *2 (-390))))) 
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    (-4 *2 (-390))))) 
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 (((*1 *2 *1 *3)
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 (((*1 *2 *3)
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 (((*1 *1 *1 *1) (-4 *1 (-116)))
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 (((*1 *1 *2)
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    (-4 *2
     (-13 (-312)
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 (((*1 *2 *3)
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-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-641 *3 *5 *6 *7))
-   (-4 *3 (-555 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *3 *5 *6 *7))
+   (-4 *3 (-554 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-645 *3 *5 *6))
-   (-4 *3 (-555 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *3 *5 *6))
+   (-4 *3 (-554 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-645 *4 *5 *6))
-   (-4 *4 (-555 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
+  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *4 *5 *6))
+   (-4 *4 (-554 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-644 *3 *4))
-   (-4 *3 (-1130)) (-4 *4 (-1130))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-585 (-1091))) (-5 *3 (-1091)) (-5 *1 (-474))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-643 *3)) (-4 *3 (-555 (-474)))))
+  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-643 *3 *4))
+   (-4 *3 (-1129)) (-4 *4 (-1129))))) 
+(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-584 (-1090))) (-5 *3 (-1090)) (-5 *1 (-473))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1090)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *2)
-  (-12 (-5 *2 (-1091)) (-5 *1 (-643 *3)) (-4 *3 (-555 (-474)))))
+  (-12 (-5 *2 (-1090)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *2 *2)
-  (-12 (-5 *2 (-1091)) (-5 *1 (-643 *3)) (-4 *3 (-555 (-474)))))
+  (-12 (-5 *2 (-1090)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *4 (-585 (-1091))) (-5 *2 (-1091)) (-5 *1 (-643 *3))
-   (-4 *3 (-555 (-474)))))) 
+  (-12 (-5 *4 (-584 (-1090))) (-5 *2 (-1090)) (-5 *1 (-642 *3))
+   (-4 *3 (-554 (-473)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-642 *3))
-   (-4 *3 (-555 (-474)))))
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-642 *3))
-   (-4 *3 (-555 (-474)))))) 
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-473)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-641 *4 *5 *6 *7))
-   (-4 *4 (-555 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))) 
+  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *4 *5 *6 *7))
+   (-4 *4 (-554 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))) 
 (((*1 *2 *3 *3)
   (-12 (-4 *3 (-258)) (-4 *3 (-146)) (-4 *4 (-322 *3)) (-4 *5 (-322 *3))
-   (-5 *2 (-2 (|:| -1974 *3) (|:| -2904 *3))) (-5 *1 (-631 *3 *4 *5 *6))
-   (-4 *6 (-629 *3 *4 *5))))
+   (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-630 *3 *4 *5 *6))
+   (-4 *6 (-628 *3 *4 *5))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-2 (|:| -1974 *3) (|:| -2904 *3))) (-5 *1 (-640 *3))
+  (-12 (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-639 *3))
    (-4 *3 (-258))))) 
-(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-632 *3)) (-4 *3 (-258)) (-5 *1 (-640 *3))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-632 *3)) (-4 *3 (-258)) (-5 *1 (-640 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-258)) (-5 *1 (-640 *3))))) 
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   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-1 (-179) (-179) (-179) (-179)))
-   (-5 *2 (-1 (-856 (-179)) (-179) (-179))) (-5 *1 (-638))))) 
+   (-5 *2 (-1 (-855 (-179)) (-179) (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *6)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1003 (-179)))
-   (-5 *6 (-585 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-638))))) 
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+   (-5 *6 (-584 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
-   (-5 *5 (-1003 (-179))) (-5 *6 (-585 (-221))) (-5 *2 (-1048 (-179)))
-   (-5 *1 (-638))))) 
+   (-5 *5 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1047 (-179)))
+   (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
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-   (-5 *1 (-638))))
+   (-5 *5 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1047 (-179)))
+   (-5 *1 (-637))))
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-   (-5 *5 (-585 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-638))))
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+   (-5 *5 (-584 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-637))))
  ((*1 *2 *2 *3 *4 *4 *5)
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-   (-5 *4 (-1003 (-179))) (-5 *5 (-585 (-221))) (-5 *1 (-638))))) 
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 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-696)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1156 *4))))
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  ((*1 *2 *2 *3 *2 *3)
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-585 (-2 (|:| |deg| (-696)) (|:| -2577 *5)))) (-4 *5 (-1156 *4))
-   (-4 *4 (-299)) (-5 *2 (-585 *5)) (-5 *1 (-170 *4 *5))))
+  (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2576 *5)))) (-4 *5 (-1155 *4))
+   (-4 *4 (-299)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5))))
  ((*1 *2 *3 *4)
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-   (-4 *5 (-1156 *4)) (-5 *2 (-585 *5)) (-5 *1 (-637 *5))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| -3732 *5) (|:| -3948 (-484))))) (-5 *4 (-484))
+   (-4 *5 (-1155 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5))))) 
 (((*1 *2 *3 *4)
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-   (-5 *1 (-637 *3)) (-4 *3 (-1156 *4))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-637 *2)) (-4 *2 (-1156 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)) (-4 *2 (-1015))))
- ((*1 *1 *1) (-12 (-4 *1 (-636 *2)) (-4 *2 (-1015))))) 
+  (-12 (-5 *4 (-484)) (-5 *2 (-584 (-2 (|:| -3732 *3) (|:| -3948 *4))))
+   (-5 *1 (-636 *3)) (-4 *3 (-1155 *4))))) 
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+ ((*1 *1 *1) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1014))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-636 *3)) (-4 *3 (-1015))
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-(((*1 *1 *2) (-12 (-5 *1 (-634 *2)) (-4 *2 (-554 (-774)))))) 
-(((*1 *1) (-12 (-5 *1 (-634 *2)) (-4 *2 (-554 (-774)))))) 
+  (-12 (-4 *1 (-635 *3)) (-4 *3 (-1014))
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 (((*1 *2 *2 *2 *2 *2 *3)
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-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))
- ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-632 *3)) (-4 *3 (-963)) (-5 *1 (-633 *3))))) 
-(((*1 *2 *2)
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-   (-4 *5 (-322 *3)) (-5 *1 (-631 *3 *4 *5 *2)) (-4 *2 (-629 *3 *4 *5))))) 
-(((*1 *2 *2)
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-   (-5 *1 (-631 *3 *4 *5 *2)) (-4 *2 (-629 *3 *4 *5))))) 
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+ ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
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+(((*1 *2 *2)
+  (|partial| -12 (-4 *3 (-495)) (-4 *3 (-146)) (-4 *4 (-322 *3))
+   (-4 *5 (-322 *3)) (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
+(((*1 *2 *2)
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 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-322 *3)) (-4 *6 (-322 *3))
-   (-5 *1 (-631 *3 *5 *6 *2)) (-4 *2 (-629 *3 *5 *6))))) 
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+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-322 *3)) (-4 *6 (-322 *3))
-   (-5 *1 (-631 *3 *5 *6 *2)) (-4 *2 (-629 *3 *5 *6))))) 
+  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-322 *3)) (-4 *6 (-322 *3))
+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-485)) (-4 *4 (-146)) (-4 *5 (-322 *4)) (-4 *6 (-322 *4))
-   (-5 *1 (-631 *4 *5 *6 *2)) (-4 *2 (-629 *4 *5 *6))))) 
+  (-12 (-5 *3 (-484)) (-4 *4 (-146)) (-4 *5 (-322 *4)) (-4 *6 (-322 *4))
+   (-5 *1 (-630 *4 *5 *6 *2)) (-4 *2 (-628 *4 *5 *6))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-629 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-322 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-322 *2))
    (-4 *4 (-322 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-629 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-322 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-322 *2))
    (-4 *4 (-322 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-629 *2 *3 *4)) (-4 *2 (-963)) (-4 *3 (-322 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-322 *2))
    (-4 *4 (-322 *2))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-629 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-322 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-322 *3))
    (-4 *5 (-322 *3))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-629 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-322 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-322 *3))
    (-4 *5 (-322 *3))))) 
 (((*1 *1 *1 *2 *2 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-629 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-322 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-322 *3))
    (-4 *5 (-322 *3))))) 
 (((*1 *1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-485)) (-4 *1 (-629 *3 *4 *5)) (-4 *3 (-963)) (-4 *4 (-322 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-322 *3))
    (-4 *5 (-322 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1015)) (-4 *5 (-1015)) (-4 *6 (-1015))
-   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-627 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-626 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1015)) (-4 *6 (-1015)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-627 *4 *5 *6)) (-4 *4 (-1015))))) 
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-626 *4 *5 *6)) (-4 *4 (-1014))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1015)) (-4 *6 (-1015)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-627 *4 *5 *6)) (-4 *5 (-1015))))) 
+  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-626 *4 *5 *6)) (-4 *5 (-1014))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1015)) (-4 *5 (-1015)) (-4 *6 (-1015))
-   (-5 *2 (-1 *6 *5)) (-5 *1 (-627 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-5 *2 (-1 *6 *5)) (-5 *1 (-626 *4 *5 *6))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1015)) (-4 *4 (-1015)) (-4 *6 (-1015))
-   (-5 *2 (-1 *6 *5)) (-5 *1 (-627 *5 *4 *6))))) 
+  (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1014)) (-4 *4 (-1014)) (-4 *6 (-1014))
+   (-5 *2 (-1 *6 *5)) (-5 *1 (-626 *5 *4 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *5 *4 *4)) (-4 *4 (-1015)) (-4 *5 (-1015)) (-5 *2 (-1 *5 *4))
-   (-5 *1 (-626 *4 *5))))) 
+  (-12 (-5 *3 (-1 *5 *4 *4)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-5 *2 (-1 *5 *4))
+   (-5 *1 (-625 *4 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1015)) (-4 *5 (-1015)) (-5 *2 (-1 *5))
-   (-5 *1 (-626 *4 *5))))) 
+  (-12 (-5 *3 (-1 *5 *4)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-5 *2 (-1 *5))
+   (-5 *1 (-625 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-626 *4 *3)) (-4 *4 (-1015))
-   (-4 *3 (-1015))))) 
+  (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-625 *4 *3)) (-4 *4 (-1014))
+   (-4 *3 (-1014))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 (-696) *2)) (-5 *4 (-696)) (-4 *2 (-1015))
-   (-5 *1 (-621 *2))))
- ((*1 *2 *2) (-12 (-5 *2 (-1 *3 (-696) *3)) (-4 *3 (-1015)) (-5 *1 (-625 *3))))) 
-(((*1 *2 *2) (-12 (-5 *1 (-625 *2)) (-4 *2 (-1015))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1 *2 *2)) (-5 *1 (-625 *2)) (-4 *2 (-1015))))
- ((*1 *2 *3 *4)
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-(((*1 *1 *2 *3) (-12 (-5 *2 (-585 (-1131))) (-5 *3 (-1131)) (-5 *1 (-624))))) 
+  (-12 (-5 *3 (-1 *2 (-695) *2)) (-5 *4 (-695)) (-4 *2 (-1014))
+   (-5 *1 (-620 *2))))
+ ((*1 *2 *2) (-12 (-5 *2 (-1 *3 (-695) *3)) (-4 *3 (-1014)) (-5 *1 (-624 *3))))) 
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+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-1 (-584 *5) (-584 *5))) (-5 *4 (-484)) (-5 *2 (-584 *5))
+   (-5 *1 (-624 *5)) (-4 *5 (-1014))))) 
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 (((*1 *2 *3 *4 *5)
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      (|:| |polypart| *6)))
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 (((*1 *2 *3 *4)
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-   (-5 *2 (-1086 (-1086 *7))) (-5 *1 (-439 *5 *6 *4 *7)) (-4 *4 (-1156 *6))))) 
+  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-962)) (-4 *7 (-962)) (-4 *6 (-1155 *5))
+   (-5 *2 (-1085 (-1085 *7))) (-5 *1 (-439 *5 *6 *4 *7)) (-4 *4 (-1155 *6))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) (-5 *4 (-632 (-1086 *8)))
-   (-4 *5 (-963)) (-4 *8 (-963)) (-4 *6 (-1156 *5)) (-5 *2 (-632 *6))
-   (-5 *1 (-439 *5 *6 *7 *8)) (-4 *7 (-1156 *6))))) 
+  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) (-5 *4 (-631 (-1085 *8)))
+   (-4 *5 (-962)) (-4 *8 (-962)) (-4 *6 (-1155 *5)) (-5 *2 (-631 *6))
+   (-5 *1 (-439 *5 *6 *7 *8)) (-4 *7 (-1155 *6))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1086 *7))
-   (-4 *5 (-963)) (-4 *7 (-963)) (-4 *2 (-1156 *5)) (-5 *1 (-439 *5 *2 *6 *7))
-   (-4 *6 (-1156 *2))))) 
+  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1085 *7))
+   (-4 *5 (-962)) (-4 *7 (-962)) (-4 *2 (-1155 *5)) (-5 *1 (-439 *5 *2 *6 *7))
+   (-4 *6 (-1155 *2))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1086 *7)) (-4 *5 (-963)) (-4 *7 (-963))
-   (-4 *2 (-1156 *5)) (-5 *1 (-439 *5 *2 *6 *7)) (-4 *6 (-1156 *2))))
+  (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1085 *7)) (-4 *5 (-962)) (-4 *7 (-962))
+   (-4 *2 (-1155 *5)) (-5 *1 (-439 *5 *2 *6 *7)) (-4 *6 (-1155 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-963)) (-4 *7 (-963)) (-4 *4 (-1156 *5))
-   (-5 *2 (-1086 *7)) (-5 *1 (-439 *5 *4 *6 *7)) (-4 *6 (-1156 *4))))) 
+  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-962)) (-4 *7 (-962)) (-4 *4 (-1155 *5))
+   (-5 *2 (-1085 *7)) (-5 *1 (-439 *5 *4 *6 *7)) (-4 *6 (-1155 *4))))) 
 (((*1 *2 *2 *2)
   (-12
    (-5 *2
-    (-2 (|:| -2014 (-632 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-632 *3))))
-   (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $))))) (-4 *4 (-1156 *3))
+    (-2 (|:| -2013 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+   (-4 *3 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $))))) (-4 *4 (-1155 *3))
    (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-632 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $)))))
-   (-4 *4 (-1156 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
+  (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $)))))
+   (-4 *4 (-1155 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-632 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $)))))
-   (-4 *4 (-1156 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))
+  (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $)))))
+   (-4 *4 (-1155 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))
  ((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-632 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $)))))
-   (-4 *4 (-1156 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
+  (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $)))))
+   (-4 *4 (-1155 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-696)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $)))))
-   (-4 *4 (-1156 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
+  (-12 (-5 *2 (-695)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $)))))
+   (-4 *4 (-1155 *3)) (-5 *1 (-437 *3 *4 *5)) (-4 *5 (-351 *3 *4))))) 
 (((*1 *2 *3 *3 *2 *4)
-  (-12 (-5 *3 (-632 *2)) (-5 *4 (-485))
-   (-4 *2 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $))))) (-4 *5 (-1156 *2))
+  (-12 (-5 *3 (-631 *2)) (-5 *4 (-484))
+   (-4 *2 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $))))) (-4 *5 (-1155 *2))
    (-5 *1 (-437 *2 *5 *6)) (-4 *6 (-351 *2 *5))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *3 (-632 *2)) (-5 *4 (-696))
-   (-4 *2 (-13 (-258) (-10 -8 (-15 -3972 ((-346 $) $))))) (-4 *5 (-1156 *2))
+  (-12 (-5 *3 (-631 *2)) (-5 *4 (-695))
+   (-4 *2 (-13 (-258) (-10 -8 (-15 -3971 ((-346 $) $))))) (-4 *5 (-1155 *2))
    (-5 *1 (-437 *2 *5 *6)) (-4 *6 (-351 *2 *5))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-696)) (-4 *5 (-299)) (-4 *6 (-1156 *5))
+  (-12 (-5 *4 (-695)) (-4 *5 (-299)) (-4 *6 (-1155 *5))
    (-5 *2
-    (-585
-     (-2 (|:| -2014 (-632 *6)) (|:| |basisDen| *6)
-      (|:| |basisInv| (-632 *6)))))
+    (-584
+     (-2 (|:| -2013 (-631 *6)) (|:| |basisDen| *6)
+      (|:| |basisInv| (-631 *6)))))
    (-5 *1 (-436 *5 *6 *7))
    (-5 *3
-    (-2 (|:| -2014 (-632 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-632 *6))))
-   (-4 *7 (-1156 *6))))) 
+    (-2 (|:| -2013 (-631 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-631 *6))))
+   (-4 *7 (-1155 *6))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-585
+    (-584
      (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3)
-      (|:| |xpnt| (-485)))))
-   (-5 *1 (-346 *3)) (-4 *3 (-496))))
+      (|:| |xpnt| (-484)))))
+   (-5 *1 (-346 *3)) (-4 *3 (-495))))
  ((*1 *2 *3 *4 *4 *4)
-  (-12 (-5 *4 (-696)) (-4 *3 (-299)) (-4 *5 (-1156 *3))
-   (-5 *2 (-585 (-1086 *3))) (-5 *1 (-436 *3 *5 *6)) (-4 *6 (-1156 *5))))) 
+  (-12 (-5 *4 (-695)) (-4 *3 (-299)) (-4 *5 (-1155 *3))
+   (-5 *2 (-584 (-1085 *3))) (-5 *1 (-436 *3 *5 *6)) (-4 *6 (-1155 *5))))) 
 (((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-433))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-429))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-429))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1130))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1129))
    (-4 *4 (-322 *3)) (-4 *5 (-322 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3997)) (-4 *1 (-427 *3))
-   (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3996)) (-4 *1 (-427 *3))
+   (-4 *3 (-1129))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-427 *4))
-   (-4 *4 (-1130)) (-5 *2 (-85))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3995)) (-4 *1 (-427 *4))
+   (-4 *4 (-1129)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-427 *4))
-   (-4 *4 (-1130)) (-5 *2 (-85))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3995)) (-4 *1 (-427 *4))
+   (-4 *4 (-1129)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *1)
-  (-12 (|has| *1 (-6 -3996)) (-4 *1 (-427 *3)) (-4 *3 (-1130)) (-4 *3 (-1015))
-   (-5 *2 (-696))))
+  (-12 (|has| *1 (-6 -3995)) (-4 *1 (-427 *3)) (-4 *3 (-1129)) (-4 *3 (-1014))
+   (-5 *2 (-695))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-427 *4))
-   (-4 *4 (-1130)) (-5 *2 (-696))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-348 (-485))) (-5 *1 (-425))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-585 (-485))) (-5 *2 (-485)) (-5 *1 (-424 *4))
-   (-4 *4 (-1156 *2))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-585 *3)) (-4 *3 (-1156 (-485))) (-5 *1 (-424 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-585 *3)) (-4 *3 (-1156 (-485))) (-5 *1 (-424 *3))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-585 *2)) (-5 *1 (-424 *2)) (-4 *2 (-1156 (-485)))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-585 *3)) (-4 *3 (-758)) (-5 *1 (-422 *3))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-445)) (-5 *3 (-585 (-787))) (-5 *1 (-421))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-445))) (-5 *1 (-49))))
- ((*1 *2 *1) (-12 (-5 *2 (-585 (-787))) (-5 *1 (-421))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3995)) (-4 *1 (-427 *4))
+   (-4 *4 (-1129)) (-5 *2 (-695))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-348 (-484))) (-5 *1 (-425))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-584 (-484))) (-5 *2 (-484)) (-5 *1 (-424 *4))
+   (-4 *4 (-1155 *2))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1155 (-484))) (-5 *1 (-424 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1155 (-484))) (-5 *1 (-424 *3))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-584 *2)) (-5 *1 (-424 *2)) (-4 *2 (-1155 (-484)))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-757)) (-5 *1 (-422 *3))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-445)) (-5 *3 (-584 (-786))) (-5 *1 (-421))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-445))) (-5 *1 (-49))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-786))) (-5 *1 (-421))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-585 (-485))) (-5 *1 (-206 *3 *4)) (-14 *3 (-585 (-1091)))
-   (-4 *4 (-963))))
+  (-12 (-5 *2 (-584 (-484))) (-5 *1 (-206 *3 *4)) (-14 *3 (-584 (-1090)))
+   (-4 *4 (-962))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-585 (-485))) (-14 *3 (-585 (-1091))) (-5 *1 (-392 *3 *4 *5))
-   (-4 *4 (-963)) (-4 *5 (-196 (-3958 *3) (-696)))))
+  (-12 (-5 *2 (-584 (-484))) (-14 *3 (-584 (-1090))) (-5 *1 (-392 *3 *4 *5))
+   (-4 *4 (-962)) (-4 *5 (-196 (-3957 *3) (-695)))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-585 (-485))) (-5 *1 (-419 *3 *4)) (-14 *3 (-585 (-1091)))
-   (-4 *4 (-963))))) 
-(((*1 *2 *3 *3 *3 *3) (-12 (-5 *3 (-485)) (-5 *2 (-85)) (-5 *1 (-418))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *1 (-418))))) 
-(((*1 *2 *3 *4)
-  (-12 (-5 *4 (-585 (-775 *5))) (-14 *5 (-585 (-1091))) (-4 *6 (-390))
-   (-5 *2 (-2 (|:| |dpolys| (-585 (-206 *5 *6))) (|:| |coords| (-585 (-485)))))
-   (-5 *1 (-409 *5 *6 *7)) (-5 *3 (-585 (-206 *5 *6))) (-4 *7 (-390))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *1 (-419 *3 *4)) (-14 *3 (-584 (-1090)))
+   (-4 *4 (-962))))) 
+(((*1 *2 *3 *3 *3 *3) (-12 (-5 *3 (-484)) (-5 *2 (-85)) (-5 *1 (-418))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-418))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-584 (-774 *5))) (-14 *5 (-584 (-1090))) (-4 *6 (-390))
+   (-5 *2 (-2 (|:| |dpolys| (-584 (-206 *5 *6))) (|:| |coords| (-584 (-484)))))
+   (-5 *1 (-409 *5 *6 *7)) (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-390))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-585 (-419 *4 *5))) (-5 *3 (-585 (-775 *4)))
-   (-14 *4 (-585 (-1091))) (-4 *5 (-390)) (-5 *1 (-409 *4 *5 *6))
+  (|partial| -12 (-5 *2 (-584 (-419 *4 *5))) (-5 *3 (-584 (-774 *4)))
+   (-14 *4 (-584 (-1090))) (-4 *5 (-390)) (-5 *1 (-409 *4 *5 *6))
    (-4 *6 (-390))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-585 (-775 *5))) (-14 *5 (-585 (-1091))) (-4 *6 (-390))
-   (-5 *2 (-585 (-585 (-206 *5 *6)))) (-5 *1 (-409 *5 *6 *7))
-   (-5 *3 (-585 (-206 *5 *6))) (-4 *7 (-390))))) 
+  (-12 (-5 *4 (-584 (-774 *5))) (-14 *5 (-584 (-1090))) (-4 *6 (-390))
+   (-5 *2 (-584 (-584 (-206 *5 *6)))) (-5 *1 (-409 *5 *6 *7))
+   (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-390))))) 
 (((*1 *1) (-5 *1 (-406)))) 
 (((*1 *1 *2 *3 *3 *4 *5)
-  (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *3 (-585 (-785)))
-   (-5 *4 (-585 (-832))) (-5 *5 (-585 (-221))) (-5 *1 (-406))))
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
+   (-5 *4 (-584 (-831))) (-5 *5 (-584 (-221))) (-5 *1 (-406))))
  ((*1 *1 *2 *3 *3 *4)
-  (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *3 (-585 (-785)))
-   (-5 *4 (-585 (-832))) (-5 *1 (-406))))
- ((*1 *1 *2) (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *1 (-406))))
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
+   (-5 *4 (-584 (-831))) (-5 *1 (-406))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-406))))
  ((*1 *1 *1) (-5 *1 (-406)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *1 (-406))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-585 (-1003 (-328)))) (-5 *1 (-221))))
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-406))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-584 (-1002 (-328)))) (-5 *1 (-221))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *2 (-585 (-1003 (-328)))) (-5 *3 (-585 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-585 (-1003 (-328)))) (-5 *1 (-406))))
- ((*1 *2 *1) (-12 (-5 *2 (-585 (-1003 (-328)))) (-5 *1 (-406))))) 
+  (-12 (-5 *2 (-584 (-1002 (-328)))) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-1002 (-328)))) (-5 *1 (-406))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-1002 (-328)))) (-5 *1 (-406))))) 
 (((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-856 (-179))) (-5 *4 (-785)) (-5 *5 (-832)) (-5 *2 (-1186))
+  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *5 (-831)) (-5 *2 (-1185))
    (-5 *1 (-406))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-856 (-179))) (-5 *2 (-1186)) (-5 *1 (-406))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1185)) (-5 *1 (-406))))
  ((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-585 (-856 (-179)))) (-5 *4 (-785)) (-5 *5 (-832))
-   (-5 *2 (-1186)) (-5 *1 (-406))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-856 (-179))) (-5 *2 (-1186)) (-5 *1 (-406))))) 
+  (-12 (-5 *3 (-584 (-855 (-179)))) (-5 *4 (-784)) (-5 *5 (-831))
+   (-5 *2 (-1185)) (-5 *1 (-406))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1185)) (-5 *1 (-406))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-585 (-585 (-856 (-179))))) (-5 *3 (-585 (-785)))
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
    (-5 *1 (-406))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-585 (-585 (-856 (-179))))) (-5 *2 (-585 (-179)))
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-584 (-179)))
    (-5 *1 (-406))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-585 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
  ((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-405))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-405))))) 
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-405))))
@@ -11187,440 +11187,440 @@
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-405))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-405))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-832)) (-5 *2 (-1180 (-1180 (-485)))) (-5 *1 (-404))))) 
+  (-12 (-5 *3 (-831)) (-5 *2 (-1179 (-1179 (-484)))) (-5 *1 (-404))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1180 (-1180 (-485)))) (-5 *3 (-832)) (-5 *1 (-404))))) 
+  (-12 (-5 *2 (-1179 (-1179 (-484)))) (-5 *3 (-831)) (-5 *1 (-404))))) 
 (((*1 *2 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-758)) (-4 *5 (-719)) (-4 *6 (-496))
-   (-4 *7 (-863 *6 *5 *3)) (-5 *1 (-400 *5 *3 *6 *7 *2))
+  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-757)) (-4 *5 (-718)) (-4 *6 (-495))
+   (-4 *7 (-862 *6 *5 *3)) (-5 *1 (-400 *5 *3 *6 *7 *2))
    (-4 *2
-    (-13 (-952 (-348 (-485))) (-312)
-     (-10 -8 (-15 -3947 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) 
+    (-13 (-951 (-348 (-484))) (-312)
+     (-10 -8 (-15 -3946 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-585 (-1091))) (-4 *4 (-146))
+  (-12 (-14 *3 (-584 (-1090))) (-4 *4 (-146))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2402 *5) (|:| -2403 *2))
-     (-2 (|:| -2402 *5) (|:| -2403 *2))))
-   (-4 *2 (-196 (-3958 *3) (-696))) (-5 *1 (-399 *3 *4 *5 *2 *6 *7))
-   (-4 *5 (-758)) (-4 *7 (-863 *4 *2 (-775 *3)))))) 
+    (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *2))
+     (-2 (|:| -2401 *5) (|:| -2402 *2))))
+   (-4 *2 (-196 (-3957 *3) (-695))) (-5 *1 (-399 *3 *4 *5 *2 *6 *7))
+   (-4 *5 (-757)) (-4 *7 (-862 *4 *2 (-774 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-585 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-696)))
+  (-12 (-14 *3 (-584 (-1090))) (-4 *4 (-146)) (-4 *5 (-196 (-3957 *3) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2402 *2) (|:| -2403 *5))
-     (-2 (|:| -2402 *2) (|:| -2403 *5))))
-   (-4 *2 (-758)) (-5 *1 (-399 *3 *4 *2 *5 *6 *7))
-   (-4 *7 (-863 *4 *5 (-775 *3)))))) 
+    (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5))
+     (-2 (|:| -2401 *2) (|:| -2402 *5))))
+   (-4 *2 (-757)) (-5 *1 (-399 *3 *4 *2 *5 *6 *7))
+   (-4 *7 (-862 *4 *5 (-774 *3)))))) 
 (((*1 *1 *2 *3 *4)
-  (-12 (-14 *5 (-585 (-1091))) (-4 *2 (-146)) (-4 *4 (-196 (-3958 *5) (-696)))
+  (-12 (-14 *5 (-584 (-1090))) (-4 *2 (-146)) (-4 *4 (-196 (-3957 *5) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2402 *3) (|:| -2403 *4))
-     (-2 (|:| -2402 *3) (|:| -2403 *4))))
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      (|:| |polj| *7)))
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-    (-585
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-696)) (|:| |poli| *6)
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       (|:| |polj| *6))))
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 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-696)) (|:| |poli| *2)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *2)
      (|:| |polj| *2)))
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-   (-4 *4 (-390)) (-4 *6 (-758))))) 
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+   (-4 *4 (-390)) (-4 *6 (-757))))) 
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-   (-4 *2 (-863 *3 *4 *5))))) 
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+   (-4 *2 (-862 *3 *4 *5))))) 
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-    (-585
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       (|:| |polj| *6))))
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    (-5 *2
-    (-585
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-696)) (|:| |poli| *6)
+    (-584
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       (|:| |polj| *6))))
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 (((*1 *2 *3 *2)
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       (|:| |polj| *3))))
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+  (-12 (-4 *4 (-390)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
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    (-5 *3
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      (|:| |polj| *7)))
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-   (-5 *3 (-585 *7))))
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-   (-5 *3 (-585 *8))))
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-   (-5 *3 (-585 *7))))
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-   (-5 *3 (-585 *8))))) 
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-   (-5 *3 (-585 *7))))
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-   (-5 *3 (-585 *8))))) 
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+   (-4 *6 (-757)) (-5 *1 (-386 *4 *5 *6 *2))))) 
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 (((*1 *2 *3 *4)
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-   (-4 *5 (-13 (-345) (-952 *4) (-312) (-1116) (-239)))))) 
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@@ -11630,319 +11630,319 @@
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 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1085 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1085 *3))))) 
 (((*1 *2)
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
@@ -11987,1176 +11987,1176 @@
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-585 (-1180 *4))) (-5 *1 (-315 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-584 (-1179 *4))) (-5 *1 (-315 *3 *4))
    (-4 *3 (-316 *4))))
  ((*1 *2)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496))
-   (-5 *2 (-585 (-1180 *3)))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495))
+   (-5 *2 (-584 (-1179 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496)) (-5 *2 (-1086 *3))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495)) (-5 *2 (-1085 *3))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496)) (-5 *2 (-1086 *3))))) 
-(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-496)) (-4 *2 (-146))))) 
-(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-496)) (-4 *2 (-146))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495)) (-5 *2 (-1085 *3))))) 
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+(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-495)) (-4 *2 (-146))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *3 (-1074)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1015)) (-4 *4 (-1015))))
- ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1015)) (-4 *3 (-1015))))) 
+  (-12 (-5 *3 (-1073)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1014)) (-4 *4 (-1014))))
+ ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1074)) (-4 *1 (-314 *3 *4)) (-4 *3 (-1015)) (-4 *4 (-1015))))) 
+  (-12 (-5 *2 (-1073)) (-4 *1 (-314 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))) 
 (((*1 *1 *1) (-4 *1 (-147)))
- ((*1 *1 *1) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1015)) (-4 *3 (-1015))))) 
+ ((*1 *1 *1) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) 
 (((*1 *2 *1)
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-(((*1 *2 *1 *2) (-12 (-4 *1 (-314 *3 *2)) (-4 *3 (-1015)) (-4 *2 (-1015))))) 
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+(((*1 *2 *1 *2) (-12 (-4 *1 (-314 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1014))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299))
+  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-299))
    (-4 *2
     (-13 (-343)
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-      (-15 -2014 ((-1180 *2) (-832))) (-15 -3929 (*2 *2)))))
+     (-10 -7 (-15 -3946 (*2 *4)) (-15 -2011 ((-831) *2))
+      (-15 -2013 ((-1179 *2) (-831))) (-15 -3928 (*2 *2)))))
    (-5 *1 (-306 *2 *4))))) 
 (((*1 *2 *3)
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-(((*1 *2 *2) (-12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-870 (-1085 *4))) (-5 *1 (-305 *4))
+   (-5 *3 (-1085 *4))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-832)) (-5 *2 (-1086 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *1) (-12 (-4 *1 (-299)) (-5 *2 (-85))))
  ((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *2)
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-   (-14 *4 (-832))))
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 (((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *1) (-4 *1 (-299)))) 
 (((*1 *2)
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-  (-12 (-5 *3 (-832))
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 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-832))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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-   (-5 *2 (-1180 (-585 (-2 (|:| -3403 *4) (|:| -2402 (-1035))))))
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 (((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *2)
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 (((*1 *2 *3)
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  ((*1 *2 *3)
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 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))) 
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 (((*1 *2 *3)
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-   (-4 *5 (-1156 (-348 *3))) (-5 *2 (-85))))
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  ((*1 *2 *3)
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-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))) 
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 (((*1 *2)
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-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))) 
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 (((*1 *2 *3)
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-   (-4 *5 (-1156 (-348 *3))) (-5 *2 (-85))))
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  ((*1 *2 *3)
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-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))) 
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 (((*1 *2)
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-   (-5 *2 (-1180 *1)) (-4 *1 (-291 *3 *4 *5))))) 
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 (((*1 *2 *1)
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 (((*1 *2 *1 *3)
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  ((*1 *2 *1 *3)
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-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))
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  ((*1 *2 *1)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-5 *2 (-85))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-1180 *1)) (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135))
-   (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-348 *4)))))) 
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 (((*1 *2 *2)
-  (-12 (-5 *2 (-1180 *1)) (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135))
-   (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-348 *4)))))) 
+  (-12 (-5 *2 (-1179 *1)) (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134))
+   (-4 *4 (-1155 *3)) (-4 *5 (-1155 (-348 *4)))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-1180 *1)) (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135))
-   (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-348 *4)))))) 
+  (-12 (-5 *2 (-1179 *1)) (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134))
+   (-4 *4 (-1155 *3)) (-4 *5 (-1155 (-348 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-632 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-5 *2 (-631 (-348 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-632 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-5 *2 (-631 (-348 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-632 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-5 *2 (-631 (-348 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-5 *2 (-632 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-5 *2 (-631 (-348 *4)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4)))
-   (-5 *2 (-2 (|:| |num| (-1180 *4)) (|:| |den| *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4)))
+   (-5 *2 (-2 (|:| |num| (-1179 *4)) (|:| |den| *4)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4)))
-   (-5 *2 (-2 (|:| |num| (-1180 *4)) (|:| |den| *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4)))
+   (-5 *2 (-2 (|:| |num| (-1179 *4)) (|:| |den| *4)))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1180 *3)) (-4 *3 (-1156 *4)) (-4 *4 (-1135))
-   (-4 *1 (-291 *4 *3 *5)) (-4 *5 (-1156 (-348 *3)))))) 
+  (-12 (-5 *2 (-1179 *3)) (-4 *3 (-1155 *4)) (-4 *4 (-1134))
+   (-4 *1 (-291 *4 *3 *5)) (-4 *5 (-1155 (-348 *3)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-291 *4 *5 *6)) (-4 *4 (-1135))
-   (-4 *5 (-1156 *4)) (-4 *6 (-1156 (-348 *5)))
-   (-5 *2 (-2 (|:| |num| (-632 *5)) (|:| |den| *5)))))) 
+  (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-291 *4 *5 *6)) (-4 *4 (-1134))
+   (-4 *5 (-1155 *4)) (-4 *6 (-1155 (-348 *5)))
+   (-5 *2 (-2 (|:| |num| (-631 *5)) (|:| |den| *5)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-1 (-856 *3) (-856 *3))) (-5 *1 (-150 *3))
-   (-4 *3 (-13 (-312) (-1116) (-917)))))
+  (-12 (-5 *2 (-1 (-855 *3) (-855 *3))) (-5 *1 (-150 *3))
+   (-4 *3 (-13 (-312) (-1115) (-916)))))
  ((*1 *2)
-  (|partial| -12 (-4 *4 (-1135)) (-4 *5 (-1156 (-348 *2))) (-4 *2 (-1156 *4))
+  (|partial| -12 (-4 *4 (-1134)) (-4 *5 (-1155 (-348 *2))) (-4 *2 (-1155 *4))
    (-5 *1 (-290 *3 *4 *2 *5)) (-4 *3 (-291 *4 *2 *5))))
  ((*1 *2)
-  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1135))
-   (-4 *4 (-1156 (-348 *2))) (-4 *2 (-1156 *3))))) 
+  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1134))
+   (-4 *4 (-1155 (-348 *2))) (-4 *2 (-1155 *3))))) 
 (((*1 *2)
-  (|partial| -12 (-4 *4 (-1135)) (-4 *5 (-1156 (-348 *2))) (-4 *2 (-1156 *4))
+  (|partial| -12 (-4 *4 (-1134)) (-4 *5 (-1155 (-348 *2))) (-4 *2 (-1155 *4))
    (-5 *1 (-290 *3 *4 *2 *5)) (-4 *3 (-291 *4 *2 *5))))
  ((*1 *2)
-  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1135))
-   (-4 *4 (-1156 (-348 *2))) (-4 *2 (-1156 *3))))) 
+  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1134))
+   (-4 *4 (-1155 (-348 *2))) (-4 *2 (-1155 *3))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-1135))
-   (-4 *6 (-1156 (-348 *5)))
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    (-5 *2 (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) (|:| |gd| *5)))
    (-4 *1 (-291 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-4 *5 (-1135)) (-4 *6 (-1156 *5))
-   (-4 *7 (-1156 (-348 *6))) (-5 *2 (-585 (-859 *5)))
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+   (-4 *7 (-1155 (-348 *6))) (-5 *2 (-584 (-858 *5)))
    (-5 *1 (-290 *4 *5 *6 *7)) (-4 *4 (-291 *5 *6 *7))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-4 *1 (-291 *4 *5 *6)) (-4 *4 (-1135))
-   (-4 *5 (-1156 *4)) (-4 *6 (-1156 (-348 *5))) (-4 *4 (-312))
-   (-5 *2 (-585 (-859 *4)))))) 
+  (-12 (-5 *3 (-1090)) (-4 *1 (-291 *4 *5 *6)) (-4 *4 (-1134))
+   (-4 *5 (-1155 *4)) (-4 *6 (-1155 (-348 *5))) (-4 *4 (-312))
+   (-5 *2 (-584 (-858 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-1135)) (-4 *5 (-1156 *4)) (-4 *6 (-1156 (-348 *5)))
-   (-5 *2 (-585 (-585 *4))) (-5 *1 (-290 *3 *4 *5 *6))
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+   (-5 *2 (-584 (-584 *4))) (-5 *1 (-290 *3 *4 *5 *6))
    (-4 *3 (-291 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
-   (-4 *5 (-1156 (-348 *4))) (-4 *3 (-318)) (-5 *2 (-585 (-585 *3)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
+   (-4 *5 (-1155 (-348 *4))) (-4 *3 (-318)) (-5 *2 (-584 (-584 *3)))))) 
 (((*1 *1 *2 *3 *3 *3 *4)
-  (-12 (-4 *4 (-312)) (-4 *3 (-1156 *4)) (-4 *5 (-1156 (-348 *3)))
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    (-4 *1 (-286 *4 *3 *5 *2)) (-4 *2 (-291 *4 *3 *5))))
  ((*1 *1 *2 *2 *3)
-  (-12 (-5 *3 (-485)) (-4 *2 (-312)) (-4 *4 (-1156 *2))
-   (-4 *5 (-1156 (-348 *4))) (-4 *1 (-286 *2 *4 *5 *6))
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+   (-4 *5 (-1155 (-348 *4))) (-4 *1 (-286 *2 *4 *5 *6))
    (-4 *6 (-291 *2 *4 *5))))
  ((*1 *1 *2 *2)
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    (-4 *1 (-286 *2 *3 *4 *5)) (-4 *5 (-291 *2 *3 *4))))
  ((*1 *1 *2)
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    (-4 *1 (-286 *3 *4 *5 *2)) (-4 *2 (-291 *3 *4 *5))))
  ((*1 *1 *2)
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-   (-4 *5 (-1156 (-348 *4))) (-4 *6 (-291 *3 *4 *5)) (-4 *3 (-312))
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+   (-4 *5 (-1155 (-348 *4))) (-4 *6 (-291 *3 *4 *5)) (-4 *3 (-312))
    (-4 *1 (-286 *3 *4 *5 *6))))) 
 (((*1 *2 *1)
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+   (-4 *5 (-1155 (-348 *4))) (-4 *6 (-291 *3 *4 *5)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-312)) (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-348 *4)))
-   (-5 *2 (-1180 *6)) (-5 *1 (-283 *3 *4 *5 *6)) (-4 *6 (-291 *3 *4 *5))))) 
+  (-12 (-4 *3 (-312)) (-4 *4 (-1155 *3)) (-4 *5 (-1155 (-348 *4)))
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 (((*1 *2 *1)
-  (-12 (-4 *3 (-312)) (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-348 *4)))
-   (-5 *2 (-1180 *6)) (-5 *1 (-283 *3 *4 *5 *6)) (-4 *6 (-291 *3 *4 *5))))) 
+  (-12 (-4 *3 (-312)) (-4 *4 (-1155 *3)) (-4 *5 (-1155 (-348 *4)))
+   (-5 *2 (-1179 *6)) (-5 *1 (-283 *3 *4 *5 *6)) (-4 *6 (-291 *3 *4 *5))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-209)) (-5 *1 (-282))))) 
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-(((*1 *2 *1) (-12 (-5 *2 (-871 (-696))) (-5 *1 (-282))))) 
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+(((*1 *2 *1) (-12 (-5 *2 (-870 (-695))) (-5 *1 (-282))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-445)) (-5 *1 (-282))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-281 *3)) (-4 *3 (-758))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-281 *3)) (-4 *3 (-757))))) 
 (((*1 *1) (-12 (-4 *1 (-280 *2)) (-4 *2 (-318)) (-4 *2 (-312))))) 
 (((*1 *1 *1 *2)
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 (((*1 *2 *1)
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+  (-12 (-4 *1 (-280 *3)) (-4 *3 (-312)) (-4 *3 (-318)) (-5 *2 (-1085 *3))))) 
 (((*1 *2 *1 *1)
   (|partial| -12 (-4 *1 (-280 *3)) (-4 *3 (-312)) (-4 *3 (-318))
-   (-5 *2 (-1086 *3))))
+   (-5 *2 (-1085 *3))))
  ((*1 *2 *1)
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 (((*1 *1 *2 *1)
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-(((*1 *1 *1 *2 *3 *1) (-12 (-4 *1 (-277 *2 *3)) (-4 *2 (-963)) (-4 *3 (-718))))) 
+  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-277 *3 *4)) (-4 *3 (-962)) (-4 *4 (-717))))) 
+(((*1 *1 *1 *2 *3 *1) (-12 (-4 *1 (-277 *2 *3)) (-4 *2 (-962)) (-4 *3 (-717))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-696)) (-4 *1 (-277 *3 *4)) (-4 *3 (-963)) (-4 *4 (-718))
+  (-12 (-5 *2 (-695)) (-4 *1 (-277 *3 *4)) (-4 *3 (-962)) (-4 *4 (-717))
    (-4 *3 (-146))))) 
 (((*1 *2 *1 *3)
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+  (-12 (-5 *3 (-484)) (-4 *1 (-274 *4 *2)) (-4 *4 (-1014)) (-4 *2 (-104))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-274 *3 *4)) (-4 *3 (-1015)) (-4 *4 (-104))))) 
+  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-274 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-104))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-274 *2 *3)) (-4 *2 (-1015)) (-4 *3 (-104)) (-4 *3 (-718))))) 
+  (-12 (-4 *1 (-274 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-104)) (-4 *3 (-717))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-485)) (-4 *4 (-719)) (-4 *5 (-758)) (-4 *2 (-963))
-   (-5 *1 (-272 *4 *5 *2 *6)) (-4 *6 (-863 *2 *4 *5))))) 
+  (-12 (-5 *3 (-484)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *2 (-962))
+   (-5 *1 (-272 *4 *5 *2 *6)) (-4 *6 (-862 *2 *4 *5))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1086 *7)) (-5 *3 (-485)) (-4 *7 (-863 *6 *4 *5)) (-4 *4 (-719))
-   (-4 *5 (-758)) (-4 *6 (-963)) (-5 *1 (-272 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-1085 *7)) (-5 *3 (-484)) (-4 *7 (-862 *6 *4 *5)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-4 *6 (-962)) (-5 *1 (-272 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1086 *6)) (-4 *6 (-963)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-5 *2 (-1086 *7)) (-5 *1 (-272 *4 *5 *6 *7)) (-4 *7 (-863 *6 *4 *5))))) 
+  (-12 (-5 *3 (-1085 *6)) (-4 *6 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-5 *2 (-1085 *7)) (-5 *1 (-272 *4 *5 *6 *7)) (-4 *7 (-862 *6 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1086 *7)) (-4 *7 (-863 *6 *4 *5)) (-4 *4 (-719)) (-4 *5 (-758))
-   (-4 *6 (-963)) (-5 *2 (-1086 *6)) (-5 *1 (-272 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1085 *7)) (-4 *7 (-862 *6 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-962)) (-5 *2 (-1085 *6)) (-5 *1 (-272 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1086 *9)) (-5 *4 (-585 *7)) (-5 *5 (-585 *8)) (-4 *7 (-758))
-   (-4 *8 (-963)) (-4 *9 (-863 *8 *6 *7)) (-4 *6 (-719)) (-5 *2 (-1086 *8))
+  (-12 (-5 *3 (-1085 *9)) (-5 *4 (-584 *7)) (-5 *5 (-584 *8)) (-4 *7 (-757))
+   (-4 *8 (-962)) (-4 *9 (-862 *8 *6 *7)) (-4 *6 (-718)) (-5 *2 (-1085 *8))
    (-5 *1 (-272 *6 *7 *8 *9))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-348 (-485))) (-5 *1 (-270 *3 *4 *5)) (-4 *3 (-312))
-   (-14 *4 (-1091)) (-14 *5 *3)))) 
+  (-12 (-5 *2 (-348 (-484))) (-5 *1 (-270 *3 *4 *5)) (-4 *3 (-312))
+   (-14 *4 (-1090)) (-14 *5 *3)))) 
 (((*1 *2 *3 *3 *3 *4 *5 *4 *6)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1003 (-179)))
-   (-5 *6 (-485)) (-5 *2 (-1126 (-840))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-484)) (-5 *2 (-1125 (-839))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1003 (-179)))
-   (-5 *6 (-485)) (-5 *7 (-1074)) (-5 *2 (-1126 (-840))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-484)) (-5 *7 (-1073)) (-5 *2 (-1125 (-839))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1003 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *2 (-1126 (-840))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *2 (-1125 (-839))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1003 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *8 (-1074)) (-5 *2 (-1126 (-840)))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *8 (-1073)) (-5 *2 (-1125 (-839)))
    (-5 *1 (-269))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-1 (-179) (-179))) (-5 *1 (-269)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *3 *3)
   (-12 (-5 *3 (-249 *6)) (-5 *4 (-86)) (-4 *6 (-362 *5))
-   (-4 *5 (-13 (-496) (-555 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
+   (-4 *5 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
  ((*1 *2 *3 *4 *3 *5)
-  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-585 *7)) (-4 *7 (-362 *6))
-   (-4 *6 (-13 (-496) (-555 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
+  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-584 *7)) (-4 *7 (-362 *6))
+   (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-585 (-249 *7))) (-5 *4 (-585 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-362 *6)) (-4 *6 (-13 (-496) (-555 (-474)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-584 (-249 *7))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *7))
+   (-4 *7 (-362 *6)) (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51))
    (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-585 (-249 *8))) (-5 *4 (-585 (-86))) (-5 *5 (-249 *8))
-   (-5 *6 (-585 *8)) (-4 *8 (-362 *7)) (-4 *7 (-13 (-496) (-555 (-474))))
+  (-12 (-5 *3 (-584 (-249 *8))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *8))
+   (-5 *6 (-584 *8)) (-4 *8 (-362 *7)) (-4 *7 (-13 (-495) (-554 (-473))))
    (-5 *2 (-51)) (-5 *1 (-268 *7 *8))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-585 *7)) (-5 *4 (-585 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-362 *6)) (-4 *6 (-13 (-496) (-555 (-474)))) (-5 *2 (-51))
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    (-5 *3
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *1) (-5 *1 (-130)))) 
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-   (-5 *1 (-126)) (-5 *3 (-585 (-585 (-856 *4))))))) 
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+     (|:| |yValues| (-1002 *4))))
+   (-5 *1 (-126)) (-5 *3 (-584 (-584 (-855 *4))))))) 
 (((*1 *2 *3)
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+  (-12 (-5 *3 (-837))
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 (((*1 *2 *3 *1)
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 (((*1 *1 *1)
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-   (-4 *2 (-1015))))) 
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 (((*1 *2 *3 *3)
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     (-2 (|:| |func| *3) (|:| |poly| *3) (|:| |c1| (-348 *5))
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 (((*1 *2 *3 *3)
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+   (-4 *3 (-1155 (-348 *4)))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-348 *6)) (-4 *5 (-1134)) (-4 *6 (-1155 *5))
+   (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3954 *3) (|:| |radicand| *6)))
+   (-5 *1 (-121 *5 *6 *7)) (-5 *4 (-695)) (-4 *7 (-1155 *3))))) 
+(((*1 *2 *3)
+  (|partial| -12 (-4 *4 (-1134)) (-4 *5 (-1155 *4))
+   (-5 *2 (-2 (|:| |radicand| (-348 *5)) (|:| |deg| (-695))))
+   (-5 *1 (-121 *4 *5 *3)) (-4 *3 (-1155 (-348 *5)))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-1134)) (-4 *5 (-1155 *4))
+   (-5 *2 (-2 (|:| -3954 (-348 *5)) (|:| |poly| *3))) (-5 *1 (-121 *4 *5 *3))
+   (-4 *3 (-1155 (-348 *5)))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-117))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-117))))
+ ((*1 *1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-117))))) 
 (((*1 *1) (-5 *1 (-117)))) 
 (((*1 *1) (-5 *1 (-117)))) 
 (((*1 *1) (-5 *1 (-117)))) 
@@ -13172,71 +13172,71 @@
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-117))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-117))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-117))))) 
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- ((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-114))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-584 (-117))) (-5 *1 (-114))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-114))))) 
 (((*1 *1) (-5 *1 (-114)))) 
 (((*1 *1) (-5 *1 (-114)))) 
 (((*1 *1) (-5 *1 (-114)))) 
 (((*1 *1) (-5 *1 (-114)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-751))) (-5 *1 (-113))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-158 (-112)))) (-5 *1 (-113))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-158 (-112)))) (-5 *1 (-113))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-750))) (-5 *1 (-113))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-158 (-112)))) (-5 *1 (-113))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-158 (-112)))) (-5 *1 (-113))))) 
 (((*1 *1 *1 *2)
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-   (-14 *4 (-696)) (-4 *5 (-146))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *1 (-108 *3 *4 *5)) (-14 *3 (-484))
+   (-14 *4 (-695)) (-4 *5 (-146))))) 
 (((*1 *1)
-  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-485)) (-14 *3 (-696)) (-4 *4 (-146))))) 
+  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-484)) (-14 *3 (-695)) (-4 *4 (-146))))) 
 (((*1 *1)
-  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-485)) (-14 *3 (-696)) (-4 *4 (-146))))) 
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 (((*1 *2 *1)
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 (((*1 *1 *1 *1) (|partial| -4 *1 (-104)))) 
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 (((*1 *1 *1 *1) (-5 *1 (-85))) ((*1 *1 *1 *1) (-4 *1 (-96)))) 
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+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3996)) (-4 *1 (-92 *2)) (-4 *2 (-1129))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-13 (-312) (-951 (-348 *2)))) (-5 *2 (-484)) (-5 *1 (-88 *4 *3))
+   (-4 *3 (-1155 *4))))) 
+(((*1 *2 *3) (|partial| -12 (-5 *3 (-86)) (-5 *1 (-87 *2)) (-4 *2 (-1014))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-86)) (-5 *1 (-87 *3)) (-4 *3 (-1014))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-86)) (-5 *3 (-585 (-1 *4 (-585 *4)))) (-4 *4 (-1015))
+  (-12 (-5 *2 (-86)) (-5 *3 (-584 (-1 *4 (-584 *4)))) (-4 *4 (-1014))
    (-5 *1 (-87 *4))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-86)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1015)) (-5 *1 (-87 *4))))
+  (-12 (-5 *2 (-86)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1014)) (-5 *1 (-87 *4))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-86)) (-5 *2 (-585 (-1 *4 (-585 *4))))
-   (-5 *1 (-87 *4)) (-4 *4 (-1015))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-585 (-878))) (-5 *1 (-78))))
- ((*1 *2 *1) (-12 (-5 *2 (-45 (-1074) (-698))) (-5 *1 (-86))))) 
+  (|partial| -12 (-5 *3 (-86)) (-5 *2 (-584 (-1 *4 (-584 *4))))
+   (-5 *1 (-87 *4)) (-4 *4 (-1014))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-877))) (-5 *1 (-78))))
+ ((*1 *2 *1) (-12 (-5 *2 (-45 (-1073) (-697))) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
@@ -13244,925 +13244,925 @@
 (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-85) (-86) (-86))) (-5 *1 (-86))))) 
 (((*1 *2 *1 *3) (-12 (-5 *3 (-445)) (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-445)) (-5 *1 (-86))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-86))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-445)) (-5 *3 (-698)) (-5 *1 (-86))))
- ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1074)) (-5 *3 (-698)) (-5 *1 (-86))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1074) (-698))) (-5 *1 (-86))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-1130)) (-5 *1 (-79 *3))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-445)) (-5 *3 (-585 (-878))) (-5 *1 (-78))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-585 *3)) (-4 *3 (-1130)) (-4 *1 (-76 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1130))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1130))))) 
-(((*1 *2 *3)
-  (-12 (|has| *2 (-6 (-3998 "*"))) (-4 *5 (-322 *2)) (-4 *6 (-322 *2))
-   (-4 *2 (-963)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1156 *2))
-   (-4 *4 (-629 *2 *5 *6))))) 
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- (-3696 . 139487) (-3697 . 139303) (-3698 . 139161) (-3699 . 138666)
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- (-3716 . 134959) (-3717 . 134679) (-3718 . 134611) (-3719 . 134413)
- (-3720 . 134233) (-3721 . 134078) (-3722 . 133971) (-3723 . 133920)
- (-3724 . 133543) (-3725 . 133015) (-3726 . 132793) (-3727 . 132571)
- (-3728 . 132332) (-3729 . 132242) (-3730 . 130500) (-3731 . 129918)
- (-3732 . 129840) (-3733 . 124380) (-3734 . 123590) (-3735 . 123213)
- (-3736 . 123142) (-3737 . 122877) (-3738 . 122702) (-3739 . 122217)
- (-3740 . 121795) (-3741 . 121355) (-3742 . 120492) (-3743 . 120368)
- (-3744 . 120241) (-3745 . 120132) (-3746 . 119980) (-3747 . 119866)
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- (-3776 . 105748) (-3777 . 105513) (-3778 . 105268) (-3779 . 105178)
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- (-3784 . 101679) (-3785 . 101278) (-3786 . 101176) (-3787 . 101094)
- (-3788 . 100936) (-3789 . 99702) (-3790 . 99620) (-3791 . 99541)
- (-3792 . 99186) (-3793 . 99129) (-3794 . 99057) (-3795 . 99000)
- (-3796 . 98943) (-3797 . 98813) (-3798 . 98611) (-3799 . 98243)
- (-3800 . 97822) (-3801 . 94012) (-3802 . 93410) (-3803 . 92943)
- (-3804 . 92730) (-3805 . 92517) (-3806 . 92351) (-3807 . 92138)
- (-3808 . 91972) (-3809 . 91806) (-3810 . 91640) (-3811 . 91474)
- (-3812 . 91204) (-3813 . 85790) (** . 82837) (-3815 . 82421) (-3816 . 82180)
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- (-3821 . 78510) (-3822 . 78346) (-3823 . 78250) (-3824 . 78132)
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- (-3829 . 77424) (-3830 . 77272) (-3831 . 77113) (-3832 . 76600)
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- (-3837 . 75251) (-3838 . 74079) (-3839 . 73873) (-3840 . 72698)
- (-3841 . 72623) (-3842 . 71442) (-3843 . 67861) (-3844 . 67497)
- (-3845 . 67220) (-3846 . 67128) (-3847 . 67035) (-3848 . 66758)
- (-3849 . 66665) (-3850 . 66572) (-3851 . 66479) (-3852 . 66095)
- (-3853 . 66024) (-3854 . 65932) (-3855 . 65774) (-3856 . 65420)
- (-3857 . 65262) (-3858 . 65154) (-3859 . 65125) (-3860 . 65058)
- (-3861 . 64904) (-3862 . 64746) (-3863 . 64352) (-3864 . 64277)
- (-3865 . 64171) (-3866 . 64099) (-3867 . 64021) (-3868 . 63948)
- (-3869 . 63875) (-3870 . 63802) (-3871 . 63730) (-3872 . 63658)
- (-3873 . 63585) (-3874 . 63344) (-3875 . 63004) (-3876 . 62856)
- (-3877 . 62783) (-3878 . 62710) (-3879 . 62637) (-3880 . 62383)
- (-3881 . 62239) (-3882 . 60903) (-3883 . 60709) (-3884 . 60438)
- (-3885 . 60290) (-3886 . 60142) (-3887 . 59902) (-3888 . 59708)
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- (-3893 . 59013) (-3894 . 58912) (-3895 . 58811) (-3896 . 58710)
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- (-3925 . 52841) (-3926 . 52483) (-3927 . 52125) (-3928 . 51973)
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- (-3945 . 45044) (-3946 . 44826) (-3947 . 36500) (-3948 . 36315)
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- (-3953 . 31333) (-3954 . 31038) (-3955 . 30690) (-3956 . 30524)
- (-3957 . 30358) (-3958 . 29945) (-3959 . 16071) (-3960 . 14964) (* . 10917)
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- (-3967 . 9140) (-3968 . 8513) (-3969 . 7240) (-3970 . 5996) (-3971 . 5127)
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\ No newline at end of file
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\ No newline at end of file